THIS EBOOK WAS PREPARED
AS A PART OF THE COMENIUS PROJECT
WHY MATHS?
by the students and the teachers from:
BERKENBOOM HUMANIORA BOVENBOUW, IN SINT-NIKLAAS
( BELGIUM)
EUREKA SECONDARY SCHOOL IN KELLS (IRELAND)
LICEO CLASSICO STATALE CRISTOFORO COLOMBO IN GENOA (ITALY)
GIMNAZJUM IM. ANNY WAZÓWNY IN GOLUB-DOBRZYŃ (POLAND)
ESCOLA SECUNDARIA COM 3.º CICLO D. MANUEL I IN BEJA (PORTUGAL)
IES ÁLVAREZ CUBERO IN PRIEGO DE CÓRDOBA (SPAIN)
This document is a student paper submitted to the University of Education in Okara that discusses mathematical chemistry. It introduces mathematical chemistry and its applications in areas like chemical graph theory. It explains how mathematics is used to model chemical phenomena and explore concepts in chemistry. The paper also outlines the scope and importance of mathematical chemistry and compares it to related fields. It concludes by discussing the history of using mathematics to model chemical phenomena.
The document discusses using linear algebra to solve chemistry problems involving balancing chemical equations and determining volumes of chemical solutions. It provides an example of using a system of equations represented in matrix form to determine that the volumes of solutions A, B, and C are 1.5 cm3, 3.1 cm3, and 2.2 cm3 based on the amounts of chemical produced under different concentration conditions. The document also demonstrates how to use the law of conservation of matter and a similar technique to balance the chemical equation C2H6 + O2 → CO2 + H2O.
1) This document discusses the relationship between maths and physics. Mathematics allows physicists to calculate and equate physical events using equations that translate elements like forces, mass, and motion into numbers.
2) An example is provided of using mathematical equations to predict how an object sliding down an inclined plane will behave based on its mass, the inclination, and distance to the ground.
3) Physics relies heavily on mathematics to calculate and help understand phenomena like motion, forces, energy, and more. Mathematics provides the logical framework for physics.
Linear algebra has applications in balancing chemical equations, cryptography, and geometry. Balancing chemical equations involves setting up a linear system to satisfy the law of conservation of mass such that the number of atoms is equal on both sides of the equation. Cryptography uses linear algebra operations like matrix multiplication for encryption and decryption of messages. In geometry, finding the equation of a circle through three points involves setting up a homogeneous linear system and calculating the determinant to obtain the equation of the circle.
This presentation compares the development of procedural fluency and conceptual understanding and argues for a systematic approach of teaching one before the other.
Top 10 importance of mathematics in everyday lifeStat Analytica
Would you like to know the importance of mathematics? If yes, then have a look at this presentation to explore the top uses of mathematics in our daily life. Watch the presentation till the end to explore the importance of mathematics.
Importance of mathematics in our daily lifeHarsh Rajput
The document discusses the history and origins of mathematics. It notes that mathematics originated from practical needs like measurement and counting, with early forms found on notched bones and cave walls. Over thousands of years, mathematics has developed from attempts to describe the natural world and arrive at logical truths. Today, mathematics is highly specialized but also applied in diverse fields from politics to traffic analysis. The document also provides examples of how concepts in commercial mathematics, algebra, statistics, geometry are useful in daily life.
Mathematics is the science of logic, quantity, and arrangement. It is used in many aspects of daily life without realizing it, whether cooking, sports, gardening, banking, navigation, or architecture. Math concepts like ratio, proportion, probability, mensuration, trigonometry, and geometry are essential for tasks like following recipes in cooking, analyzing sports performance, measuring land for gardening, calculating interest for banking, using coordinates for navigation, and constructing buildings. Mathematics is a universal language that is important everywhere.
This document is a student paper submitted to the University of Education in Okara that discusses mathematical chemistry. It introduces mathematical chemistry and its applications in areas like chemical graph theory. It explains how mathematics is used to model chemical phenomena and explore concepts in chemistry. The paper also outlines the scope and importance of mathematical chemistry and compares it to related fields. It concludes by discussing the history of using mathematics to model chemical phenomena.
The document discusses using linear algebra to solve chemistry problems involving balancing chemical equations and determining volumes of chemical solutions. It provides an example of using a system of equations represented in matrix form to determine that the volumes of solutions A, B, and C are 1.5 cm3, 3.1 cm3, and 2.2 cm3 based on the amounts of chemical produced under different concentration conditions. The document also demonstrates how to use the law of conservation of matter and a similar technique to balance the chemical equation C2H6 + O2 → CO2 + H2O.
1) This document discusses the relationship between maths and physics. Mathematics allows physicists to calculate and equate physical events using equations that translate elements like forces, mass, and motion into numbers.
2) An example is provided of using mathematical equations to predict how an object sliding down an inclined plane will behave based on its mass, the inclination, and distance to the ground.
3) Physics relies heavily on mathematics to calculate and help understand phenomena like motion, forces, energy, and more. Mathematics provides the logical framework for physics.
Linear algebra has applications in balancing chemical equations, cryptography, and geometry. Balancing chemical equations involves setting up a linear system to satisfy the law of conservation of mass such that the number of atoms is equal on both sides of the equation. Cryptography uses linear algebra operations like matrix multiplication for encryption and decryption of messages. In geometry, finding the equation of a circle through three points involves setting up a homogeneous linear system and calculating the determinant to obtain the equation of the circle.
This presentation compares the development of procedural fluency and conceptual understanding and argues for a systematic approach of teaching one before the other.
Top 10 importance of mathematics in everyday lifeStat Analytica
Would you like to know the importance of mathematics? If yes, then have a look at this presentation to explore the top uses of mathematics in our daily life. Watch the presentation till the end to explore the importance of mathematics.
Importance of mathematics in our daily lifeHarsh Rajput
The document discusses the history and origins of mathematics. It notes that mathematics originated from practical needs like measurement and counting, with early forms found on notched bones and cave walls. Over thousands of years, mathematics has developed from attempts to describe the natural world and arrive at logical truths. Today, mathematics is highly specialized but also applied in diverse fields from politics to traffic analysis. The document also provides examples of how concepts in commercial mathematics, algebra, statistics, geometry are useful in daily life.
Mathematics is the science of logic, quantity, and arrangement. It is used in many aspects of daily life without realizing it, whether cooking, sports, gardening, banking, navigation, or architecture. Math concepts like ratio, proportion, probability, mensuration, trigonometry, and geometry are essential for tasks like following recipes in cooking, analyzing sports performance, measuring land for gardening, calculating interest for banking, using coordinates for navigation, and constructing buildings. Mathematics is a universal language that is important everywhere.
Mathematics is present in everyday activities like cooking, decorating, shopping, business, and more. It is used to measure quantities of ingredients in cooking, surface areas when painting rooms, calculating sales and profits in business. Geometry specifically is applied in building structures, kitchen utensils, sports equipment, traffic signals, musical instruments, and transportation. Math underlies many activities in daily life without us consciously realizing it.
This document discusses congruent and similar triangles. It begins by introducing the concepts and explaining how recognizing similar shapes can simplify design work. It then defines congruent triangles as having equal sides and angles, while similar triangles have the same shape but not necessarily the same size. The document notes that two figures can be similar but not congruent, but not vice versa. It provides examples of similar and congruent figures. It further explains that similar triangles have corresponding sides and angles in the same locations that are in the same ratio. It demonstrates using ratios and proportions to determine unknown side lengths in similar figures. Finally, it discusses ways to prove triangles are similar, including having congruent corresponding angles (AA similarity) or proportional corresponding sides (SS
Linear algebra is used in many applications including search engine ranking, error correcting codes, graphics, facial recognition, signal analysis, prediction, computer gaming, and quantum computing. It was used in the original Google ranking algorithm and remains important for search today. Linear algebra also allows encoding of data for error correction and is fundamental to representing and projecting 3D graphics onto 2D screens. Facial recognition systems use principal component analysis from linear algebra to identify faces.
Applications of mathematics in our daily lifeAbhinav Somani
The document discusses the history of mathematics. It states that the study of mathematics as its own field began in ancient Greece with Pythagoras, who coined the term "mathematics." Greek mathematics refined methods and expanded subject matter. Beginning in the 16th century Renaissance, new mathematical developments interacting with scientific discoveries occurred at an increasing pace. The document also notes that mathematics has been used since ancient times, with early uses including building the pyramids in Egypt.
This document discusses the prevalence and importance of mathematics in everyday life. It provides examples of how mathematics is used in areas like health, weather, transportation, society, and more. While some applications are directly observable, others involve more complex systems that are still being understood mathematically, like DNA. The document also discusses the historical foundations of mathematics over centuries, with concepts building upon each other like a pyramid, and provides a brief biography of the mathematician Aryabhata, who made important contributions in astronomy and mathematics.
For over 2000 years, mathematics has evolved from practical applications to a field of rigorous inquiry and back again. Early civilizations developed basic arithmetic and geometry to solve practical problems. The Greeks were first to study mathematics with a philosophical spirit, seeking inherent truths. Their work in geometry, algebra, and other areas remains valid today. Over centuries, mathematics spread across cultures through trade, exploration, and scholarship. It has grown increasingly specialized while also finding new applications, aided by computers. Today, mathematics is more valuable than ever as a way of understanding both natural and human systems through abstraction and modeling.
Matrices are rectangular arrangements of numbers or expressions that are organized into rows and columns. They have many applications in fields like physics, computer science, mathematics, and engineering. Specifically, matrices are used to model electrical circuits, for image projection and page ranking algorithms, in matrix calculus, for encrypting messages, in seismic surveys, representing population data, calculating GDP, and programming robot movements. Matrices play a key role in solving problems across many domains through their representation of relationships between variables.
The document discusses basic concepts in set theory, including defining sets using tabulation and set-builder forms, operations on sets like union and intersection, and classifications of sets as finite or infinite. Key concepts covered are subsets, the empty or null set, equal sets, and forms of sets including tabulation which lists elements and set-builder which defines a set using properties.
