1) Pressure is defined as force per unit area. The greater the force on a given area, the greater the pressure.
2) Gas pressure is caused by collisions of gas molecules with each other and surfaces. The pressure exerted by a gas depends on its volume, temperature, and number of molecules.
3) Boyle's law, Charles' law, and Gay-Lussac's law describe the relationships between pressure, volume, and temperature for an ideal gas. Boyle's law states that pressure and volume are inversely proportional at constant temperature. Charles' law states that volume and temperature are directly proportional at constant pressure. Gay-Lussac's law states that pressure and temperature are directly proportional at constant
Here are the densities of the gases at STP:
Hydrogen: 0.0899 g/L or 0.0899 g/m3
Oxygen: 1.429 g/L or 1.429 g/m3
Chlorine: 3.214 g/L or 3.214 g/m3
Radon: 9.73 g/L or 9.73 g/m3
This chapter discusses the kinetic theory of gases and ideal gas equations. It covers three gas laws: Boyle's law relating pressure and volume at constant temperature, Charles's law relating volume and temperature at constant pressure, and Gay-Lussac's law relating pressure and temperature at constant volume. The chapter derives the ideal gas equation relating pressure, volume, amount of gas, and temperature. It provides examples of using the gas laws and ideal gas equation to solve problems involving gases at different conditions reaching equilibrium.
The document discusses key concepts about gases from the kinetic molecular theory and gas laws. It introduces gases in the atmosphere and how they were studied historically. It then covers gas pressure, units of pressure, Boyle's law, Charles' law, Avogadro's law, the ideal gas law, gas stoichiometry, Dalton's law of partial pressures, and the kinetic molecular theory of gases. Examples are provided to demonstrate calculations using these gas laws and concepts.
Unit cells describe the repeating arrangements of atoms or molecules in crystalline solids. A unit cell contains the smallest group of particles that can be repeated to form the entire crystal structure. Common unit cell types include cubic, hexagonal, and body-centered cubic, with the specific arrangement depending on the bonding and packing of particles within the solid material.
This document discusses Boyle's law, which states that the pressure and volume of a gas are inversely proportional when temperature and amount of gas are kept constant. It provides examples of how Boyle's law can be applied to calculate changes in pressure or volume. For instance, if the volume of a gas decreases, the pressure must increase according to the relationship PV=constant. The document also explains how Boyle's law relates to breathing through examples of how lung pressure and volume change during inhalation and exhalation. It includes sample problems and solutions for calculating new volumes or pressures using the formula for Boyle's law.
This document discusses the gas laws and their clinical applications. It covers the key gas laws including Boyle's law, Charles' law, Gay-Lussac's law, Dalton's law of partial pressures, Henry's law, and the combined gas law. Some clinical applications mentioned are spirometry, effects of altitude on oxygen levels, use of cryoprobes, and properties of gases like nitrous oxide that are relevant to anesthesia. The document also defines important gas properties and concepts such as the ideal gas, STP, critical temperature, and pseudocritical temperature.
Gases have no definite volume and assume the volume of any vessel. The behavior of gases is described by gas laws including Boyle's law, Charles' law, Avogadro's law, and the ideal gas law. Real gases deviate from ideal behavior at high pressures and low temperatures and are better described by equations like van der Waals. Key gas properties include gas formation volume factor, gas compressibility factor, gas viscosity, and gas solubility in oil. Gas formation volume factor relates the volume of gas at reservoir conditions to standard surface conditions.
Here are the densities of the gases at STP:
Hydrogen: 0.0899 g/L or 0.0899 g/m3
Oxygen: 1.429 g/L or 1.429 g/m3
Chlorine: 3.214 g/L or 3.214 g/m3
Radon: 9.73 g/L or 9.73 g/m3
This chapter discusses the kinetic theory of gases and ideal gas equations. It covers three gas laws: Boyle's law relating pressure and volume at constant temperature, Charles's law relating volume and temperature at constant pressure, and Gay-Lussac's law relating pressure and temperature at constant volume. The chapter derives the ideal gas equation relating pressure, volume, amount of gas, and temperature. It provides examples of using the gas laws and ideal gas equation to solve problems involving gases at different conditions reaching equilibrium.
The document discusses key concepts about gases from the kinetic molecular theory and gas laws. It introduces gases in the atmosphere and how they were studied historically. It then covers gas pressure, units of pressure, Boyle's law, Charles' law, Avogadro's law, the ideal gas law, gas stoichiometry, Dalton's law of partial pressures, and the kinetic molecular theory of gases. Examples are provided to demonstrate calculations using these gas laws and concepts.
Unit cells describe the repeating arrangements of atoms or molecules in crystalline solids. A unit cell contains the smallest group of particles that can be repeated to form the entire crystal structure. Common unit cell types include cubic, hexagonal, and body-centered cubic, with the specific arrangement depending on the bonding and packing of particles within the solid material.
This document discusses Boyle's law, which states that the pressure and volume of a gas are inversely proportional when temperature and amount of gas are kept constant. It provides examples of how Boyle's law can be applied to calculate changes in pressure or volume. For instance, if the volume of a gas decreases, the pressure must increase according to the relationship PV=constant. The document also explains how Boyle's law relates to breathing through examples of how lung pressure and volume change during inhalation and exhalation. It includes sample problems and solutions for calculating new volumes or pressures using the formula for Boyle's law.
This document discusses the gas laws and their clinical applications. It covers the key gas laws including Boyle's law, Charles' law, Gay-Lussac's law, Dalton's law of partial pressures, Henry's law, and the combined gas law. Some clinical applications mentioned are spirometry, effects of altitude on oxygen levels, use of cryoprobes, and properties of gases like nitrous oxide that are relevant to anesthesia. The document also defines important gas properties and concepts such as the ideal gas, STP, critical temperature, and pseudocritical temperature.
Gases have no definite volume and assume the volume of any vessel. The behavior of gases is described by gas laws including Boyle's law, Charles' law, Avogadro's law, and the ideal gas law. Real gases deviate from ideal behavior at high pressures and low temperatures and are better described by equations like van der Waals. Key gas properties include gas formation volume factor, gas compressibility factor, gas viscosity, and gas solubility in oil. Gas formation volume factor relates the volume of gas at reservoir conditions to standard surface conditions.
Charles' Law describes how gases tend to expand when heated at a constant pressure. It states that the volume of a gas is directly proportional to its temperature. The document outlines an experiment using a cylinder with a piston immersed in water to demonstrate this law. It provides the equation that shows the relationship between the initial and final volumes and temperatures of a gas. The law is important because it explains why hot air balloons are able to rise by having less dense, expanded air than the surrounding cooler air.
1. The document discusses the importance of anesthetists understanding gas laws and their application in anesthesia. Key gas laws discussed include Boyle's law, Charles' law, Gay-Lussac's law, Dalton's law of partial pressures, and Joule-Thomson effect.
2. Calculations are provided to demonstrate how to determine gas pressures and volumes based on temperature changes using the gas laws. The properties and filling of nitrous oxide cylinders are also explained.
3. Understanding gas laws is essential for the safe use of anesthesia machines and gas cylinders, as well as interpreting changes in gas volumes and pressures based on temperature and mixtures of gases.
This document summarizes an experiment conducted to demonstrate Boyle's law. The experiment was conducted on October 29, 2013 by a student to measure the relationship between the pressure and volume of a gas. Boyle's law states that the pressure and volume of a gas are inversely related when temperature is held constant. The equipment used in the experiment included tanks and valves to control the pressure and volume of the gas sample. The student recorded measurements as the pressure and volume were varied and analyzed the results to validate Boyle's law.
This document discusses several examples of converting between different units of pressure (atm, torr, kPa) using dimensional analysis and appropriate conversion factors. It provides the calculations for converting specific pressure values between these units. Additionally, it discusses using a manometer to measure gas pressure and calculating gas properties using the ideal gas law.
The document discusses ideal gases and how they differ from real gases. It provides definitions and key characteristics of ideal gases, including that they obey the gas laws under all conditions, cannot be liquefied, and have molecules that undergo perfectly elastic collisions. The document also summarizes the gas laws of Boyle, Charles, Avogadro, Gay-Lussac, and derives the ideal gas law. Sample problems are provided to demonstrate use of the ideal gas law.
The van der Waals gas model takes into account intermolecular interactions that the ideal gas model neglects. It explains the liquid-gas phase transition through a critical point, where the vapor and liquid phases become indistinguishable. The model approximates molecules as rigid spheres that experience short-range repulsion and long-range attraction. It derives an equation of state relating pressure, volume, and temperature. This equation reduces to the ideal gas law under conditions of high temperature or low density.