The document is an acknowledgement from a group of 5 students - Abhishek Mahto, Lakshya Kumar, Mohan Kumar, Ritik Kumar, and Vivek Singh of class X E. They are thanking their principal Dr. S.V. Sharma and math teacher Mrs. Shweta Bhati for their guidance and support in completing their project on triangles and similarity. They also thank their parents and group members for their advice and assistance during the project.
Among the disciplines that utilize calculus include physics, engineering, economics, statistics, and medicine. It is used to create mathematical models in order to arrive into an optimal solution. For example, in physics, calculus is used in a lot of its concepts.
This document provides an overview of real world applications of algebra and calculus. It introduces Laplace transformations, matrices and determinants, and calculus. Examples are given of using matrices in C programming and solving differential equations using Laplace transforms. Applications discussed include using calculus in fields like engineering, biology, and space flight. In computer science, matrices are useful for graphics and calculus is applied to physics engines in video games. The conclusion states that algebra and calculus are applied across many fields like engineering and to solve equations.
Role of mathematics in science and engineeringDhanush Kumar
This document discusses the applications of mathematics in various fields of science and engineering. It provides examples of how mathematics is used in biotechnology, astronomy, mechanics, chemistry, medicine, electronics, and physics. Mathematics is crucial in fields like engineering, where it is used extensively in areas like physics, graphics, civil engineering, and various applications in electrical, mechanical, civil, and energy systems engineering. The document emphasizes that engineering without mathematics would not be possible, demonstrating the important role mathematics plays across science and engineering.
This document discusses the correlation between mathematics and other disciplines. It defines correlation as the relationship between two or more variables where a change in one variable creates a corresponding change in the other. It provides examples of the correlation between different branches of mathematics like algebra and geometry. It also explains how mathematics is correlated with sciences by expressing scientific laws with mathematical equations, with social sciences by using math for maps, dates, and geography, with language by using math terms and definitions, and with fine arts by applying mathematical concepts of ratio, proportion, symmetry and rhythm. It concludes that mathematics provides relationships and applications across many fields of study.
This is the the " Physics Solved Question" for 9th class. These notes are prepared by chapter wise and solved last 5 years papers of Lahore Board.
You can get high marks by these notes. for more notes visit.
https://www.urduearth.com/2019/02/physics-short-questions-9th-class.html
This was an Inter Collegiate and a State Level Contest named SIGMA '08. Won a special prize for this paper. This research emphasized on how simple concepts of Mathematics helps into constructing complex mathematical models for space programming and their individual importance in real time applications.
Mathematics is essential in many areas of daily life. It underlies natural phenomena like honeycomb structures [SENTENCE 1]. It is also useful for tasks like calculating savings from bulk purchases, spotting misleading statistics in advertisements, and mental arithmetic for quick calculations in shopping [SENTENCE 2]. Engineering, medicine, music, forensics and many other fields rely heavily on mathematical concepts like geometry, calculus, statistics and more to function [SENTENCE 3].
This document provides an overview of mathematics and its relationship to concepts of beauty, architecture, and human life. It discusses how mathematical patterns like the golden ratio and Fibonacci sequence are found in nature and influence concepts of beauty. It also explores how mathematics influenced ancient architecture and how geometry guides both fields. Additionally, it examines how mathematicians think and how numbers are fundamental to mathematics, similar to how words are to language. The document aims to convey the breadth of mathematics and its applications beyond numerical calculations.
Mathematics is the study of topics such as quantity, structure, space, and change. It is used in many fields including science, engineering, and finance. Art includes activities that create visual works, performing arts, literature, and other media. Mathematics and art are closely related through concepts like fractals, the golden ratio, symmetry, patterns, and geometric shapes that appear in both natural and human-made works. Many artists use mathematical principles in their compositions to achieve balance, proportion and other aesthetic goals.
Chemistry word can be represented as C for chemistry, H for health, E for environment, M for medicines, I for industries, S for sciences, T for teaching, R for research and Y for you.
we are a living chemistry as we are made of chemicals only and there are a lot of chemical reactions going in our body.
This document provides teaching notes for a lesson on balancing chemical equations. The lesson objectives are to teach students the differences between reactants and products, the types of chemical reactions, and how to balance chemical equations according to the law of conservation of mass. The lesson uses a Chemical Balance tool on TI-Nspire handheld devices to allow students to practice balancing equations through changing coefficients and subscripts. The document provides examples of balanced and unbalanced equations, as well as discussion points and assessments.
This document provides an overview of gas laws and the kinetic molecular theory. It begins with learning objectives about the gas laws, pressure, volume, temperature, moles, density, and molar mass. It then discusses the kinetic molecular theory and its assumptions that gases are made of particles in constant random motion. Temperature is proportional to particle kinetic energy. Gas behavior can be explained by kinetic molecular theory, with pressure being due to particle collisions with containers. Several gas laws are introduced relating pressure, volume, temperature, and moles of a gas sample before and after a change. These include Boyle's law, Charles' law, Avogadro's law, and the combined gas law. Problem-solving strategies for using the gas laws
Mathematics is present in everyday activities like cooking, decorating, shopping, business, and more. It is used to measure quantities of ingredients in cooking, surface areas when painting rooms, calculating sales and profits in business. Geometry specifically is applied in building structures, kitchen utensils, sports equipment, traffic signals, musical instruments, and transportation. Math underlies many activities in daily life without us consciously realizing it.
This document discusses congruent and similar triangles. It begins by introducing the concepts and explaining how recognizing similar shapes can simplify design work. It then defines congruent triangles as having equal sides and angles, while similar triangles have the same shape but not necessarily the same size. The document notes that two figures can be similar but not congruent, but not vice versa. It provides examples of similar and congruent figures. It further explains that similar triangles have corresponding sides and angles in the same locations that are in the same ratio. It demonstrates using ratios and proportions to determine unknown side lengths in similar figures. Finally, it discusses ways to prove triangles are similar, including having congruent corresponding angles (AA similarity) or proportional corresponding sides (SS
Linear algebra is used in many applications including search engine ranking, error correcting codes, graphics, facial recognition, signal analysis, prediction, computer gaming, and quantum computing. It was used in the original Google ranking algorithm and remains important for search today. Linear algebra also allows encoding of data for error correction and is fundamental to representing and projecting 3D graphics onto 2D screens. Facial recognition systems use principal component analysis from linear algebra to identify faces.
Applications of mathematics in our daily lifeAbhinav Somani
The document discusses the history of mathematics. It states that the study of mathematics as its own field began in ancient Greece with Pythagoras, who coined the term "mathematics." Greek mathematics refined methods and expanded subject matter. Beginning in the 16th century Renaissance, new mathematical developments interacting with scientific discoveries occurred at an increasing pace. The document also notes that mathematics has been used since ancient times, with early uses including building the pyramids in Egypt.
This document discusses the prevalence and importance of mathematics in everyday life. It provides examples of how mathematics is used in areas like health, weather, transportation, society, and more. While some applications are directly observable, others involve more complex systems that are still being understood mathematically, like DNA. The document also discusses the historical foundations of mathematics over centuries, with concepts building upon each other like a pyramid, and provides a brief biography of the mathematician Aryabhata, who made important contributions in astronomy and mathematics.
For over 2000 years, mathematics has evolved from practical applications to a field of rigorous inquiry and back again. Early civilizations developed basic arithmetic and geometry to solve practical problems. The Greeks were first to study mathematics with a philosophical spirit, seeking inherent truths. Their work in geometry, algebra, and other areas remains valid today. Over centuries, mathematics spread across cultures through trade, exploration, and scholarship. It has grown increasingly specialized while also finding new applications, aided by computers. Today, mathematics is more valuable than ever as a way of understanding both natural and human systems through abstraction and modeling.
Matrices are rectangular arrangements of numbers or expressions that are organized into rows and columns. They have many applications in fields like physics, computer science, mathematics, and engineering. Specifically, matrices are used to model electrical circuits, for image projection and page ranking algorithms, in matrix calculus, for encrypting messages, in seismic surveys, representing population data, calculating GDP, and programming robot movements. Matrices play a key role in solving problems across many domains through their representation of relationships between variables.
The document discusses basic concepts in set theory, including defining sets using tabulation and set-builder forms, operations on sets like union and intersection, and classifications of sets as finite or infinite. Key concepts covered are subsets, the empty or null set, equal sets, and forms of sets including tabulation which lists elements and set-builder which defines a set using properties.
The document is an acknowledgement from a group of 5 students - Abhishek Mahto, Lakshya Kumar, Mohan Kumar, Ritik Kumar, and Vivek Singh of class X E. They are thanking their principal Dr. S.V. Sharma and math teacher Mrs. Shweta Bhati for their guidance and support in completing their project on triangles and similarity. They also thank their parents and group members for their advice and assistance during the project.
Among the disciplines that utilize calculus include physics, engineering, economics, statistics, and medicine. It is used to create mathematical models in order to arrive into an optimal solution. For example, in physics, calculus is used in a lot of its concepts.
This document provides an overview of real world applications of algebra and calculus. It introduces Laplace transformations, matrices and determinants, and calculus. Examples are given of using matrices in C programming and solving differential equations using Laplace transforms. Applications discussed include using calculus in fields like engineering, biology, and space flight. In computer science, matrices are useful for graphics and calculus is applied to physics engines in video games. The conclusion states that algebra and calculus are applied across many fields like engineering and to solve equations.
Role of mathematics in science and engineeringDhanush Kumar
This document discusses the applications of mathematics in various fields of science and engineering. It provides examples of how mathematics is used in biotechnology, astronomy, mechanics, chemistry, medicine, electronics, and physics. Mathematics is crucial in fields like engineering, where it is used extensively in areas like physics, graphics, civil engineering, and various applications in electrical, mechanical, civil, and energy systems engineering. The document emphasizes that engineering without mathematics would not be possible, demonstrating the important role mathematics plays across science and engineering.
This document discusses the correlation between mathematics and other disciplines. It defines correlation as the relationship between two or more variables where a change in one variable creates a corresponding change in the other. It provides examples of the correlation between different branches of mathematics like algebra and geometry. It also explains how mathematics is correlated with sciences by expressing scientific laws with mathematical equations, with social sciences by using math for maps, dates, and geography, with language by using math terms and definitions, and with fine arts by applying mathematical concepts of ratio, proportion, symmetry and rhythm. It concludes that mathematics provides relationships and applications across many fields of study.
This is the the " Physics Solved Question" for 9th class. These notes are prepared by chapter wise and solved last 5 years papers of Lahore Board.
You can get high marks by these notes. for more notes visit.
https://www.urduearth.com/2019/02/physics-short-questions-9th-class.html
This was an Inter Collegiate and a State Level Contest named SIGMA '08. Won a special prize for this paper. This research emphasized on how simple concepts of Mathematics helps into constructing complex mathematical models for space programming and their individual importance in real time applications.
Mathematics is essential in many areas of daily life. It underlies natural phenomena like honeycomb structures [SENTENCE 1]. It is also useful for tasks like calculating savings from bulk purchases, spotting misleading statistics in advertisements, and mental arithmetic for quick calculations in shopping [SENTENCE 2]. Engineering, medicine, music, forensics and many other fields rely heavily on mathematical concepts like geometry, calculus, statistics and more to function [SENTENCE 3].
This document provides an overview of mathematics and its relationship to concepts of beauty, architecture, and human life. It discusses how mathematical patterns like the golden ratio and Fibonacci sequence are found in nature and influence concepts of beauty. It also explores how mathematics influenced ancient architecture and how geometry guides both fields. Additionally, it examines how mathematicians think and how numbers are fundamental to mathematics, similar to how words are to language. The document aims to convey the breadth of mathematics and its applications beyond numerical calculations.
Mathematics is the study of topics such as quantity, structure, space, and change. It is used in many fields including science, engineering, and finance. Art includes activities that create visual works, performing arts, literature, and other media. Mathematics and art are closely related through concepts like fractals, the golden ratio, symmetry, patterns, and geometric shapes that appear in both natural and human-made works. Many artists use mathematical principles in their compositions to achieve balance, proportion and other aesthetic goals.
Chemistry word can be represented as C for chemistry, H for health, E for environment, M for medicines, I for industries, S for sciences, T for teaching, R for research and Y for you.
we are a living chemistry as we are made of chemicals only and there are a lot of chemical reactions going in our body.
This document provides teaching notes for a lesson on balancing chemical equations. The lesson objectives are to teach students the differences between reactants and products, the types of chemical reactions, and how to balance chemical equations according to the law of conservation of mass. The lesson uses a Chemical Balance tool on TI-Nspire handheld devices to allow students to practice balancing equations through changing coefficients and subscripts. The document provides examples of balanced and unbalanced equations, as well as discussion points and assessments.
This document provides an overview of gas laws and the kinetic molecular theory. It begins with learning objectives about the gas laws, pressure, volume, temperature, moles, density, and molar mass. It then discusses the kinetic molecular theory and its assumptions that gases are made of particles in constant random motion. Temperature is proportional to particle kinetic energy. Gas behavior can be explained by kinetic molecular theory, with pressure being due to particle collisions with containers. Several gas laws are introduced relating pressure, volume, temperature, and moles of a gas sample before and after a change. These include Boyle's law, Charles' law, Avogadro's law, and the combined gas law. Problem-solving strategies for using the gas laws
This document provides an overview of gas laws and the kinetic molecular theory. It begins with learning objectives and a concept map showing how gas properties are related by the gas laws. It then discusses the kinetic molecular theory and its assumptions that gases are made of particles in constant, rapid, random motion. This theory can explain gas behavior such as how pressure, volume, temperature, and number of moles are related. The document provides definitions and examples of these gas properties and laws including Boyle's law, Charles' law, Avogadro's law, and the combined gas law. It emphasizes that the combined gas law can be used to solve all gas law problems by transforming it based on what variables are held or changed.
The document provides information and examples about calculating density in chemistry. It defines density as the mass of a substance divided by its volume. Several examples are given of how to calculate density using the mass, volume, and known density of different substances like silver, ethanol, gasoline, ice, and lithium. The last example calculates the mass of air in a room given its dimensions and the known density of air.
This chapter discusses stoichiometry, including atomic masses, the mole concept, molar masses, percent composition of compounds, determining empirical and molecular formulas, writing and balancing chemical equations, and stoichiometric calculations involving amounts of reactants and products. Key aspects covered are determining the limiting reagent, using balanced equations to determine mole ratios, and calculating mass relationships in chemical reactions based on these mole ratios.
This document provides an introduction to concepts related to chemical equations and oxidation-reduction reactions. It defines key terms like oxidation number, oxidizing and reducing agents, and describes methods for balancing chemical equations including the ion-electron method and changing oxidation numbers. It also discusses concepts in electrochemistry and provides examples of balancing equations using different methods.
This activity is designed to introduce a convenient unit used by.docxhowardh5
This activity is designed to introduce a convenient unit used by chemists and to illustrate uses of the unit.
Part I: What Is a Mole And Why Are Chemists Interested in It?
Counting things is a normal part of everyday life. How many days left until vacation? How many eggs do I need for the recipe? If large numbers of things are involved, we use grouping
strategies to make the numbers easier to manage. For example, 4 more
weeks
until vacation, tells
us that there are twenty-eight days. One
dozen
eggs is the common way of expressing the quantity
12.
Half of a dozen of anything would be 6 units. One
gross
is 144 items (12 dozen) and a
ream
of paper contain 500 sheets.
Chemist are faced with a unique problem when dealing with numbers of atoms or molecules. The particles are so small that any amount of them that we are able to physically handle contains a number of particles so large that there is nothing else in our experience that contains so many units. This
incredibly
large number calls for a special counting group -
the MOLE.
A
MOLE
is
6.022
x
1023
particles
. This is often referred to as
Avogadro=s
number
. Let=s make sure we understand how big this is. One mole of the element carbon has a mass of 12.01 grams. The smallest particle of an element is an atom. So one mole of carbon contains 602,200,000,000,000,000,000,000 atoms of carbon.
Look for the element carbon on the periodic table. Do you notice anything special about the value 12.01? Explain
The mass of one mole of the element magnesium is 24.30 grams. How many atoms does a sample of magnesium with a mass of 24.30 grams contain?
Stated in general terms, the mass of one mole of any element is equal to the
of that element expressed in grams. The mass of a mole of any element can be found by looking on .
The mass of 0.5000 moles of carbon is and contains
atoms of carbon.
Remember when dividing numbers written in scientific notation the number portion is divided
normally and the exponents are subtracted.
6.022x1023
divided by 2 is the same as 6.022 x1023/2
x
100.
So the answer is found by dividing 6.022 by 2 = 3.011 and the subtracting exponent 0
from exponent 23.
The answer in scientific notation is 3.011x1023
atoms
of carbon.
Calculator tip
: for exponential notation use the EE or EXP key (not 10^)
If you have a bottle containing 8.10 grams of magnesium, how many Mg atoms are present in the bottle? Show your work. What is different about this problem compared to the last one involving carbon?
Remember that some elements, when alone, exist in the form of diatomic molecules: H2, O2, N2, I2, F2, Cl2, Br2, Their smallest piece is a molecule containing two atoms. If one mole of oxygen were required for an experiment you would be using O2 the gas. One mole of O2 would have a mass of
and contain particles (molecules).
The characteristic unit of the compound CO2 is a molecule. Each CO2 molecule has atoms. In order to find the mass .
Analytical chemistry is a branch of chemistry that focuses on determining the qualitative and quantitative composition of substances. It has two main branches - qualitative analysis which reveals the identity of elements/compounds in a sample, and quantitative analysis which determines the amount of each substance. There are several methods used in analytical chemistry including gravimetric, volumetric, electroanalytical, and spectroscopic methods. Analytical chemistry plays important roles in fields like clinical chemistry, environmental analysis, quality control, and various industrial sectors. Key concepts covered include atomic and molecular weights, chemical equations, moles, molar mass, equivalent weight, and their applications and calculations.
Chemistry zimsec chapter 2 atoms, molecules and stoichiometryalproelearning
This document provides an overview of Chapter 2 in a chemistry textbook, which covers topics including:
- The mass of atoms and molecules, including relative atomic mass and molecular mass
- Using a mass spectrometer to determine relative isotopic masses and abundances
- The mole concept and amount of substance in relation to mass, volume of gases, and concentration of solutions
- Calculating empirical formulas from combustion data or elemental composition by mass and deducing molecular formulas
- Stoichiometry, including writing balanced chemical equations and ionic equations
Topic 1 formulae, equations and amount of substancethahseen_rafe
The document provides an overview of key chemistry concepts related to formulae, equations, and amount of substance including:
1) Definitions of common chemistry terms like elements, compounds, atoms, molecules, and ions.
2) Explanations of relative atomic mass, relative molecular mass, molar mass, moles, and the Avogadro constant.
3) How to write and balance chemical equations, including state symbols, and derive ionic equations from full equations.
4) Calculations involving molar concentration, mass concentration, empirical and molecular formulae, reacting masses from equations.
5) Use of the ideal gas law, molar volume of gases, and calculations involving
This document discusses chemical formulas and percent composition. It provides examples of calculating the percent composition of different compounds from their chemical formulas, such as NaCl, glucose, and Mg(OH)2. Empirical formulas can be determined from percent composition data by assuming 100 grams of the compound and calculating the moles of each element. Chemical equations are used to represent chemical reactions, and examples are given for writing and balancing equations. Common types of chemical reactions are also outlined.
1. The document outlines a route map for a chemistry module covering topics like alkanes, alcohols, carboxylic acids, and energy changes over 24 lessons.
2. Lesson C7.9 focuses on rates of reaction and how factors like temperature, concentration, and particle size can influence the rate. Collision theory and activation energy are also discussed.