The document discusses various gas laws and their applications in anesthesia and respiratory physiology. It begins by using Boyle's law to calculate the volume of oxygen remaining in a cylinder at a pressure of 15 psig. It then explains Charles, Gay-Lussac's, Avogadro's, Dalton's laws and their relevance. Further sections cover Hagen-Poiseuille's law, Reynolds number, Graham's law, Bernoulli's principle, Venturi effect, Coanda effect, critical temperature, Poynting effect, adiabatic changes, and other gas laws and their importance in areas like gas delivery, flow dynamics, and equipment function.
Phy351 ch 1 ideal law, gas law, condensed, triple point, van der waals eqMiza Kamaruzzaman
This document summarizes key concepts from Chapter 1 of PHY351 including:
1) The ideal gas law and how it relates pressure, volume, temperature and moles of gas. Real gases deviate from ideal behavior at low temperatures or high pressures.
2) Gas laws including Boyle's, Charles', and Gay-Lussac's laws and how the ideal gas law combines these relationships.
3) Concepts of absolute zero, the Kelvin temperature scale, and standard temperature and pressure.
4) Kinetic theory and how it relates gas properties to molecular motion, including molecular speed distributions and effects of temperature.
5) Phase diagrams and the different phases of matter as well as the triple point.
6
Here are the key steps to solve this problem using Charles' Law:
1) Convert temperatures to Kelvin:
T1 = 297.0 K
T2 = 216.5 K
2) Use the Charles' Law equation:
V1/T1 = V2/T2
3) Solve for V2:
V2 = V1 * T2/T1
= 20.0 L * 216.5 K/297.0 K
= 14.6 L
So the volume outside at -70°F would be 14.6 L.
The document describes several key concepts relating to gases:
1) It outlines the postulates of kinetic molecular theory and how they describe the behavior of ideal gases.
2) It then discusses how real gases differ from ideal gases and how their behavior is affected by factors like pressure and temperature.
3) Several gas laws are introduced that describe the relationships between pressure, volume, temperature, and number of moles for gases including Boyle's law, Charles' law, Gay-Lussac's law, Avogadro's law, Dalton's law of partial pressures, and the ideal gas law.
This document summarizes an investigation into the behavior of gases at different temperatures, pressures, and volumes. Three experiments were conducted: 1) Boyle's law experiment showing an inverse relationship between pressure and volume at constant temperature, 2) Charles' law experiment showing a direct relationship between volume and temperature at constant pressure, and 3) Gay-Lussac's law experiment showing a direct relationship between pressure and temperature at constant volume. The results of the experiments validated the theoretical gas laws and supported the conclusion that the volume, pressure, and temperature of gases are mutually related as described by the general gas equation.
This document summarizes several important laws of fluids and gases:
- Pascal's principle states that pressure applied to any part of a confined fluid is transmitted equally throughout the fluid.
- Boyle's law states that for a gas at constant temperature, the product of pressure and volume is a constant.
- Charles's law describes how the volume of a gas increases or decreases as temperature increases or decreases at constant pressure.
The statistical mechanical derivation of the van der waals equation of stateUNICAMP
The document provides a statistical mechanical derivation of the van der Waals equation of state and its associated thermodynamic properties. Some key points:
- It accounts for finite molecular size and intermolecular attractive forces in the van der Waals fluid model.
- Expressions are derived for various thermodynamic properties like pressure, internal energy, heat capacities in terms of temperature and molar volume.
- Conditions for vapor-liquid equilibrium are obtained by setting the Gibbs free energy of vaporization to zero and equating chemical potentials.
The document discusses the gas laws, including Boyle's law, Charles' law, Gay-Lussac's law, Avogadro's law, the combined gas law, and the ideal gas law. It provides the key relationships and equations for each law, along with example problems and solutions demonstrating how to apply each law to calculate pressure, volume, temperature, or moles of gas under different conditions.
This document discusses key concepts relating to the behavior of gases, including the definitions of pressure and how it relates to force and area. It describes how pressure decreases with increasing altitude due to lower atmospheric pressure. Boyle's Law and Charles' Law are also summarized, with Boyle's Law stating that gas pressure increases as volume decreases if temperature remains constant, while Charles' Law indicates that gas temperature increases as volume increases if pressure remains constant. Charles' Law is used to calculate the temperature at which gas volume would reach absolute zero.
Interpretation of arterial blood gases:Traditional versus Modern Gamal Agmy
This document discusses the interpretation of arterial blood gases and acid-base disorders. It begins by outlining the Handerson-Hasselbalch equation and normal blood gas values. It then defines respiratory failure and describes the four types based on PaO2 and PaCO2 levels. The document details how to evaluate oxygen status, ventilation, and acid-base disorders from a blood gas analysis. It provides examples of metabolic and respiratory acidosis and alkalosis, explaining compensation mechanisms. Mixed disorders and a step-wise approach to interpretation are also outlined. Three sample problems are worked through as examples.
This document provides an overview of key concepts in elements of mechanical engineering related to prime movers and thermodynamics. It defines prime movers as engines that convert fuel to useful work and lists various energy sources and types of prime movers. The document also defines fundamental concepts such as force, mass, pressure, work, power, energy, heat, temperature and thermodynamic laws. It describes gas properties and the gas laws including Boyle's law, Charles' law, Gay-Lussac's law, the combined gas law and the ideal gas law.
Charles' Law describes how gases tend to expand when heated at a constant pressure. It states that the volume of a gas is directly proportional to its temperature. The document outlines an experiment using a cylinder with a piston immersed in water to demonstrate this law. It provides the equation that shows the relationship between the initial and final volumes and temperatures of a gas. The law is important because it explains why hot air balloons are able to rise by having less dense, expanded air than the surrounding cooler air.
1. The document discusses the importance of anesthetists understanding gas laws and their application in anesthesia. Key gas laws discussed include Boyle's law, Charles' law, Gay-Lussac's law, Dalton's law of partial pressures, and Joule-Thomson effect.
2. Calculations are provided to demonstrate how to determine gas pressures and volumes based on temperature changes using the gas laws. The properties and filling of nitrous oxide cylinders are also explained.
3. Understanding gas laws is essential for the safe use of anesthesia machines and gas cylinders, as well as interpreting changes in gas volumes and pressures based on temperature and mixtures of gases.
This document summarizes an experiment conducted to demonstrate Boyle's law. The experiment was conducted on October 29, 2013 by a student to measure the relationship between the pressure and volume of a gas. Boyle's law states that the pressure and volume of a gas are inversely related when temperature is held constant. The equipment used in the experiment included tanks and valves to control the pressure and volume of the gas sample. The student recorded measurements as the pressure and volume were varied and analyzed the results to validate Boyle's law.
This document discusses several examples of converting between different units of pressure (atm, torr, kPa) using dimensional analysis and appropriate conversion factors. It provides the calculations for converting specific pressure values between these units. Additionally, it discusses using a manometer to measure gas pressure and calculating gas properties using the ideal gas law.
The document discusses ideal gases and how they differ from real gases. It provides definitions and key characteristics of ideal gases, including that they obey the gas laws under all conditions, cannot be liquefied, and have molecules that undergo perfectly elastic collisions. The document also summarizes the gas laws of Boyle, Charles, Avogadro, Gay-Lussac, and derives the ideal gas law. Sample problems are provided to demonstrate use of the ideal gas law.
The van der Waals gas model takes into account intermolecular interactions that the ideal gas model neglects. It explains the liquid-gas phase transition through a critical point, where the vapor and liquid phases become indistinguishable. The model approximates molecules as rigid spheres that experience short-range repulsion and long-range attraction. It derives an equation of state relating pressure, volume, and temperature. This equation reduces to the ideal gas law under conditions of high temperature or low density.
The document discusses various gas laws and their applications in anesthesia and respiratory physiology. It begins by using Boyle's law to calculate the volume of oxygen remaining in a cylinder at a pressure of 15 psig. It then explains Charles, Gay-Lussac's, Avogadro's, Dalton's laws and their relevance. Further sections cover Hagen-Poiseuille's law, Reynolds number, Graham's law, Bernoulli's principle, Venturi effect, Coanda effect, critical temperature, Poynting effect, adiabatic changes, and other gas laws and their importance in areas like gas delivery, flow dynamics, and equipment function.
Phy351 ch 1 ideal law, gas law, condensed, triple point, van der waals eqMiza Kamaruzzaman
This document summarizes key concepts from Chapter 1 of PHY351 including:
1) The ideal gas law and how it relates pressure, volume, temperature and moles of gas. Real gases deviate from ideal behavior at low temperatures or high pressures.
2) Gas laws including Boyle's, Charles', and Gay-Lussac's laws and how the ideal gas law combines these relationships.
3) Concepts of absolute zero, the Kelvin temperature scale, and standard temperature and pressure.
4) Kinetic theory and how it relates gas properties to molecular motion, including molecular speed distributions and effects of temperature.
5) Phase diagrams and the different phases of matter as well as the triple point.
6
Here are the key steps to solve this problem using Charles' Law:
1) Convert temperatures to Kelvin:
T1 = 297.0 K
T2 = 216.5 K
2) Use the Charles' Law equation:
V1/T1 = V2/T2
3) Solve for V2:
V2 = V1 * T2/T1
= 20.0 L * 216.5 K/297.0 K
= 14.6 L
So the volume outside at -70°F would be 14.6 L.
The document describes several key concepts relating to gases:
1) It outlines the postulates of kinetic molecular theory and how they describe the behavior of ideal gases.
2) It then discusses how real gases differ from ideal gases and how their behavior is affected by factors like pressure and temperature.
3) Several gas laws are introduced that describe the relationships between pressure, volume, temperature, and number of moles for gases including Boyle's law, Charles' law, Gay-Lussac's law, Avogadro's law, Dalton's law of partial pressures, and the ideal gas law.
This document summarizes an investigation into the behavior of gases at different temperatures, pressures, and volumes. Three experiments were conducted: 1) Boyle's law experiment showing an inverse relationship between pressure and volume at constant temperature, 2) Charles' law experiment showing a direct relationship between volume and temperature at constant pressure, and 3) Gay-Lussac's law experiment showing a direct relationship between pressure and temperature at constant volume. The results of the experiments validated the theoretical gas laws and supported the conclusion that the volume, pressure, and temperature of gases are mutually related as described by the general gas equation.
This document summarizes several important laws of fluids and gases:
- Pascal's principle states that pressure applied to any part of a confined fluid is transmitted equally throughout the fluid.
- Boyle's law states that for a gas at constant temperature, the product of pressure and volume is a constant.
- Charles's law describes how the volume of a gas increases or decreases as temperature increases or decreases at constant pressure.
The statistical mechanical derivation of the van der waals equation of stateUNICAMP
The document provides a statistical mechanical derivation of the van der Waals equation of state and its associated thermodynamic properties. Some key points:
- It accounts for finite molecular size and intermolecular attractive forces in the van der Waals fluid model.
- Expressions are derived for various thermodynamic properties like pressure, internal energy, heat capacities in terms of temperature and molar volume.
- Conditions for vapor-liquid equilibrium are obtained by setting the Gibbs free energy of vaporization to zero and equating chemical potentials.
The document discusses the gas laws, including Boyle's law, Charles' law, Gay-Lussac's law, Avogadro's law, the combined gas law, and the ideal gas law. It provides the key relationships and equations for each law, along with example problems and solutions demonstrating how to apply each law to calculate pressure, volume, temperature, or moles of gas under different conditions.
This document discusses key concepts relating to the behavior of gases, including the definitions of pressure and how it relates to force and area. It describes how pressure decreases with increasing altitude due to lower atmospheric pressure. Boyle's Law and Charles' Law are also summarized, with Boyle's Law stating that gas pressure increases as volume decreases if temperature remains constant, while Charles' Law indicates that gas temperature increases as volume increases if pressure remains constant. Charles' Law is used to calculate the temperature at which gas volume would reach absolute zero.
Interpretation of arterial blood gases:Traditional versus Modern Gamal Agmy
This document discusses the interpretation of arterial blood gases and acid-base disorders. It begins by outlining the Handerson-Hasselbalch equation and normal blood gas values. It then defines respiratory failure and describes the four types based on PaO2 and PaCO2 levels. The document details how to evaluate oxygen status, ventilation, and acid-base disorders from a blood gas analysis. It provides examples of metabolic and respiratory acidosis and alkalosis, explaining compensation mechanisms. Mixed disorders and a step-wise approach to interpretation are also outlined. Three sample problems are worked through as examples.
This document provides an overview of key concepts in elements of mechanical engineering related to prime movers and thermodynamics. It defines prime movers as engines that convert fuel to useful work and lists various energy sources and types of prime movers. The document also defines fundamental concepts such as force, mass, pressure, work, power, energy, heat, temperature and thermodynamic laws. It describes gas properties and the gas laws including Boyle's law, Charles' law, Gay-Lussac's law, the combined gas law and the ideal gas law.
This document discusses acid-base balance and disorders. It covers 3 key mechanisms to maintain blood pH: 1) blood buffers, 2) respiratory regulation, and 3) renal regulation. The blood's bicarbonate buffer system uses carbonic acid, while tissues also use phosphate and protein buffers. Respiration controls pH by regulating CO2 exhalation. The kidneys compensate for acid-base imbalances over hours by regulating bicarbonate reabsorption and acid excretion. Acid-base disorders include respiratory and metabolic acidosis and alkalosis.
The document provides an introduction to gas laws including Boyle's law, Charles' law, the pressure law, and the combined gas law. It includes objectives, demonstrations, examples, graphs, and a quiz. The key points covered are:
- Boyle's law states that the pressure and volume of a gas are inversely proportional at constant temperature.
- Charles' law states that the volume of a gas is directly proportional to its temperature when pressure remains constant.
- The pressure law states that the pressure of a gas is directly proportional to its temperature at constant volume.
- The combined gas law relates the pressure, volume, and temperature of a gas, stating their product over temperature is a constant.
The document summarizes several gas laws including Boyle's law, Charles' law, Gay-Lussac's law, Dalton's law of partial pressures, and the combined gas law. It defines each law using the kinetic molecular theory and provides sample problems and equations to demonstrate how to use each law to calculate changes in gas properties like volume, pressure and temperature. Sample problems are worked through step-by-step to show how the gas laws can be applied to different scenarios involving gases.
Charles' Law states that the volume of a gas is directly proportional to its absolute temperature when pressure is held constant. As temperature increases, the molecules move faster and push outward, increasing the volume. This relationship is expressed mathematically as V1/V2 = T1/T2, where V is volume and T is temperature measured on the Kelvin scale. Absolute zero is defined as 0K or -273°C, the lowest possible temperature.
Boyle's Law states that the pressure and volume of a gas are inversely proportional at a constant temperature. It can be expressed as a formula: Pressure x Volume = Constant. An experiment was conducted where the pressure of a gas was increased while the volume decreased, keeping the pressure x volume constant. When the results were graphed with volume on the y-axis and the reciprocal of pressure on the x-axis, the points lay along a straight line, illustrating that volume is inversely proportional to pressure according to Boyle's Law.
- Boyle's law describes the inverse relationship between the pressure and volume of a gas at constant temperature. It states that the pressure of a gas varies inversely with its volume.
- The document discusses Boyle's law, providing its mathematical expression and examples of its application. It also provides sample problems demonstrating how to use the law to calculate pressure or volume given one variable.
- The document then moves on to discuss Charles' law, which describes the direct relationship between the volume and temperature of a gas at constant pressure. Charles' law is similarly expressed mathematically and sample problems are provided.
The document discusses the four main gas laws:
1) Boyle's law states that at a constant temperature, the pressure and volume of a gas are inversely proportional.
2) Charles' law explains that at constant pressure, the volume of a gas is directly proportional to its temperature.
3) Avogadro's law says that equal volumes of gases under the same conditions contain equal numbers of molecules.
4) The ideal gas law combines these to give the equation of state that relates pressure, volume, temperature and moles of gas.
Kinetic molecular theory explains gas behavior using several assumptions: gas particles are small, far apart, and in constant random motion. The theory can predict how gas properties like pressure, volume, and temperature relate based on the kinetic energy and number of particles. Specifically, Boyle's law states that pressure and volume are inversely related at constant temperature, Charles's law relates volume and temperature directly at constant pressure, and Gay-Lussac's law directly relates pressure and temperature at constant volume. Together these combine to form the ideal gas law.