3. Examples of reversible reactions are given where the direction can change based on conditions like temperature and pressure. Equilibrium is reached when the rates of the forward and reverse reactions are equal and concentrations no longer change.
This document provides information about chemical reactions including:
1. Chemical reactions involve the rearrangement of atoms to form new substances, as evidenced by changes in properties.
2. Chemical reactions are modeled using chemical formulas, symbols, and equations to represent the reactants and products.
3. Chemical reactions can be endothermic, requiring energy input, or exothermic, releasing energy to the surroundings.
This document discusses stoichiometry, which is the calculation of quantities in chemical reactions using balanced chemical equations. It explains that balanced equations show the mole ratios of reactants and products, which can be used to determine the amounts of substances involved. Examples are given of how to calculate quantities in moles, masses, and volumes using mole-mole, mass-mole, mole-mass, and mass-mass methods based on the mole ratios from balanced equations. The concept of a limiting reagent is also introduced, which determines the maximum amount of product that can be formed.
1. The document provides an overview of basic concepts in chemistry covered in an 11th grade chemistry course, including the divisions of chemistry, laws of chemical combination, Dalton's atomic theory, significant figures, stoichiometric coefficients, the mole, Avogadro's number, and the limiting reagent.
2. Key concepts are explained, such as how the limiting reagent determines how much of a product can be formed in a chemical reaction.
3. Example problems are provided to illustrate calculating molarity, empirical and molecular formulas, and amount of products formed using stoichiometric calculations and identifying the limiting reagent.
Stoichiometry is the study of quantitative relationships between amounts of substances involved in chemical reactions. It allows chemists to determine mole and particle quantities. The mole is the standard unit for measuring amounts of substances and refers to 6.022x1023 elementary entities. Molar mass is the mass of one mole of a substance and is calculated differently for elements versus compounds. Percent composition by mass can be determined by dividing the mass of each element by the total molar mass. Empirical and molecular formulas relate the simplest and actual ratios of elements in a compound.
1. The relative formula mass of calcium carbonate (CaCO3) is 100 g/mol.
2. One mole of calcium carbonate will react with 2 moles of hydrochloric acid (HCl).
3. Therefore, the mass of hydrochloric acid that will react with 1 mole (100 g) of calcium carbonate is 2 x 36.5 g = 73 g, since the molar mass of HCl is 36.5 g/mol.
The document discusses chemical equations and balancing reactions. It provides examples of chemical equations showing the formation of glucose from carbon dioxide and water during photosynthesis, the formation of carbon dioxide from carbon and oxygen, and the formation of water from hydrogen and oxygen. It also discusses the law of conservation of mass, which states that the total mass of reactants must equal the total mass of products in a chemical reaction.
This document discusses stoichiometry, which is the quantitative study of chemical reactions. It provides definitions of key terms used in stoichiometry such as mole, molar mass, and molar volume. Examples are given to demonstrate how to calculate the percent composition of compounds and determine empirical formulas from elemental analysis data. The three main stoichiometric laws - the law of conservation of mass, the law of definite proportions, and the law of multiple proportions - are also summarized. Overall, the document outlines fundamental concepts and principles of stoichiometry used in quantitative chemical calculations.
The document provides guidance on using the features and tools available on the TwinSpace online platform for eTwinning projects. It explains how to set up pages, forums, and multimedia galleries to organize project content and discussions. Instructions are given for inviting students and teachers, setting permissions, and using chat and other communication features.
This document provides information about Małgorzata Garkowska, a math teacher of 25 years who has been involved with eTwinning since 2006. It discusses tools she uses for teaching like Google Maps, Google Earth, Google Tour Builder, and GeoGebra. It provides examples of student activities and projects that can be done with these tools including creating maps, virtual field trips, and interactive math constructions. Hands-on instructions are given for students to collaboratively create maps, tours, and complete math tasks using the tools.
This document provides information about Małgorzata Garkowska, a math teacher with over 20 years of experience who has been involved with eTwinning since 2006. It then discusses several free online tools that can be used for educational purposes: Google My Maps for creating customized maps; Google Earth for virtual exploration of places; Google Tour Builder for creating geographic storytelling tours; and GeoGebra for interactive math learning. Instructions are provided on features and functions of each tool. The document concludes with directions for partners to work together using the hands-on tasks of creating maps and tours with Google tools, and constructing geometric shapes and graphs with GeoGebra.
The European Commission has selected the 2012-1-ES1-COM06-52752 project "Why Maths?" as a "success story" based on its impact, contribution to policy-making, innovative results, and creative approach. As a result of this selection, the project will receive increased visibility on Commission websites and social media, and at conferences. The project coordinator may also be contacted by ECORYS, the Commission's contractor for disseminating and exploiting project results, to provide additional materials about the project. The selection recognizes the commitment, enthusiasm, and high-quality work of the project partners.
1) Se presentan ecuaciones diferenciales ordinarias que involucran funciones trigonométricas como seno, coseno y sus derivadas.
2) Se resuelven las ecuaciones aplicando técnicas como separación de variables y sustitución de funciones.
3) Se obtienen expresiones para las funciones desconocidas en términos de constantes.
1) Se presentan ecuaciones diferenciales ordinarias que involucran funciones trigonométricas como seno, coseno y sus derivadas.
2) Se resuelven las ecuaciones aplicando propiedades de las funciones trigonométricas y técnicas de resolución de ecuaciones diferenciales.
3) Se obtienen las soluciones en función de constantes arbitrarias y el intervalo de definición indicado para cada una.
THIS BROCHURE WAS PREPARED
AS A PART OF THE COMENIUS PROJECT
WHY MATHS?
by the students and the teachers from:
BERKENBOOM HUMANIORA BOVENBOUW, IN SINT-NIKLAAS
( BELGIUM)
EUREKA SECONDARY SCHOOL IN KELLS (IRELAND)
LICEO CLASSICO STATALE CRISTOFORO COLOMBO IN GENOA (ITALY)
GIMNAZJUM IM. ANNY WAZÓWNY IN GOLUB-DOBRZYŃ (POLAND)
ESCOLA SECUNDARIA
COM
3.º CICLO D. MANUEL I IN BEJA (PORTUGAL)
IES ÁLVAREZ CUBERO IN PRIEGO DE CÓRDOBA (SPAIN)
THIS EBOOK WAS PREPARED
AS A PART OF THE COMENIUS PROJECT
WHY MATHS?
by the students and the teachers from:
BERKENBOOM HUMANIORA BOVENBOUW, IN SINT-NIKLAAS
( BELGIUM)
EUREKA SECONDARY SCHOOL IN KELLS (IRELAND)
LICEO CLASSICO STATALE CRISTOFORO COLOMBO IN GENOA (ITALY)
GIMNAZJUM IM. ANNY WAZÓWNY IN GOLUB-DOBRZYŃ (POLAND)
ESCOLA SECUNDARIA COM 3.º CICLO D. MANUEL I IN BEJA (PORTUGAL)
IES ÁLVAREZ CUBERO IN PRIEGO DE CÓRDOBA (SPAIN)
THIS EBOOK WAS PREPARED
AS A PART OF THE COMENIUS PROJECT
WHY MATHS?
by the students and the teachers from:
BERKENBOOM HUMANIORA BOVENBOUW, IN SINT-NIKLAAS
( BELGIUM)
EUREKA SECONDARY SCHOOL IN KELLS (IRELAND)
LICEO CLASSICO STATALE CRISTOFORO COLOMBO IN GENOA (ITALY)
GIMNAZJUM IM. ANNY WAZÓWNY IN GOLUB-DOBRZYŃ (POLAND)
ESCOLA SECUNDARIA COM 3.º CICLO D. MANUEL I IN BEJA (PORTUGAL)
IES ÁLVAREZ CUBERO IN PRIEGO DE CÓRDOBA (SPAIN)
Maths in Art and Architecture Why Maths? Comenius projectGosia Garkowska
THIS EBOOK WAS PREPARED
AS A PART OF THE COMENIUS PROJECT
WHY MATHS?
by the students and the teachers from:
BERKENBOOM HUMANIORA BOVENBOUW, IN SINT-NIKLAAS ( BELGIUM)
EUREKA SECONDARY SCHOOL IN KELLS (IRELAND)
LICEO CLASSICO STATALE CRISTOFORO COLOMBO IN GENOA (ITALY)
GIMNAZJUM IM. ANNY WAZÓWNY IN GOLUB-DOBRZYŃ (POLAND)
ESCOLA SECUNDARIA COM 3.º CICLO D. MANUEL I IN BEJA (PORTUGAL)
IES ÁLVAREZ CUBERO IN PRIEGO DE CÓRDOBA (SPAIN)
This document contains trivia questions and answers about mathematics, art, geography, and astronomy related to the Comenius project involving schools from Portugal, Spain, Italy, Belgium, Poland, and Ireland. There are over 100 multiple choice and short answer questions covering topics like the capital cities and populations of the countries involved, famous artists and their use of mathematical concepts in works of art, properties of planets and galaxies, and principles of map making and geography.
Maths and Astronomy Why Maths Comenius projectGosia Garkowska
This document discusses various topics related to math and astronomy. It begins by introducing distance units used in space like astronomical units (AU), light years, parsecs and larger multiples. It then discusses how to calculate acceleration due to gravity on different planets using Newton's law of universal gravitation. Next, it examines weight on other planets and how gravity differs based on planetary characteristics. The document concludes by calculating the orbital speeds of planets around the sun.
हिंदी वर्णमाला पीपीटी, hindi alphabet PPT presentation, hindi varnamala PPT, Hindi Varnamala pdf, हिंदी स्वर, हिंदी व्यंजन, sikhiye hindi varnmala, dr. mulla adam ali, hindi language and literature, hindi alphabet with drawing, hindi alphabet pdf, hindi varnamala for childrens, hindi language, hindi varnamala practice for kids, https://www.drmullaadamali.com
Communicating effectively and consistently with students can help them feel at ease during their learning experience and provide the instructor with a communication trail to track the course's progress. This workshop will take you through constructing an engaging course container to facilitate effective communication.
Philippine Edukasyong Pantahanan at Pangkabuhayan (EPP) CurriculumMJDuyan
(𝐓𝐋𝐄 𝟏𝟎𝟎) (𝐋𝐞𝐬𝐬𝐨𝐧 𝟏)-𝐏𝐫𝐞𝐥𝐢𝐦𝐬
𝐃𝐢𝐬𝐜𝐮𝐬𝐬 𝐭𝐡𝐞 𝐄𝐏𝐏 𝐂𝐮𝐫𝐫𝐢𝐜𝐮𝐥𝐮𝐦 𝐢𝐧 𝐭𝐡𝐞 𝐏𝐡𝐢𝐥𝐢𝐩𝐩𝐢𝐧𝐞𝐬:
- Understand the goals and objectives of the Edukasyong Pantahanan at Pangkabuhayan (EPP) curriculum, recognizing its importance in fostering practical life skills and values among students. Students will also be able to identify the key components and subjects covered, such as agriculture, home economics, industrial arts, and information and communication technology.
𝐄𝐱𝐩𝐥𝐚𝐢𝐧 𝐭𝐡𝐞 𝐍𝐚𝐭𝐮𝐫𝐞 𝐚𝐧𝐝 𝐒𝐜𝐨𝐩𝐞 𝐨𝐟 𝐚𝐧 𝐄𝐧𝐭𝐫𝐞𝐩𝐫𝐞𝐧𝐞𝐮𝐫:
-Define entrepreneurship, distinguishing it from general business activities by emphasizing its focus on innovation, risk-taking, and value creation. Students will describe the characteristics and traits of successful entrepreneurs, including their roles and responsibilities, and discuss the broader economic and social impacts of entrepreneurial activities on both local and global scales.
Leveraging Generative AI to Drive Nonprofit InnovationTechSoup
In this webinar, participants learned how to utilize Generative AI to streamline operations and elevate member engagement. Amazon Web Service experts provided a customer specific use cases and dived into low/no-code tools that are quick and easy to deploy through Amazon Web Service (AWS.)
This document provides an overview of wound healing, its functions, stages, mechanisms, factors affecting it, and complications.
A wound is a break in the integrity of the skin or tissues, which may be associated with disruption of the structure and function.
Healing is the body’s response to injury in an attempt to restore normal structure and functions.
Healing can occur in two ways: Regeneration and Repair
There are 4 phases of wound healing: hemostasis, inflammation, proliferation, and remodeling. This document also describes the mechanism of wound healing. Factors that affect healing include infection, uncontrolled diabetes, poor nutrition, age, anemia, the presence of foreign bodies, etc.
Complications of wound healing like infection, hyperpigmentation of scar, contractures, and keloid formation.
Chapter wise All Notes of First year Basic Civil Engineering.pptxDenish Jangid
Chapter wise All Notes of First year Basic Civil Engineering
Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps.
Chapter 4
Buildings: Selection of site for Buildings, Layout of Building Plan, Types of buildings, Plinth area, carpet area, floor space index, Introduction to building byelaws, concept of sun light & ventilation. Components of Buildings & their functions, Basic concept of R.C.C., Introduction to types of foundation
Chapter 5
Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures.
Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
Text Books:
1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
4. BCP, Surveying volume 1
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UPRAHUL
This Dissertation explores the particular circumstances of Mirzapur, a region located in the
core of India. Mirzapur, with its varied terrains and abundant biodiversity, offers an optimal
environment for investigating the changes in vegetation cover dynamics. Our study utilizes
advanced technologies such as GIS (Geographic Information Systems) and Remote sensing to
analyze the transformations that have taken place over the course of a decade.
The complex relationship between human activities and the environment has been the focus
of extensive research and worry. As the global community grapples with swift urbanization,
population expansion, and economic progress, the effects on natural ecosystems are becoming
more evident. A crucial element of this impact is the alteration of vegetation cover, which plays a
significant role in maintaining the ecological equilibrium of our planet.Land serves as the foundation for all human activities and provides the necessary materials for
these activities. As the most crucial natural resource, its utilization by humans results in different
'Land uses,' which are determined by both human activities and the physical characteristics of the
land.
The utilization of land is impacted by human needs and environmental factors. In countries
like India, rapid population growth and the emphasis on extensive resource exploitation can lead
to significant land degradation, adversely affecting the region's land cover.
Therefore, human intervention has significantly influenced land use patterns over many
centuries, evolving its structure over time and space. In the present era, these changes have
accelerated due to factors such as agriculture and urbanization. Information regarding land use and
cover is essential for various planning and management tasks related to the Earth's surface,
providing crucial environmental data for scientific, resource management, policy purposes, and
diverse human activities.
Accurate understanding of land use and cover is imperative for the development planning
of any area. Consequently, a wide range of professionals, including earth system scientists, land
and water managers, and urban planners, are interested in obtaining data on land use and cover
changes, conversion trends, and other related patterns. The spatial dimensions of land use and
cover support policymakers and scientists in making well-informed decisions, as alterations in
these patterns indicate shifts in economic and social conditions. Monitoring such changes with the
help of Advanced technologies like Remote Sensing and Geographic Information Systems is
crucial for coordinated efforts across different administrative levels. Advanced technologies like
Remote Sensing and Geographic Information Systems
9
Changes in vegetation cover refer to variations in the distribution, composition, and overall
structure of plant communities across different temporal and spatial scales. These changes can
occur natural.
Walmart Business+ and Spark Good for Nonprofits.pdfTechSoup
"Learn about all the ways Walmart supports nonprofit organizations.
You will hear from Liz Willett, the Head of Nonprofits, and hear about what Walmart is doing to help nonprofits, including Walmart Business and Spark Good. Walmart Business+ is a new offer for nonprofits that offers discounts and also streamlines nonprofits order and expense tracking, saving time and money.
The webinar may also give some examples on how nonprofits can best leverage Walmart Business+.
The event will cover the following::
Walmart Business + (https://business.walmart.com/plus) is a new shopping experience for nonprofits, schools, and local business customers that connects an exclusive online shopping experience to stores. Benefits include free delivery and shipping, a 'Spend Analytics” feature, special discounts, deals and tax-exempt shopping.
Special TechSoup offer for a free 180 days membership, and up to $150 in discounts on eligible orders.
Spark Good (walmart.com/sparkgood) is a charitable platform that enables nonprofits to receive donations directly from customers and associates.
Answers about how you can do more with Walmart!"
2. Page 2
THIS EBOOK WAS PREPARED
AS A PART OF THE COMENIUS PROJECT
WWHHYY MMAATTHHSS??
by the students and the teachers from:
BERKENBOOM HUMANIORA BOVENBOUW, IN SINT-NIKLAAS ( BELGIUM)
EUREKA SECONDARY SCHOOL IN KELLS (IRELAND)
LICEO CLASSICO STATALE CRISTOFORO COLOMBO IN GENOA (ITALY)
GIMNAZJUM IM. ANNY WAZÓWNY IN GOLUB-DOBRZYŃ (POLAND)
ESCOLA SECUNDARIA COM 3.º CICLO D. MANUEL I IN BEJA (PORTUGAL)
IES ÁLVAREZ CUBERO IN PRIEGO DE CÓRDOBA (SPAIN)
This project has been funded with support from the European Commission.
This publication reflects the views only of the author, and the
Commission cannot be held responsible for any use which may be made of the
information contained therein.
4. Page 4
Math is everywhere. It is an universal language which everyone needs. We use math every day, everywhere and anytime. We use it automatically. It can be applied in simple tasks, like figuring out how many time you have until your next class, or in long and complicated tasks, for example doing your tasks.
Chemists use math for a variety of tasks. We balance the equation of a chemical reaction, use mathematical calculations that are absolutely necessary to explore important concepts in chemistry, and utilize dimensional analysis to find any range of information about reactions from finding the mass of chemicals reacted to the concentration of a chemical in a solution. Math is also used to calculate energy in reactions, compression of a gas, grams needed to add to a solution to reach desired concentration, and quantities of reactants needed to reach a desired product. It is important to know how to mathematically handle chemistry problems in order to understand what they mean and how to prepare specific quantities of chemicals.
Math applied to Chemistry
Overall and simpler operations
Math and chemistry are closely linked. We practically need mathematical operations to do everything in chemistry. Sum, subtraction, division and multiplication are essential things we need to know before starting to think about being a chemist. Other operations, like the simple rule of three and proportions, are basic tools you need to know before starting to study chemistry. Have no doubt that those are key components to have success in chemistry.
Ex:
If there’s 1 mol of Cl in one molecule of NaCl how many moles are in 5 molecules of NaCl
1 1
5 x
x = 5 mol
We used the simple rule of three to figure out the chemical quantity of sodium in 5 molecules of sodium chlorite NaCl.
5. Page 5
Take chemistry out of the equation
Equations are perhaps the most important math principal you need to learn. We use all kinds of equations in chemistry.
Ex: N = n x NA
A = Z + N
Eradiation = Eremoval + Ekinetics
If you need to succeed in chemistry you need to know how to make all kinds of equations.
Different sizes, different views
Chemists transform very often some units of measure into others, according to the variables of the experiment. To do this they need math. For example, to transform meters in light-years we use this formula:
1 l.y. = 9.47 ·1015 m
Another example is changing Celsius to Kelvin, two units to measure temperature.
T(K) = T(ºC) + 273
Measuring
To measure a certain object you need math. If you measure it directly, which means you are there measuring at the spot, you need to know the units therefore you need math. If you are measuring it indirectly, through an equation or an expression, you also need math because you need to know how to solve them. Here are some examples:
Directly:
What is the length of the book?
6. Page 6
To measure the length of the book you need to know which unit is the ruler. Of course it is probably cm and you know this without thinking, but that happens because you learn it in math class.