The document summarizes several gas laws:
- Boyle's law relates the inverse relationship between gas volume and pressure at constant temperature
- Charles' law describes how gas volume increases with temperature at constant pressure
- Gay-Lussac's law explains how gas pressure rises with increasing temperature at constant volume
- Combined gas law incorporates changes in pressure, volume, and temperature for a fixed amount of gas
- Dalton's law of partial pressures states that the total pressure of a gas mixture equals the sum of the individual gas pressures
This document discusses properties of gases and how mass, volume, temperature, and pressure are related for gases. It provides information on gas laws including Boyle's law, Charles' law, Gay-Lussac's law, combined gas law, Avogadro's principle, ideal gas law, Dalton's law, and Graham's law. Equations for each gas law are given and example problems are worked through applying the various gas laws.
1. The document discusses gas laws, including Boyle's law relating volume and pressure at constant temperature, and Charles' law relating volume and temperature at constant pressure.
2. It provides examples of using the gas laws to calculate volume or pressure changes given initial and final conditions.
3. The kinetic molecular theory is described as explaining the gas laws based on the random motion and elastic collisions of gas molecules.
The document discusses several gas laws:
- Boyle's law states that for a fixed amount of gas at constant temperature, the volume is inversely proportional to the pressure.
- Charles's law describes the direct relationship between volume and temperature for a fixed amount of gas at constant pressure.
- Gay-Lussac's law explains that pressure and temperature are directly proportional for a fixed volume of gas.
- The combined gas law incorporates all three by relating pressure, volume, and temperature for a fixed amount of gas. It can be used to derive the other gas laws by holding one variable constant. Sample problems demonstrate applying the gas laws to calculate unknown properties.
1. Pressure of a gas is caused by particle collisions with the container walls. Higher temperature means higher particle kinetic energy, causing more frequent and forceful collisions and higher pressure.
2. Boyle's law states that at constant temperature, pressure and volume of a gas are inversely proportional. Charles' law says volume and temperature are directly proportional at constant pressure. Gay-Lussac's law finds pressure and temperature directly proportional at constant volume.
3. These gas laws can be combined into the ideal gas law: pV = nRT, relating pressure, volume, amount of gas, temperature, and the universal gas constant. This law approximates gas behavior except at low temperatures or high pressures.
Charles' law describes how gas volume changes with temperature. It states that the volume of a gas is directly proportional to its temperature when pressure is kept constant. The document provides the formula for Charles' law and shows examples of using it to calculate unknown volumes or temperatures given other variables like initial and final volumes and temperatures. It also discusses the limitations of Charles' law and provides sample problems and solutions demonstrating how to apply the law to calculate unknown values.
This document discusses the behavior of gases through summarizing the kinetic molecular theory and gas laws. It describes five assumptions of the kinetic theory, including that gas particles are in constant random motion and collisions are perfectly elastic. It then discusses how temperature, pressure, volume, and number of moles are related for a gas based on the gas laws of Boyle, Charles, Gay-Lussac, combined, and ideal gases. It provides examples of using the gas laws to solve problems involving changes in pressure, volume, temperature, or number of moles of a gas.
1. The document summarizes key concepts from chemistry chapter 12 on gas laws, including Boyle's law relating pressure and volume at constant temperature, Charles' law relating temperature and volume at constant pressure, and Dalton's law of partial pressures.
2. Boyle's law states that the volume of a gas is inversely proportional to its pressure when temperature is kept constant. Charles' law specifies that the volume of a gas is directly proportional to its temperature when pressure remains constant.
3. Dalton's law of partial pressures states that in a mixture of gases, the total pressure is equal to the sum of the partial pressures of the individual gases.
The document summarizes the kinetic molecular theory and gas laws. It explains that kinetic molecular theory models gases as particles in constant, random motion that exert pressure during collisions. It describes the gas laws of Boyle's law, Charles' law, Gay-Lussac's law, Avogadro's hypothesis, and Dalton's law of partial pressures which relate the variables of pressure, volume, temperature, and moles of gas. Examples are provided to illustrate applications of the gas laws.
The document summarizes the kinetic molecular theory and gas laws relating pressure, temperature, volume and amount of gases. It defines key terms like ideal gas, diffusion and effusion. The kinetic molecular theory has 5 assumptions including gases being made of particles in random motion with no interparticle forces. Gas laws discussed include Boyle's law, Charles' law, Gay-Lussac's law and combined gas law. Dalton's law of partial pressures states the total pressure of a gas mixture equals the sum of partial pressures of individual gases.
This document discusses the key gas laws and their relationships. It begins by introducing the four main properties that determine gas behavior: pressure, volume, amount of gas, and temperature. It then explains each gas law in more detail: Boyle's Law describes the inverse relationship between pressure and volume; Charles' Law specifies the direct relationship between volume and temperature; Gay-Lussac's Law shows the direct link between pressure and temperature; and the Combined Gas Law incorporates all three. The document also presents sample problems demonstrating applications of the gas laws.
The kinetic molecular theory of gases explains gas behavior using the idea that gases are made of molecules or atoms that are in constant, random motion and have space between them. It describes gases as having no intermolecular forces, occupying no volume, and undergoing elastic collisions. This theory allows for deriving gas laws such as Boyle's law (inverse relationship between pressure and volume at constant temperature), Charles's law (direct relationship between volume and temperature at constant pressure), and Gay-Lussac's law (direct relationship between pressure and temperature at constant volume). The combined gas law incorporates all three simpler gas laws. These gas laws allow for calculations involving pressure, volume, temperature, and amount of gas.
1) The document summarizes an experiment on Boyle's law and Gay-Lussac's law.
2) Boyle's law states that for a fixed amount of gas at constant temperature, the product of pressure and volume is constant. Gay-Lussac's law states that for a fixed amount of gas at constant volume, pressure and temperature are directly proportional.
3) The experiment aims to demonstrate these gas laws experimentally by measuring how the pressure of air changes with volume at constant temperature for Boyle's law and how pressure changes with temperature at constant volume for Gay-Lussac's law.
Here is a one page paper relating chemistry and gases:
Chemistry and gases are intimately related. Many of the most important discoveries and applications in chemistry involve gases. Historically, scientists like Robert Boyle, Jacques Charles, and Joseph Gay-Lussac made seminal discoveries about gas behavior through careful experimentation. Their gas laws laid the foundation for understanding the properties and interactions of gases.
One area where gases play a huge role is in industry and energy. The Haber process converts nitrogen gas and hydrogen gas into ammonia, a key component of fertilizers that have enabled the growth of the global population. Natural gas, composed primarily of methane, heats homes and fuels power plants around the world. Greenhouse gases like carbon dioxide
The document summarizes key aspects of the male and female reproductive systems. It describes the main sex organs and their functions, including the testes, ovaries, uterus and other accessory organs. It also discusses processes like the menstrual cycle, puberty, pregnancy and childbirth. Reproductive cancers, disorders and other imbalances are also outlined.
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The rough endoplasmic reticulum (ER) is a network of membranes found throughout the cell that has ribosomes attached to its surface. It plays a key role in protein translation by reading DNA instructions to synthesize and package proteins with its coworkers like the Golgi apparatus and ribosomes. The rough ER is vital for producing proteins according to the cell's genetic blueprint.
Ribosomes are organelles found in all cells that are responsible for protein synthesis. They produce proteins using mRNA and tRNA to translate DNA codes based on a cell's needs. Ribosomes have a small and large subunit and can be free-floating or attached to the endoplasmic reticulum. They produce essential proteins for cellular functions and structures like microtubules, centrioles, and histones. Dysfunction or mutations in ribosomal production can lead to diseases.
The nucleus and nucleolus are running for president and vice president of the cell. The nucleus is described as the brain and leader of the cell, containing the DNA and directing major cellular activities. The DNA in the nucleus allows for protein synthesis. The nucleolus is the largest organelle in the nucleus and acts as the ribosome factory, regulating protein and cellular functions. It has a dense fibrilla component, fibrilla centers, and granular components that make up its structure.
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The three main chambers of the heart are the two atria which receive blood, and the two ventricles which pump blood out of the heart. The right side receives deoxygenated blood and pumps it to the lungs, while the left side receives oxygenated blood from the lungs and pumps it out to the body. One-way flow is ensured by atrioventricular and semilunar valves. The cardiac cycle involves the coordinated contraction and relaxation of the heart chambers.
Blood vessels form a closed system that begins and ends at the heart. There are three main types of blood vessels - arteries, which transport blood away from the heart; capillaries, which allow for exchange of materials between blood and tissues; and veins, which carry blood from the capillaries back towards the heart. Arteries branch into smaller arteries and then arterioles, which feed into capillary beds. Blood then drains from the capillaries into venules and veins of increasing size until emptying back into the heart, completing its 60,000 mile journey through the body transporting blood to and from tissues.