Indirectly:
A certain object has a weight of 210 g and a volume of 20 mL. Calculate the density of the object.
Solution: p = m : V (=)
(=) p = 10,5 g/mL
In this case, we are using an equation to measure a chemical greatness (density).
Scientific Notation
There are certain greatness’s used in chemistry that are too big or too small to represent the full number. So in chemistry is frequently used something we learn in math, scientific notation. For example, to represent the number of meters in one parsec we use this number 3.09·1016m because it’s too big. However to represent mercury’s ionization energy we use this number 1,21·10-18 J/e. Also, operations with numbers in scientific notation is commonly used in chemistry-
Ex: In the hydrogen atom, an electron “jumps” from the first level of energy to the second one. Determine the energy of the photon necessary for this transition to happen.
Resolution: Ef = E2 – E1
7. Page 7
Avogadro’s number
Fractions
Scientific notation is not the only form of number representation used in chemistry. Fractions were invented by mathematicians and now is commonly used in chemistry to represent exact numbers.
Ex: 1:3 = 0.(3)
Statistics
Sometimes it’s used in chemistry charts, tables, graphics, and averages, among others. Are often used to organize a very large group or to determine or register something’s behavior. A much known example of the use of statistic in chemistry is the Periodic Table. The Periodic Table is a table (concept taken from math) that contains every known chemical element in the world, organized by their atomic number and with some of the atom’s properties. In this case chemists used statistic to have an organized and easy way to access information. Another common use for statistics is graphics. Chemists regularly use graphics to predict or register something’s behavior. For example, it is used a line graphic to register the several ionization energies of the first 20 elements of the Periodic Table.
We can use line graphics but we can also use other types. It’s frequently used bar graphs to represent and understand better the evolution of the Earth’s atmosphere. Diagrams is another concept that is very used in chemistry, especially when trying to explain an argument. It is sometimes easier to understand when is summarized in a diagram. These are the forms of data representation. However, are used calculus learnt in statistics. A common example is average. In chemistry is used to calculate the relative isotopic mass or to compare results. In conclusion, knowing statistics is very important in chemistry.
8. Page 8
In conclusion
To study chemistry, we need math. It is inevitable. Math is an essential part of the human knowledge, we can’t live without it.
You can also watch the presentation prepared by the Portuguese student here: LINK
9. Page 9
Picture from: www.wyckoffps.org
Balancing chemical equations
Stoichiometry - is a branch of chemistry that deals with the relative quantities of reactants and products in chemical reactions. Stoichiometry is the mathematics behind the science of chemistry.
A chemical equation is an easy way to represent a chemical reaction—it shows which elements react together and what the resulting products will be. By the Law of Conservation of Mass, the number of atoms must be the same on both sides because these atoms cannot be created or destroyed in a reaction.
The number of atoms that we start with at the beginning of the reaction must equal the number of atoms that you end up with.
When the number of atoms of reactants matches the number of atoms of products, then the chemical equation is said to be balanced.
We would like to present a simple method of defining the coefficients in the equations of chemical reactions with the help of a system of linear algebraic equations that describes the material balance in a chemical reaction.
Example 1:
CH4 + O2 → CO2 + H2O
I. First we use each element to produce an equation involving the
coefficient letters. We need to find the smallest possible positive
integers a, b, c, and d such that the following chemical equation. aCH4 + bO2 → cCO2 + dH2O
is balanced.
Carbon: a = c There is 1 carbon atom in the a term and 1 in the c term.
Hydrogen: 4a = 2d There are 4 hydrogen atoms in the a term and 2 in the d term.
Oxygen: 2b = 2c + d There are 2 oxygen atoms in the b term and 2 in the c term and 1 in the d term.
II. As a result we get a system of three linear equations with four unknowns:
10. Page 10
Picture from: www.earthtimes.org
III. This system has an infinite number of solutions, but we have to get the minimal natural values only. Since we would like the smallest integral solutions, = 1 works well. The system has the following solution - the coefficients are = 1, = 2, = 1 and = 2 When writing our balanced equation, the coefficient 1 is assumed and can be omitted, yielding the formula: CH4 + 2O2 → CO2 + 2H2O
The balanced chemical equation has one mole of methane reacting with two moles of oxygen gas to form one mole of carbon dioxide and two moles of water.
Example 2:
Plants use the process of photosynthesis to convert carbon dioxide and water into glucose and oxygen. This process helps remove carbon dioxide from the atmosphere. Balance the following equation for the production of glucose and oxygen from carbon dioxide and water.
CO2 + H2O → C6H12O6 + O2
This equation needs to be balanced. We must find coefficients a, b, c and d in the reactants and products - rewrite the equation as:
aCO2 + bH2O → cC6H12O6 + dO2
where the numbers of carbon, hydrogen, and oxygen atoms are the same on both sides of the equation:
Carbon: a = 6c
Oxygen: 2a + b = 6c + 2d
Hydrogen: 2b = 12c Since we would like the smallest integral solutions, = 6 works well and the coefficients are = 6, = 6, = 1 and = 6
11. Page 11
Picture from: www.commons.wikimedia.org
Examples of Balancing Chemical Equations
Consider the unbalanced reactions.
1. FeCl3 + NH4OH → Fe(OH)3 + NH4Cl
Assign each molecule a variable a, b, c, d since we have 4 expressions in the reaction
We need to find the smallest possible positive integers a, b, c, and d such that the following chemical equation.
aFeCl3 + bNH4OH → cFe(OH)3 + dNH4Cl
We can obtain a set of linear equations in these variables by considering the number of times each type of atom occurs on each side of this equation
1) Fe: a = c There is 1 iron atom in the a term and 1 in the c term.
Cl: 3a = d There are 3 chlorine atoms in the a term and 1 in the d term
N: b = d There is 1 nitrogen atom in the b term and d in the c term
H: 5b = 3c + 4d There are 5 hydrogen atoms in the b term and 3 in the c term and 4 in d term.
O: b = 3c There is 1 oxygen atom in the a term and 1 in the c term
2) As a result we will get a system of five linear equations with four unknowns:
3)
4)
FeCl3 + 3NH4OH → Fe(OH)3 + 3NH4Cl
2. aNaCl + bSO2 + cH2O + dO2 → eNa2SO4 + f HCl
From this equation we obtain the following relations in the unknowns a, b, c, d, e, and f:
1) Na: a = 2e
Cl: a = f
12. Page 12
S: b = e
O: 2b + c + 2d = 4e
H: 2c = f
2)
3)
4)
To calculate the smallest possible positive integer value of a, we have to find the least common denominator of b, c, d, and e which in this case is 4. If we work out the above equations we calculate the values of our 5 variables to be:
For a = 4 we have:
b = 2
c = 2
d = 1
e = 2
f = 4
4NaCl + 2SO2 + 2H20 + 02 → 2Na2SO4 + 4 HCl
3. aCaCO3 + bHNO3 → cCa(NO3)2 + dH2O + eCO2
Specifying the values a, b, c, d and e for the coefficients of this equation we have:
1) Ca: a = c
13. Page 13
Picture from: www.chemistrysmostwanted.wikispaces.com
C: a = e
H: b = 2d = 2a
N: b = 2c = 2a
O: 3a + 3b = 6c + d + 2e
Solving simultaneously and using the smallest integers we have
1)
2) For a = 1
b = 2a = 2
c = a = 1
d = a = 1
e = a = 1
CaCO3 + 2 HNO3 → Ca(NO3)2 + H2O + CO2
How is marble eroded by acid rain? Atmospheric sulfur dioxide combines with rainwater to create sulfurous acid. The primary component of marble is calcium carbonate (CaCO3). The sulfurous acid reacts with the CaCO3 in the marble and dissolves it. Marble statues (CaCO3) attacked by acid rain (containing HNO3).
4. aHCl + bK2CO3 → cCO2 + dH2O + eKCl
The equation for each atom looks like:
1) H: a = 2d d =
Cl: a = e
K: 2b = e b =
C: b = c c =
O: 3b = 2c + d
So we have now after some canceling:
2) b =
c =
14. Page 14
d =
e =
For a = 2 we have:
3) b = 1
c = 1
d = 1
e = 2
2HCl + K2CO3 → CO2 + H2O + 2KCl
15. Page 15
How to calculate density
Density is a characteristic property of a substance. The density of
a substance is the relationship between the mass of the substance and how
much space it takes up (volume). The density, or more precisely, the
volumetric mass density, of a substance is its mass per unit volume.
Mathematically, density is defined as mass divided by volume :
v
m
volume
mass
d
To calculate the specific gravity (S.G.) of an object, you compare the object's
density to the density of water.
Examples of densities:
Solids: Liquids: Gases:
Silver = 10.49 Milk = 1.020-1.050 Air = 0.001293
Aluminum = 2.7 Glucose = 1.350-1.440 Argon = 0.001784
Diamond = 3.01-3.25 Glycerine = 1.259 Chlorine= 0.0032
Gold = 19.3 Flourine = 0.001696
Magnesium = 1.7 Helium = 0.000178
Platinum = 21.4 Neon = 0.0008999
Example 1
Calculate the density of the cube made of silver, whose weight is 262.5 grams and the volume
is 25 cm ³.
Given: Calculate
m = 262.5 g d = ?
V = 25 cm³
1 d =
Answer: Density of silver is 10.5
.
Example 2
There is 250 cm ³ of ethyl alcohol in the glass vessel. The volume of alcohol is 0.197 kg
Calculate the density of alcohol and enter the result in grams per cubic centimeter.
Given: Calculate:
m = 0.197 kg d = ?
V = 250 cm³
1 m = 0.197kg= 0.197 g
16. Page 16
Picture from: www.bonnibrodnick.com
2 d =
The density of ethyl alcohol is 0.79
Example 3
Calculate the mass of 300 cm³ gasoline which density is 0.75 .
Given: Calculate:
V = 300 cm³ m = ?
d = 0.75
1 d = m = d V
2 m = 0.75 300cm³ = 225 g
Answer: The mass of gasoline is 225g.