Genetic mutations are changes in DNA sequence that can be caused by environmental factors or spontaneously. There are three main types of mutations: point mutations which change a single base pair, frameshift mutations which add or delete a base changing subsequent amino acids, and chromosomal mutations such as deletions, insertions, inversions or translocations of chromosome segments. Mutations can cause genetic disorders like cystic fibrosis, osteogenesis imperfecta, multiple neurofibromatosis, Klinefelter syndrome, twin-to-twin transfusion syndrome, fragile X syndrome, and Tay-Sachs disease.
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Blood is composed of plasma and formed elements including red blood cells, white blood cells, and platelets. Red blood cells carry oxygen and carbon dioxide throughout the body. White blood cells help protect the body from infection and disease. Platelets are cell fragments that help form blood clots to stop bleeding. Careful matching of blood types is important for safe transfusions, as incompatible blood can cause a dangerous immune response.
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The document summarizes the processes of DNA replication and protein synthesis. DNA replication involves separating DNA into two strands and using each strand as a template to make an identical copy, resulting in two double-stranded DNA molecules. Protein synthesis involves transcription of DNA into mRNA, which is then translated on ribosomes into a polypeptide chain using transfer RNA to add amino acids specified by mRNA codons.
The document discusses the history and structure of DNA. It describes how DNA was discovered to be the genetic material through experiments in the 1800s and 1900s. Key figures like Watson, Crick, Franklin and Chargaff contributed to determining DNA's double helix structure and the rules of base pairing between A-T and G-C. The structure forms a spiral with the bases on the inside and a sugar-phosphate backbone on the outside, held together by hydrogen bonds between the paired bases.
Chemical bonds form between atoms to achieve more stable arrangements with lower potential energy. The type of bonding depends on differences in electronegativity between atoms. Ionic bonds form between ions, covalent bonds involve shared electron pairs, and metallic bonds result from delocalized electrons shared among many atoms in a lattice. Molecular geometry and intermolecular forces also influence molecular properties.
Beyond Degrees - Empowering the Workforce in the Context of Skills-First.pptxEduSkills OECD
Iván Bornacelly, Policy Analyst at the OECD Centre for Skills, OECD, presents at the webinar 'Tackling job market gaps with a skills-first approach' on 12 June 2024
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.
Leveraging Generative AI to Drive Nonprofit InnovationTechSoup
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This presentation was provided by Racquel Jemison, Ph.D., Christina MacLaughlin, Ph.D., and Paulomi Majumder. Ph.D., all of the American Chemical Society, for the second session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session Two: 'Expanding Pathways to Publishing Careers,' was held June 13, 2024.
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.
This presentation was provided by Rebecca Benner, Ph.D., of the American Society of Anesthesiologists, for the second session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session Two: 'Expanding Pathways to Publishing Careers,' was held June 13, 2024.
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!"
Walmart Business+ and Spark Good for Nonprofits.pdf
Gases
1. Pressure and Force
Pressure (P) is defined as the force per unit
area on a surface.
Gas pressure is caused by collisions of the gas
molecules with each other and with
surfaces with which they come into contact.
The pressure exerted by a gas depends on
volume, temperature, and the number of
molecules present.
The greater the number of collisions of gas
molecules,
3. Pressure and Force
The SI unit for force is the newton, (N), the
force that will increase the speed of a
one-kilogram mass by one meter per
second each second that the force is
applied.
example: consider a person with a mass of
51 kg. At Earth’s surface, gravity has an
acceleration of 9.8 m/s2.
The force the person exerts on the ground
2
4. Pressure is force per unit area, so
the pressure of a 500 N person
on an area of the floor that is
325 cm2 is:
500 N 325 cm2 = 1.5 N/cm2
The greater the force on a given
area, the greater
the pressure.
The smaller the area is on which a
given force acts, the greater the
6. Measuring Pressure
A barometer is a device used to measure
atmospheric pressure. The first barometer
was introduced by Evangelista Torricelli in
the early 1600s.
The common unit of pressure is millimeters
of mercury, symbolized mm Hg. A
pressure of 1 mm Hg is also called 1 torr in
honor of Torricelli for his invention of
the barometer.
Pressures can also be measured in units of
atmospheres. Because the average
atmospheric pressure at sea level at 0°C is
760 mm Hg, one atmosphere of pressure
(atm) is defined as being exactly equivalent
7. Measuring Pressure
In SI, pressure is expressed in pascals.
One pascal (Pa) is defined as the
pressure exerted by a force of one
newton (1 N) acting on an area of one
square meter.
The unit is named for Blaise Pascal, a
French mathematician and philosopher
who studied pressure during the
seventeenth century.
One pascal is a very small unit of
pressure, so in many cases, it is more
9. Sample Problem A
The average atmospheric pressure
in Denver, Colorado is 0.830 atm.
Express this pressure in
a. millimeters of mercury (mm
Hg) and
b. kilopascals (kPa)
10. Sample Problem A Solution
Given: atmospheric pressure = 0.830 atm
Unknown: a. pressure in mm Hg
b. pressure in kPa
Solution:
conversion factor
760 mm Hg
a. atm mm Hg; atm mm Hg
atm
b. 101.325 kPa
atm kPa; atm kPa
atm
11. Dalton’s Law of Partial
The pressure Pressuresa mixture is
of each gas in
called the partial pressure of that
gas.
John Dalton, the English chemist who
proposed the atomic theory,
discovered that the pressure exerted
by each gas in a mixture is independent
of that exerted by other gases
present.
Dalton’s law of partial pressures
states that the total pressure of a
12. Gases Collected by Water
Displacement
Gases produced in the laboratory are
often collected over water. The gas
produced by the reaction displaces
the water in the reaction bottle.
Dalton’s law of partial pressures can
be applied to calculate the pressures
of gases collected in this way.
Water molecules at the liquid surface
evaporate and mix with the gas
13. To determine the pressure of a gas inside a
collection bottle, you would use the
following equation, which is an instance of
Dalton’s law of partial pressures.
P H2O
Patm = Pgas +
If you raise the bottle until the water levels
inside and outside the bottle are the same, the
total pressure outside and inside the bottle
will be the same.
Reading the atmospheric pressure from a
PH2O
barometer and looking up the value of
at the temperature of the experiment in a
table, you
can calculate Pgas.
14. Sample Problem B
Oxygen gas from the decomposition
of potassium chlorate, KClO3, was
collected by water displacement.
The barometric pressure and the
temperature during the experiment
were 731.0 torr and 20.0 C.
respectively. What was the partial
pressure of the oxygen collected?
15. Section 2 The Gas Laws
Chapter 11
Boyle’s Law: Pressure-Volume Relationship
Robert Boyle discovered that doubling the pressure on a sample of gas at
constant temperature reduces its volume by one-half.
This is explained by the kinetic-molecular theory:
The pressure of a gas is caused by moving molecules hitting the
container walls.
If the volume of a gas is decreased, more collisions will occur, and
the pressure will therefore increase.
Likewise, if the volume of a gas is increased, less
collisions will occur, and the pressure will decrease.
16. Section 2 The Gas Laws
Chapter 11
Boyle’s Law
Click below to watch the Visual Concept.
17. Section 2 The Gas Laws
Chapter 11
Boyle’s Law: Pressure-Volume Relationship
Boyle’s Law states that the volume of a
fixed mass of gas varies inversely
with the pressure at constant
temperature.
Plotting the values of volume versus
pressure for a gas at constant
temperature gives a curve like that
shown at right.
18. Section 2 The Gas Laws
Chapter 11
Boyle’s Law: Pressure-Volume Relationship
Mathematically, Boyle’s law can be expressed as:
PV = k
P is the pressure, V is the volume, and k is a constant. Since P and V vary
inversely, their product is a constant.
19. Section 2 The Gas Laws
Chapter 11
Boyle’s Law: Pressure-Volume Relationship, continued
Because two quantities that are equal to the same thing are equal to each
other, Boyle’s law can also be expressed as:
P1V1 = P2V2
P1 and V1 represent initial conditions, and P2 and V2 represent another set of
conditions.
Given three of the four values P1, V1, P2, and V2, you can use this equation to
calculate the fourth value for a system at constant temperature.
20. Section 2 The Gas Laws
Chapter 11
Equation for Boyle’s Law
Click below to watch the Visual Concept.
Visual Concept
21. Section 2 The Gas Laws
Chapter 11
Boyle’s Law: Pressure-Volume Relationship, continued
•Sample Problem C
•A sample of oxygen gas has a volume of
150.0 mL when its pressure is 0.947 atm.
What will the volume of the gas be at a
pressure of 0.987 atm if the temperature
remains constant?
22. Section 2 The Gas Laws
Chapter 11
Boyle’s Law: Pressure-Volume Relationship, continued
• Sample Problem C Solution
• Given:V1 of O2 = 150.0 mL
• P1 of O2 = 0.947 atm
• P2 of O2 = 0.987 atm
• Unknown: V2 of O2 in mL
• Solution:
• Rearrange the equation for Boyle’s law (P1V1 = P2V2) to obtain V2.
PV1
1
V2
• P2
23. Section 2 The Gas Laws
Chapter 11
Boyle’s Law: Pressure-Volume Relationship, continued
• Sample Problem C Solution, continued
• Substitute the given values of P1, V1, and P2 into the equation to
obtain the final volume, V2:
PV1
1 (0.947 atm)(150.0 mL O2 )
• V2 P2 0.987 atm
144 mL O2
24. Section 2 The Gas Laws
Chapter 11
Charles’s Law: Volume-Temperature Relationship,
continued
If pressure is constant, gases expand when heated.
When the temperature increases, the volume of a fixed number of gas
molecules must increase if the pressure is to stay constant.
At the higher temperature, the gas molecules move faster. They
collide with the walls of the container more frequently and with
more force.
The volume of a flexible container must then increase in order for
the pressure to remain the same.
25. Section 2 The Gas Laws
Chapter 11
Charles’s Law
Click below to watch the Visual Concept.
26. Section 2 The Gas Laws
Chapter 11
Charles’s Law: Volume-Temperature Relationship,
continued
The quantitative relationship between volume and temperature was discovered by
the French scientist Jacques Charles in 1787.
Charles found that the volume changes by 1/273 of the original volume for each
Celsius degree, at constant pressure and at an initial temperature of 0 C.
The temperature –273.15°C is referred to as absolute zero, and is given a value of
zero in the Kelvin temperature scale. The relationship between the two
temperature scales is K = 273.15 + °C.
27. Section 2 The Gas Laws
Chapter 11
Absolute Zero
Click below to watch the Visual Concept.
Visual Concept
28. Section 2 The Gas Laws
Chapter 11
Charles’s Law: Volume-Temperature Relationship, continued
Charles’s law states
that the volume of a fixed mass of
gas at constant pressure varies
directly with the Kelvin
temperature.
Gas volume and Kelvin temperature
are directly proportional to each
other at constant pressure, as
shown at right.
29. Section 2 The Gas Laws
Chapter 11
Charles’s Law: Volume-Temperature Relationship,
continued
Mathematically, Charles’s law can be expressed as:
V
V kT or k
T
V is the volume, T is the Kelvin temperature, and
k is a constant. The ratio V/T for any set of volume-temperature values
always equals the same k.
This equation reflects the fact that volume and temperature are directly
proportional to each other
at constant pressure.
30. Section 2 The Gas Laws
Chapter 11
Charles’s Law: Volume-Temperature Relationship,
continued
The form of Charles’s law that can be applied directly to most volume-
temperature gas problems is:
V1 V2
T1 T2
V1 and T1 represent initial conditions, and V2 and T2 represent another set of
conditions.
Given three of the four values V1, T1, V2, and T2, you can use this equation to
calculate the fourth value for
a system at constant pressure.
31. Section 2 The Gas Laws
Chapter 11
Equation for Charles’s Law
Click below to watch the Visual Concept.
Visual Concept
32. Section 2 The Gas Laws
Chapter 11
Charles’s Law: Volume-Temperature
Relationship, continued
•Sample Problem D
•A sample of neon gas occupies a volume of
752 mL at 25 C. What volume will the gas
occupy at 50 C if the pressure remains
constant?
33. Section 2 The Gas Laws
Chapter 11
Charles’s Law: Volume-Temperature
Relationship, continued
• Sample Problem D Solution
• Given: V1 of Ne = 752 mL
• T1 of Ne = 25 C + 273 = 298 K
• T2 of Ne = 50 C + 273 = 323 K
• Unknown: V2 of Ne in mL
• Solution: V1 V2
• Rearrange the equation for Charles’s law T1
VT Tto obtain V2.
2
1 2
V2
• T1
34. Section 2 The Gas Laws
Chapter 11
Charles’s Law: Volume-Temperature
Relationship, continued
• Sample Problem D Solution, continued
• Substitute the given values of V1, T1, and T2 into the equation to
obtain the final volume, V2:
V1T2 (752 mL Ne)(323 K)
V2 815 mL Ne
• T1 298 K
35. Section 2 The Gas Laws
Chapter 11
Gay-Lussac’s Law: Pressure-Temperature Relationship
At constant volume, the pressure of a gas increases with increasing
temperature.
Gas pressure is the result of collisions of molecules with container walls.
The energy and frequency of collisions depend on the average kinetic
energy of molecules.
Because the Kelvin temperature depends directly on average kinetic
energy, pressure is directly proportional to Kelvin temperature.
36. Section 2 The Gas Laws
Chapter 11
Gay-Lussac’s Law
Click below to watch the Visual Concept.
37. Section 2 The Gas Laws
Chapter 11
Gay-Lussac’s Law: Pressure-Temperature Relationship,
continued
Gay-Lussac’s law states that the
pressure of a fixed mass of gas at
constant volume varies directly with
the Kelvin temperature.
This law is named after Joseph Gay-
Lussac, who discovered it in 1802.
38. Section 2 The Gas Laws
Chapter 11
Gay-Lussac’s Law: Pressure-Temperature Relationship,
continued
Mathematically, Gay-Lussac’s law can be expressed as:
P
P kT or k
T
P is the pressure, T is the Kelvin temperature, and
k is a constant. The ratio P/T for any set of volume-temperature values always
equals the same k.
This equation reflects the fact that pressure and temperature are directly
proportional to each other
at constant volume.
39. Section 2 The Gas Laws
Chapter 11
Gay-Lussac’s Law: Pressure-Temperature Relationship,
continued
The form of Gay-Lussac’s law that can be applied directly to most pressure-
temperature gas problems is:
P1 P2
T1 T2
P1 and T1 represent initial conditions, and P2 and T2 represent another set of
conditions.
Given three of the four values P1, T1, P2, and T2, you can use this equation to
calculate the fourth value for
a system at constant pressure.
40. Section 2 The Gas Laws
Chapter 11
Equation for Gay-Lussac’s Law
Click below to watch the Visual Concept.
Visual Concept
41. Section 2 The Gas Laws
Chapter 11
Gay-Lussac’s Law: Volume-Temperature
Relationship, continued
•Sample Problem E
•The gas in a container is at a pressure of 3.00
atm at 25 C. Directions on the container warn
the user not to keep it in a place where the
temperature exceeds 52 C. What would the
gas pressure in the container be at 52 C?
42. Section 2 The Gas Laws
Chapter 11
Gay-Lussac’s Law: Volume-Temperature
Relationship, continued
• Sample Problem E Solution
• Given: P1 of gas = 3.00 atm
• T1 of gas = 25 C + 273 = 298 K
• T2 of gas = 52 C + 273 = 325 K P1 P2
• Unknown: P2 of gas in atm T1 T2
• Solution: P2
PT2
1
• T1
Rearrange the equation for Gay-Lussac’s law
to obtain V2.
43. Section 2 The Gas Laws
Chapter 11
Gay-Lussac’s Law: Volume-Temperature
Relationship, continued
• Sample Problem E Solution, continued
• Substitute the given values of P1, T1, and
T2 into the equation to obtain the final
volume,1T22: (3.00 atm)(325 K)
VP
V2 3.27 atm
T1 298 K
•
44. Section 2 The Gas Laws
Chapter 11
Summary of the Basic Gas Laws
45. Section 2 The Gas Laws
Chapter 11
The Combined Gas Law
Boyle’s law, Charles’s law, and Gay-Lussac’s law can be combined into a single
equation that can be used for situations in which temperature, pressure, and
volume, all vary at the same time.
The combined gas law expresses the relationship between pressure, volume,
and temperature of a fixed amount of gas. It can be expressed as follows:
PV
k
T
46. Section 2 The Gas Laws
Chapter 11
Equation for the Combined Gas Law
Click below to watch the Visual Concept.
Visual Concept
47. Section 2 The Gas Laws
Chapter 11
The Combined Gas Law, continued
The combined gas law can also be written as follows.