Example 4
A container of volume 0.05m3 is full of ice. When the ice melts into water, how many kg of water should be added to fill it up? (density of ice = 900 ; density of water = 1000 )
Given: Calculate:
dice = 900 mwater = ?
dwater = 1000
Vice = 0.05 m³
1 mice = d V
mice =
2
We should add 5 kg of water to fill the container up.
Example 5
A rubber ball has a radius of 2.5 cm. The density of rubber is 1.2 . What is the mass of the ball?
Given: Calculate:
r = 2.5 cm m = ?
d = 1.2
1 First we calculate the volume of a ball:
2
Answer: The mass of the ball is about 78.5 g.
17. Page 17
Example 6
A 5.6-gram marble put in a graduated cylinder raises the water from 30 mL to 32 mL. What is the marble’s density?
Given: Calculate:
m = 6g d = ?
1 First we calculate the volume of marble:
2
d =
The density of marble is .
Example 7
A small rectangular slab of lithium has the dimensions 20.9 mm by 11.1 mm by 11.9 mm. Its mass is 1.49·103 mg. What is the density of lithium in ?
Given: Calculate:
a = 20.9 mm = 2.09 cm d = ?
b = 11.1 mm = 1.11 cm
c = 11.9 mm = 1.19 cm
m = 1.49·103 mg = 1490 mg = 1.49 g
1
V
2
d =
The density of lithium is 0.53 .
Example 8
Find the mass of air inside a room measuring 10m×8m×3m, if the density of air is 1.28 .
Given: Calculate:
a = 10m m = ?
b = 8m
c = 3m
d = 1.28
1
V
2
m = d V
m =
The mass of the air inside the room is
2mL
18. Page 18
Picture from:www.monarchbearing.com
Example 9
You have two stainless steel balls. The larger has a mass of 25 grams and a volume of 3.2cm3. The smaller has a mass of 10 grams. Calculate the volume of the smaller ball.
Given: Calculate:
m1 = 25g V2 = ?
V1 = 3.2cm3
m2 = 10g
1
dsteel =
2
V2 = =
The volume of the smaller ball is
Since density is a characteristic property of a substance, each liquid has its own characteristic density. The density of a liquid determines whether it will float on or sink in another liquid. A liquid will float if it is less dense than the liquid it is placed in. A liquid will sink if it is more dense than the liquid it is placed in.
Example 10
A rectangular object is 10 centimeters long, 5 centimeters high, and 20 centimeters wide. Its mass is 800 grams. Will the object float or sink in water? Remember that the density of water is about 1 .
Given: Calculate:
a = 10cm d = ?
b = 5cm
c = 20cm
m = 800g
1
V
2 d =
The object will float.
19. Page 19
carbon oxygen
carbon hydrogen oxygen
Picture from: www.annekeckler.com
Percentage composition
Percentage composition is just a way to describe what proportions of the different elements there are in a compound.
If you have the formula of a compound, you should be able to work out the percentage by mass of an element in it.
%Composition A=
Example 1
What is the percentage composition of carbon and oxygen in ?
First we need to find the mass of the compound.
Molar mass of compound: 12.01+ 2
Next we need to find the mass of carbon and oxygen in the compound.
Molar mass of carbon: 12.01
Molar mass of oxygen: 32
Then we should divide the mass of each element by the mass of the compound and multiply by 100%.
The percentage composition of carbon is:
%C =
The percentage composition of oxygen is:
% O = 72.71%
Example 2
What is the percentage composition by mass of the elements in the compound
We start by finding the atomic weights. Molar mass of C: = 12.01
Molar mass of H: = 1.01
Molar mass of O: = 16.00
Work out the molecular weight of glucose: 6 12.01 + 12 1.01 + 6 16 = 180
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potassium chromium oxygen
Picture from: www.commons.wikimedia.org
Picture from: www.aromaticscience.com
Mass of carbon: 6 12.01 = 72.06
Mass of hydrogen: 12 1.01 = 12.12
Mass of oxygen: 6 16 = 96
The percentage composition of carbon is:
The percentage composition of hydrogen is:
The percentage composition of oxygen is:
Examples 3
What is the percentage composition of chromium in ?
Molar mass of compound: 2 39 + 2 52 + 7 16 = 249
Molar mass of chromium:
The percentage composition of Cr is:
Examples 4
What is the percentage by mass of nitrogen in ammonium nitrate, NH4NO3 an important source of fertilizer?
Molar mass of N: = 14.01
Molar mass of compound: 2 + 4 + 3 16 =
The percentage composition of nitrogen is:
The percentage composition of N is 35%
Examples 5
Cinnamaldehyde, C9H8O, is responsible for the characteristic odour of cinnamon. Determine the percentage composition of cinnamaldehyde by calculating the mass percents of carbon, hydrogen, and oxygen.
The molecular formula of cinnamaldehyde is C9H8O.
Molar mass of C: = 12.01
21. Page 21
Molar mass of H: = 1.01
Molar mass of O: = 16.00
First we calculate the molar mass of cinnamaldehyde:
12.01 + 8 1.01 + 16 = 132.17
Mass of carbon: = 9 12.01 = 108.09
Mass of hydrogen: = 8 1.01 = 8.08
Mass of oxygen: = 16
The percentage composition of carbon is:
The percentage composition of hydrogen is:
The percentage composition of oxygen is:
22. Page 22
Determining empirical and molecular formulas
The empirical formula is the simplest formula for a compound. A molecular formula is the same as or a multiple of the empirical formula, and is based on the actual number of atoms of each type in the compound. For example, if the empirical formula of a compound is C3H8 , its molecular formula may be C3H8 , C6H16 , etc.
An empirical formula is often calculated from elemental composition data. The weight percentage of each of the elements present in the compound is given by this elemental composition.
Using basic mathematics skills like ratio, percentage, linear equations and system of linear equations we can determine the empirical formula of an unknown compound from its atomic masses and percent composition.
Example 1
Analysis of a compound gives 30.43 % N and 69.57% O. The mass for this compound is 92u. What is its molecular formula?
Given Find
Formula:
%N = 30.43%
%O = 69.57%
Molar mass of N: = 14
Molar mass of O: = 16
First method
We assume that the molecular weight is 100% and calculate the mass of nitrogen
It means that 28 in the compound is for the atoms of nitrogen and the rest: 92 - 28 = 64 is for the oxygen.
The numbers of atoms in the compound is:
atoms of N
atoms of O
The formula is .
Picture from: www.chem4kids.com
23. Page 23
Second method
In the second method we use the system of linear equations.
First equation: Second equation:
The formula molecular is .
Empirical Formula Calculation Steps
Step 1
If we have masses go onto step 2.
If we have %. Assume the mass to be 100g, so the % becomes grams e.g. 40% of a compound is carbon. 40% of 100 g is 40 grams.
Step 2
Determine the moles of each element.
Step 3
Determine the mole ratio by dividing each elements number of moles by the smallest value from step 2.
Picture from:www.commons.wikimedia.org
24. Page 24
Step 4
Round your ratio to the nearest whole number as long as it is “close.” For example, 1.99987 can be rounded to 2, but 1.3333 cannot be rounded to 1. It is four-thirds, so we must multiply all ratios by 3 to rid ourselves of the fraction. If we have the empirical formula C1.5H3O1 we should convert all subscripts to whole numbers, multiply each subscript by 2. This gives us the empirical formula C3H6O2. Thus, a ratio that involves a decimal ending in .5 must be doubled. We should double, triple to get an integer if they are not all whole numbers.
Example 2
A sulfide of iron was formed by combining 2.233 g of Fe with 1.926 g of S calculate the empirical formula.
Molar mass of iron: = 55.85
Molar mass of sulfur: = 32.1
1 Mass of iron: = 2.233g
Mass of sulfur: = 1.926g
2 Convert masses to amounts in moles
Numbers of moles of iron:
Numbers of moles of sulfur:
3 Divide these numbers of moles by the smallest number (0.03998 in this case)
Fe ⇒ S ⇒
Preliminary formula is:
Now we should multiply to get a whole number. In order to turn 1.5 into a whole number, we need to multiply by 2 – therefore all results must be multiplied by 2.
The simplest formula is:
Example 3
Find the empirical formula for a compound containing 36.5% sodium, 25.4% sulfur and 38.1% oxygen.
Molar mass of sodium Na: = 23
Molar mass of sulfur S: = 32.1
Molar mass of oxygen O: = 16
·2
25. Page 25
1
We assume that we have 100g of total material, and % becomes grams
Mass of sodium: = 36.5g
Mass of hydrogen: = 25.4g
Mass of oxygen: = 38.1g
2 Convert masses to amounts in moles
Numbers of moles of sodium:
Numbers of moles of sulfur:
Numbers of moles of oxygen:
3 Divide these numbers of moles by the smallest number (0.79 in this case)
Na ⇒ S ⇒ O ⇒
The formula is sodium sulfite.
Example 4
The composition of ascorbic acid (vitamin C) is 40.92% carbon, 4.58% hydrogen, and 54.50% oxygen. What is the empirical formula for vitamin C?
Molar mass of carbon C: = 12.01
Molar mass of hydrogen H: = 1.01
Molar mass of oxygen O: = 16
1
We are only given mass %, and no weight of the compound so we will assume 100g of the compound, and % becomes grams
Mass carbon = 40.92g
Mass hydrogen = 4.58g
Mass oxygen = 54.5g
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26. Page 26
Picture from:www:rippedclub.net
2 Convert masses to amounts in moles
numbers of moles of carbon:
numbers of moles of hydrogen:
numbers of moles of oxygen:
3 Divide these numbers of moles by the smallest number (3.4 in this case)
C ⇒ H ⇒ 4.533.4=1.33 O ⇒ 3.43.4=1
Preliminary formula is:
Multiply to get a whole number. In order to turn 1.33 into a whole number, we need to multiply by 3 – therefore all results must be multiplied by 3
The simplest empirical formula of vitamin C is C3H4O3
Example 5
Muscle soreness from physical activity is caused by a buildup of lactic acid in muscle tissue. Analysis of lactic acid reveals it to be 40.0% carbon, 6.7% hydrogen, and 53.3% oxygen by mass. Its molar mass is 90.088 . What are the empirical and molecular formulas?