PV1
1 P2V2
T1 T2
The subscripts 1 and 2 represent two different sets of conditions.
As in Charles’s law and Gay-Lussac’s law,
T represents Kelvin temperature.
Each of the gas laws can be obtained from the combined gas law when the
proper variable is
kept constant.
48. Section 2 The Gas Laws
Chapter 11
Combined Gas Law
Click below to watch the Visual Concept.
49. Section 2 The Gas Laws
Chapter 11
The Combined Gas Law, continued
•Sample Problem F
•A helium-filled balloon has a volume of 50.0
L at 25 C and 1.08 atm. What volume will it
have at 0.855 atm and 10.0 C?
50. Section 2 The Gas Laws
Chapter 11
The Combined Gas Law, continued
• Sample Problem F Solution
• Given: V1 of He = 50.0 L
• T1 of He = 25 C + 273 = 298 K
• T2 of He = 10 C + 273 = 283 K
• P1 of He = 1.08 atm
• P2 of He = 0.855 atm
•
51. Section 2 The Gas Laws
Chapter 11
The Combined Gas Law, continued
• Sample Problem F Solution, continued
• Solution:
• Rearrange the equation for the
combined gas law T
PV1 2 PV1 P2V2
1
1
to obtain V2. V2
PT T T
2 1 1 2
Substitute the given values of P1, T1, and T2 into the equation to obtain
the final volume, P2:
PV1T2
1 (1.08 atm)(50.0 L He)(283 K)
V2 60.0 L He
P2T1 (0.855 atm)(298 K)
52. Section 3 Gas Volumes and the Ideal Gas
Chapter 11 Law
Preview
Lesson Starter
Objectives
Measuring and Comparing the Volumes of Reacting Gases
Avogadro’s Law
Molar Volume of a Gas
Gas Stoichiometry
The Ideal Gas Law
53. Section 3 Gas Volumes and the Ideal Gas
Chapter 11 Law
Lesson Starter
Write balanced chemical equations for the two chemical reactions indicated
below.
hydrogen gas + oxygen gas → water vapor
(2 liters) (1 liter) (2 liters)
hydrogen gas + chlorine gas → hydrogen chloride
(1 liter) (1 liter) (2 liters)
Compare the balanced equations with the expressions above. What do you
notice?
54. Section 3 Gas Volumes and the Ideal Gas
Chapter 11 Law
Objectives
State the law of combining volumes.
State Avogadro’s law and explain its significance.
Define standard molar volume of a gas and use it to calculate gas masses and
volumes.
State the ideal gas law.
Using the ideal gas law, calculate pressure, volume, temperature, or amount of
gas when the other three quantities are known.
55. Section 3 Gas Volumes and the Ideal Gas
Chapter 11 Law
Measuring and Comparing the Volumes of Reacting
Gases
In the early 1800s, French chemist Joseph Gay-Lussac observed that 2 L of
hydrogen can react with
1 L of oxygen to form 2 L of water vapor.
hydrogen gas + oxygen gas → water vapor
2 L (2 volumes) 1 L (1 volume) 2 L (2 volumes)
The reaction shows a simple 2:1:2 ratio in the volumes of reactants and
products. This same ratio applies to any volume proportions: for example,
2 mL, 1 mL, and 2 mL; or 600 L, 300 L, and 600 L.
56. Section 3 Gas Volumes and the Ideal Gas
Chapter 11 Law
Measuring and Comparing the Volumes of Reacting
Gases
The same simple and definite volume proportions can be observed in other gas
reactions.
hydrogen gas + chlorine gas → hydrogen chloride gas
1 L (2 volumes) 1 L (1 volume) 2 L (2 volumes)
Gay-Lussac’s law of combining volumes of gases states that at constant
temperature and pressure, the volumes of gaseous reactants and products
can be expressed as ratios of small whole numbers.
57. Section 3 Gas Volumes and the Ideal Gas
Chapter 11 Law
Gay-Lussac’s Law of Combining
Volumes of Gases
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Visual Concept
58. Section 3 Gas Volumes and the Ideal Gas
Chapter 11 Law
Avogadro’s Law
In 1811, Amedeo Avogadro explained Gay-Lussac’s law of combining volumes of
gases without violating Dalton’s idea of indivisible atoms.
Avogadro reasoned that, instead of always being in monatomic form when they
combine to form products, gas molecules can contain more than one atom.
He also stated an idea known today as Avogadro’s law. The law states that equal
volumes of gases at
the same temperature and pressure contain equal numbers of molecules.
59. Section 3 Gas Volumes and the Ideal Gas
Chapter 11 Law
Avogadro’s Law
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Visual Concept
60. Section 3 Gas Volumes and the Ideal Gas
Chapter 11 Law
Avogadro’s Law, continued
Avogadro’s law also indicates that gas volume is directly proportional to the
amount of gas, at a given temperature and pressure.
The equation for this relationship is shown below, where V is the volume, k is a
constant, and n is the amount of moles of the gas.
V = kn
61. Section 3 Gas Volumes and the Ideal Gas
Chapter 11 Law
Avogadro’s Law, continued
Avogadro’s law applies to the combining volumes in gas reactions, and helped
him to deduce chemical formulas in reactions.
Dalton had guessed that the formula for water
was HO, but Avogadro’s reasoning established
that water must contain twice as many H atoms as
O atoms because of the volume ratios in which the gases combine:
hydrogen gas + oxygen gas → water vapor
2 L (2 volumes) 1 L (1 volume) 2 L (2 volumes)
62. Section 3 Gas Volumes and the Ideal Gas
Chapter 11 Law
Avogadro’s Law, continued
Given Avogadro’s law, the simplest possible chemical formula for a water
molecule indicated two hydrogen atoms and one oxygen atom.
hydrogen gas + oxygen gas → water vapor
(2 volumes) (1 volume) (2 volumes)
2H2 (g ) O2 (g ) 2H2O(g )
Avogadro’s idea that some gases, such as hydrogen and oxygen, must be
diatomic, was thus consistent with Avogadro’s law and a chemical
formula for water of H2O.
63. Section 3 Gas Volumes and the Ideal Gas
Using
Chapter 11 Law Gay-Lussac’s Law of
Combining Volumes of Gases and
Avogadro’s Law to Find Mole
Ratios
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Visual Concept
64. Section 3 Gas Volumes and the Ideal Gas
Chapter 11 Law
Molar Volume of a Gas
Recall that one mole of a substance contains a number of particles equal to
Avogadro’s constant (6.022 1023).
example: one mole of oxygen, O2, contains 6.022 × 1023 diatomic
molecules.
According to Avogadro’s law, one mole of any gas will occupy the same volume
as one mole of any other gas at the same conditions, despite mass
differences.
The volume occupied by one mole of gas at STP is known as the standard molar
volume of a gas,
which is 24.414 10 L (rounded to 22.4 L).
65. Section 3 Gas Volumes and the Ideal Gas
Chapter 11 Law
Molar Volume of a Gas, continued
Knowing the volume of a gas, you can use the conversion factor 1 mol/22.4 L to
find the moles (and therefore also mass) of a given volume of gas at STP.
example: at STP,
1 mol
5.00 L of gas 0.223 mol of gas
22.4 L
You can also use the molar volume of a gas to find the volume, at STP, of a
known number of moles or a known mass of gas.
example: at STP,
22.4 L
0.768 mol of gas 17.2 L of gas
1 mol
66. Section 3 Gas Volumes and the Ideal Gas
Chapter 11 Law
Molar Volume of a Gas, continued
• Sample Problem G
a. What volume does 0.0685 mol of gas
occupy at STP?
b. What quantity of gas, in moles, is contained
in 2.21 L at STP?
67. Section 3 Gas Volumes and the Ideal Gas
Chapter 11 Law
Molar Volume of a Gas, continued
• Sample Problem G Solution
• a.
• Given: 0.0865 mol of gas at STP
• Unknown: volume of gas
22.4 L
• Solution: Multiply the amount in moles
1 mol by
22.4 L
0.0685 mol of gas 1.53 L of gas
the conversion factor,
1 mol .
68. Section 3 Gas Volumes and the Ideal Gas
Chapter 11 Law
Molar Volume of a Gas, continued
• Sample Problem G Solution, continued
• b.
• Given: 2.21 L of gas at STP
• Unknown: moles of gas
1 mol
• Solution: L
22.4 Multiply the volume in liters by the
1 mol
conversion factor,4 L 0.0987 mol of gas
2.21 L of gas
22. .