Molar mass of carbon C: = 12.01
Molar mass of hydrogen H: = 1.01
Molar mass of oxygen O: = 16
1
We are only given mass %, and no weight of the compound so we will assume 100g of the compound, and % becomes grams
Mass carbon = 40g
Mass hydrogen = 6.7g
Mass oxygen = 53.3g
2 Convert masses to amounts in moles
numbers of moles of carbon:
·3
27. Page 27
numbers of moles of hydrogen:
numbers of moles of oxygen:
3 Divide these numbers of moles by the smallest number
C ⇒ H ⇒ O ⇒
The empirical formula of lactic acid C is C1H2O1
4 Next we calculate the empirical formula weight: 12.01 + 21.01+ 16 = 30.03
5 Divide the molecule weight 90.08 by the empirical formula weight
The molecular formula of lactic acid is C3H6O3.
Example 6
A compound is found to contain 50.05 % sulfur and 49.95 % oxygen by weight. The molecular weight for this compound is 64.07 . What is its molecular formula?
Molar mass of sulfur S: = 32.1
Molar mass of oxygen O: = 16
1 First we will find the empirical formula. We assume 100 g of the compound is present and change the percents to grams:
Mass sulfur = 50.05g
Mass oxygen = 49.95g
2 Then we convert the masses to moles:
Numbers of moles of sulfur:
Numbers of moles of oxygen:
3 Divide by the lowest, seeking the smallest whole-number ratio:
S ⇒ O ⇒
4 And now we can write the empirical formula: SO2
5 Next we calculate the empirical formula weight
32 + 216 = 64
28. Page 28
6 Divide the molecule weight by the empirical formula weight
7 Use the scaling factor computed just above to determine the molecular formula:
SO2 times 1 gives SO2 for the molecular formula.
Example 7
An analysis of nicotine, an addictive compound found in tobacco leaves, shows that it is 74.0% C, 8.65% H, and 17.35% N. Its molar mass is 162 g/mol. What are its empirical and molecular formulas?
Molar mass of carbon C: = 12.01
Molar mass of hydrogen H: = 1.01
Molar mass of nitrogen N: = 14
1
We assume 100g of the compound, and % becomes grams
Mass carbon = 74g
Mass hydrogen = 8.65g
Mass nitrogen = 17.35g
2 Convert masses to amounts in moles
Numbers of moles of carbon:
Numbers of moles of hydrogen:
Numbers of moles of nitrogen:
3 Divide by the lowest, seeking the smallest whole-number ratio:
C ⇒ O ⇒ N ⇒
4 And now we can write the empirical formula:
5 Next we calculate the empirical formula weight
5·12.01 + 71.01+ 14 = 81.12
29. Page 29
Picture from:www.previewcf.turbosquid.com
6 Divide the molecule weight by the empirical formula weight
The molecular formula of nicotine is .
30. Page 30
Concentration by percent
Medicated syrup is an example of
the concentration.
Brine and syrup
Brine is a concentrated solution of sodium chloride in water.
In Poland we use brine to prepare our special cucumbers - gherkins.
Syrup is a concentrated solution of sugar in water. Example of syrup is fruit syrup
Calculating concentration of a chemical solution requires basic math skills like knowing percentage, equations or system of equations.
Solutions are homogeneous mixtures of solute and solvent.
Solvent - the most abundant substance in a solution. In a liquid solution, the solvent does the dissolving.
Solute - the other substance in a solution. In a liquid solution, the solute is dissolved.
Concentration refers to the amount of solute that is dissolved in a solvent. The concentration of a solution in percent can be expressed in two ways: as the ratio of the volume of the solute to the volume of the solution or as the ratio of the mass of the solute to the mass of the solution.
To calculate percent concentration we use a formula:
The mass percent of a solution is a way of expressing its concentration. Mass percent is found by dividing the mass of the solute by the mass of the solution and multiplying by 100; e.g. a solution of NaOH that is 28% NaOH by mass contains 28 g of NaOH for each 100 g of solution.
Picture from: www.styl.pl
31. Page 31
Example 1:
Calculate concentration of sugar in compote. For every kilogram of fruits you need syrup made from 0.4 liter of water and 0.4 kilogram of sugar.
Given Calculate
mwater = 0.4L= 400g Cp = ?
mfruit = 0.4kg= 400g
msyrup = 400g+ 400g= 800g
Answer: Concentration of syrup is 50%.
Example 2:
We mingled 200L milk which contain 2% butterfat and 50L milk which contain 4% butterfat. Calculate final percent concentration in milk.
Given: Calculate
Cp = ?
1
2
Answer: We got 2.4% milk.
Example 3
A bottle of the antiseptic hydrogen peroxide H2O2 is labeled 3%. How many mL H2O2 are in a 473 mL bottle of this solution?
Given: Calculate
Cp = 3%
1
Answer: There are about 14.2mL of H2O2 in a bottle of this solution.
Picture from:www.net/human-medications-to-give-at-home
32. Page 32
Example 4
How many grams of salt do you need to make 500 grams of a solution with a concentration of 5% salt?
Given Calculate
Cp = 5% msolute = x ?
msolution =500g
msolute = x = 25g
Answer: We need 25g of salt.
Example 5
How many grams of water must be evaporated from 10 grams of a 40% saline solution to produce a 50% saline solution?
Given Calculate
x the amount of evaporated water
( in grams)
The amount of salt in the beginning and after the evaporation of water is the same,
Answer: 2 grams of water must be evaporated from the 40% saline solution.
Picture from:www.blog.farwestclimatecontrol.com
In the beginning
In the end
10g of solution 40%·10 the amount of salt
(10-x) of solution 50%·(10-x) the amount of salt
x g of water
33. Page 33
Example 6
How many grams of salt must be added to 30kilos of a 10% salt solution to increase the salt concentration to 25%. How many kilos of salt were added?
Given Calculate
x the amount of added salt ( in kilos)
The amount of water in the beginning and after adding salt is the same.
Answer: 0.6 kilograms of salt must be added to the solution to increase the salt concentration.
To solve word problems involving percent concentration amounts, knowledge of solving systems of equations and percents is necessary. Below there are some percent concentration problems involve solving systems of equations when mixing two liquids with differing percent concentration amounts.
Example 7
A 16% salt solution is mixed with a 4% salt solution. How many milliliters of each solution are needed to obtain 600 milliliters of a 10% solution?
The table below help us organise information.
Amount of solution
(in mL)
Percent
Total 16% salt solution x 0.16 0.16x
4% salt solution
y
0.4
0.4y mixture x + y = 600 0.10 0.10·600 = 60
The liters of salt solution from the 16% solution, plus the liters of acid in the 30% solution, add up to the liters of acid in the 10% solution
The first column is for the amount of each item we have.
In the beginning
In the end
30kg of solution 10%·30 the amount of salt 90%·30 the amount of water
(30+x) of solution 25%·(30+x) the amount of salt 75%·(30+x) the amount of salt
x g of salt
34. Page 34
Answer: 300mL of these solutions are needed to obtain 600 milliliters of a 10% solution.
Example 8
How much 10% sulfuric acid (H2SO4) must be mixed with how much 30% sulfuric acid to make 200 milliliters of 15% sulfuric acid?
Let's organise the information in the table
Volume
Percent
Amount of salt 10% sulfuric acid x 0.10 0.1x
30% sulfuric acid
y
0.30
0.3y mixture x + y = 200 0.15 0.15·200 = 30
Now that the table is filled, we can use it to get two equations. The "volume" and "amount of acid" columns will let us get two equations.
Since x + y = 600, then x = 600 – y.
We can substitute for x in our second equation, and eliminate one of the variables
Since x + y = 200, then x = 200 – y.
The liters of sulfuric acid from the 10% solution, plus the liters of acid in the 30% solution, add up to the liters of acid in the 15% solution
The first column is for the amount of each item we have.
35. Page 35
Answer: 150mL 10% sulfuric acid must be mixed with 50mL 30% sulfuric acid to make 200 milliliters of 15% sulfuric acid.
We can substitute for x in our second equation, and eliminate one of the variables
36. Page 36
PH AND LOGARITHMS
WHAT IS pH? SOME INFORMATION ABOUT pH
PH is the scale of the measure of acidity and basicity of a liquid solution, based on the concentration of positive ions and negative ions.
The term "PH" was introduced in 1909 by the Danish chemist Soren Sorensen.
The PH's scale goes from 0 to 14. 0 stands for the maximum acidity (for example hydrochloric acid), 14 stands for the maximum basicity (so it is sodium hydroxide). The medium value is 7 and it belongs to distilled water at the temperature of 25°C and stands for a neutral solution.
The traditional indicator for PH is the litmus test, a special paper that turns from green to red immersed in an acid solution. At the contrary in a basic solution the paper turns from green to dark blue.
37. Page 37
WHAT IS pOH?
The pOH scale calculates the concentration of OH ions in a liquid solution. It is the exact opposite of the pH and they are complementary. The logarithmic function of one completes the one of the other too.
WHAT IS A LOGARITHM?
It defines logarithm in basis a of a number N the exponent it has to give to a to get the number N (N is called the argument of the logarithm).
CONNECTION BETWEEN LOGARITHMS AND PH
We have already given a definition of the pH, but it can be given another definition linked to the logarithms. In fact the pH is the negative logarithm to the base 10 of the concentration of H+ ions (the same definition is right for the pOH). So the pH grows and shrinks in a logarithm scale, while at the opposite the pOH shrinks and grows complementary.
38. Page 38
Example
Calculate the pH of 0.06 mol/L HCl.
pH = −log0.06 = 1.22
You can see some examples how to calculate ph and about oxidation numbers and vectors watching the presentation prepared by the Belgian students here: LINK