69. Section 3 Gas Volumes and the Ideal Gas
Chapter 11 Law
Gas Stoichiometry
Gay-Lussac’s law of combining volumes of gases and Avogadro’s law can be
applied in calculating the stoichiometry of reactions involving gases.
The coefficients in chemical equations of gas reactions reflect not only molar
ratios, but also volume ratios (assuming conditions remain the same).
example—reaction of carbon dioxide formation:
2CO(g) + O2(g) → 2CO2(g)
2 molecules 1 molecule 2 molecules
2 mole 1 mole 2 mol
2 volumes 1 volume 2 volumes
70. Section 3 Gas Volumes and the Ideal Gas
Chapter 11 Law
Gas Stoichiometry, continued
2CO(g) + O2(g) → 2CO2(g)
2 molecules 1 molecule 2 molecules
2 mole 1 mole 2 mol
2 volumes 1 volume 2 volumes
You can use the volume ratios as conversion
factors in gas stoichiometry problems as you would mole ratios:
2 volumes CO 1 volume O2
or
1 volume O2 2 volumes CO
2 volumes CO 2 volumes CO2
or
2 volumes CO2 2 volumes CO
etc….
71. Section 3 Gas Volumes and the Ideal Gas
Chapter 11 Law
Gas Stoichiometry
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Visual Concept
72. Section 3 Gas Volumes and the Ideal Gas
Chapter 11 Law
Gas Stoichiometry, continued
•Sample Problem H
•Propane, C3H8, is a gas that is sometimes used
as a fuel for cooking and heating. The
complete combustion of propane occurs
according to the following balanced equation.
• C3H8(g) + 5O2(g) → 3CO2(g) + 4H2O(g)
•(a) What will be the volume, in liters, of
oxygen required for the complete combustion
of 0.350 L of propane?
•(b) What will be the volume of carbon dioxide
73. Section 3 Gas Volumes and the Ideal Gas
Chapter 11 Law
Gas Stoichiometry, continued
• Sample Problem H Solution
• a.
• Given: balanced chemical equation;
V of propane = 0.350 L
• Unknown: V of O2
• Solution: Because all volumes are to be
compared at 5 L O2
0.350 L C3H8 1.75 L O2
the same conditions, volume ratios can be
1 L C3H8
used like mole ratios.
74. Section 3 Gas Volumes and the Ideal Gas
Chapter 11 Law
Gas Stoichiometry, continued
• Sample Problem H Solution, continued
• b.
• Given: balanced chemical equation;
V of propane = 0.350 L
• Unknown: V of CO2
• Solution: Because all volumes are to be
compared at 3 L CO2
0.350 L C3H8 1.05 L CO2
the same conditions, 3volume ratios can be
1 L C H8
used like mole ratios.
75. Section 3 Gas Volumes and the Ideal Gas
Chapter 11 Law
The Ideal Gas Law
You have learned about equations describing the relationships between two or
three of the four variables—pressure, volume, temperature, and moles—
needed to describe a gas sample at a time.
All of the gas laws you have learned thus far can be combined into a single
equation, the ideal gas law: the mathematical relationship among pressure,
volume, temperature, and number of moles of a gas.
It is stated as shown below, where R is a constant:
PV = nRT
76. Section 3 Gas Volumes and the Ideal Gas
Chapter 11 Law
Equation for the Ideal Gas Law
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Visual Concept
77. Section 3 Gas Volumes and the Ideal Gas
Chapter 11 Law
The Ideal Gas Law, continued
The Ideal Gas Constant
In the equation representing the ideal gas law, the constant R is known as the
ideal gas constant.
Its value depends on the units chosen for pressure, volume, and
temperature in the rest of the equation.
Measured values of P, V, T, and n for a gas at near-ideal conditions
can be used to calculate R:
PV (1 atm)(22.414 10 L) L atm
R 0.082 057 84
nT (1 mol)(273.15 K) mol K
78. Section 3 Gas Volumes and the Ideal Gas
Chapter 11 Law
The Ideal Gas Law, continued
The Ideal Gas Constant, continued
The calculated value of R is usually rounded to 0.0821 (L•atm)/(mol•K).
Use this value in ideal gas law calculations when the
volume is in liters, the pressure is in atmospheres, and
the temperature is in kelvins.
The ideal gas law can be applied to determine the existing conditions of a gas
sample when three of the four values, P, V, T, and n, are known.
Be sure to match the units of the known quantities
and the units of R.
79. Section 3 Gas Volumes and the Ideal Gas
Chapter 11 Law
Numerical Values of the Gas Constant
80. Section 3 Gas Volumes and the Ideal Gas
Chapter 11 Law
Ideal Gas Law
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Visual Concept
81. Section 3 Gas Volumes and the Ideal Gas
Chapter 11 Law
The Ideal Gas Law, continued
•Sample Problem I
•What is the pressure in atmospheres
exerted by a 0.500 mol sample of
nitrogen gas in a 10.0 L container at 298
K?
82. Section 3 Gas Volumes and the Ideal Gas
Chapter 11 Law
The Ideal Gas Law, continued
• Sample Problem I Solution
• Given: V of N2 = 10.0 L
n of N2 = 0.500 mol
• T of N2 = 298 K
• Unknown: P of N2 in atm
• Solution: Use the ideal gas law, which can be
find P nRT
rearranged to nRT the pressure, as follows.
PV
V
83. Section 3 Gas Volumes and the Ideal Gas
Chapter 11 Law
The Ideal Gas Law, continued
• Sample Problem I Solution, continued
• Substitute the given values into the
nRT
equation: P
V
(0.500 mol)(0.0821 L atm)(298 K)
P 1.22 atm
10.0 L
84. Section 4 Diffusion and Effusion
Chapter 11
Preview
Objectives
Diffusion and Effusion
Graham’s Law of Effusion
85. Section 4 Diffusion and Effusion
Chapter 11
Objectives
Describe the process of diffusion.
State Graham’s law of effusion.
State the relationship between the average molecular velocities of two gases
and their molar masses.
86. Section 4 Diffusion and Effusion
Chapter 11
Diffusion and Effusion
The constant motion of gas molecules causes them to spread out to fill any
container they are in.
The gradual mixing of two or more gases due to their spontaneous, random
motion is known as diffusion.
Effusion is the process whereby the molecules of a gas confined in a container
randomly pass through a tiny opening in the container.
87. Section 4 Diffusion and Effusion
Chapter 11
Comparing Diffusion and Effusion
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Visual Concept
88. Section 4 Diffusion and Effusion
Chapter 11
Graham’s Law of Effusion
Rates of effusion and diffusion depend on the relative velocities of gas
molecules. The velocity of a gas varies inversely with the square root of its
molar mass.
Recall that the average kinetic energy of the molecules in any gas
depends only the temperature and equals .
1
mv 2
2
For two different gases, A and B, at the same temperature, the
following relationship is true.
1 1
M Av A2 MBv B 2
2 2
89. Section 4 Diffusion and Effusion
Chapter 11
Graham’s Law of Effusion
From the equation relating the kinetic energy of two different gases at the same
conditions, one can derive an equation relating the rates of effuses of two
gases with their molecular mass:
rate of effusion of A MB
rate of effusion of B MA
This equation is known as Graham’s law of effusion, which states that the rates
of effusion
of gases at the same temperature and pressure
are inversely proportional to the square roots of
their molar masses.
90. Section 4 Diffusion and Effusion
Chapter 11
Graham’s Law of Effusion
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Visual Concept
91. Section 4 Diffusion and Effusion
Chapter 11
Equation for Graham’s Law of Effusion
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Visual Concept
93. Section 4 Diffusion and Effusion
Chapter 11
Graham’s Law of Effusion, continued
•Sample Problem J
•Compare the rates of effusion of hydrogen
and oxygen at the same temperature and
pressure.
94. Section 4 Diffusion and Effusion
Chapter 11
Graham’s Law of Effusion, continued
• Sample Problem J Solution
• Given: identities of two gases, H2 and O2
• Unknown: relative rates of effusion
• Solution: The ratio of the rates of effusion of
two gases at the same temperature and
pressurerate of be foundAfrom Graham’s law.
can effusion of M B
rate of effusion of B MA
95. Section 4 Diffusion and Effusion
Chapter 11
Graham’s Law of Effusion, continued
• Sample Problem J Solution, continued
• Substitute the given values into the
equation:
rate of effusion of A M 32.00 g/mol
B 32.00 g/mol
3.98
rate of effusion of B MA 2.02 g/mol 2.02 g/mol
• Hydrogen effuses 3.98 times faster than
oxygen.