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- 1. Gas Laws
- 2. • To state the laws that govern gas behavior and express the gas laws in equation form Learning Objective
- 3. • Understanding the laws that govern gas behavior and the use of ideal gas equation to calculate pressure, volume, temperature, or number of moles of a gas Key Understanding • What are the laws that govern gas behavior? Key Question
- 4. • At constant temperature, the pressure of a fixed quantity of a gas varies inversely with the volume. This means that if the pressure on a gas sample is increased without changing the temperature, the volume of the gas will decrease proportionally or that if the pressure on the gas is doubled, the volume will be halved. The law may be expressed mathematically by the equation: P1V1 = P2V2 • The inverse relationship between P and V can be seen from a plot of P versus V at constant temperature called an isotherm. Boyle’s Law
- 5. Robert Boyle (1627–1691) was born at Lismore Castle, Munster, Ireland, the 14th child of the Earl of Cork. Boyle’s chief scientific interest was chemistry but his first published scientific work entitled “New Experiments Physico- Mechanical, Touching the Spring of the Air and Its Effects” (1660), concerned the physical nature of air. This was shown in his experiments where he used an air pump to create a vacuum. The second edition of this work (1662) described the quantitative relationship that Boyle derived from experimental values, presently known as “Boyle’s law”: that the volume of a gas varies inversely with pressure.
- 6. Sample Problem: ▪ A gas sample exerts a pressure of 3.0 kPa when it occupies a 12.0-L vessel at 20oC. What pressure would the gas exert at 20oC if same gas sample is transferred to a 9.0-L vessel? Given: P1 = 3.0 kPa P2 = unknown V1 = 12.0 L V2 = 9.0 L T1 = 20 + 273 = 293 K T2 = 293 K Solution: The temperature is unchanged; therefore, Boyle’s Law will be used.
- 7. Practical Applications of Boyle’s Law ➢ Syringes operate by Boyle’s Law: When the plunger is pulled, the volume inside the syringe increases, causing a decrease in pressure inside the syringe. The decrease in pressure causes the causes the liquid to be drawn into the drawn into the syringe, thereby causing the volume of the air to decrease again. ➢ Spray cans used in spray paint and air freshener are governed by Boyle’s Law. High pressure inside the can pushes on the liquid inside the can and forces the liquid out when the cap is opened.
- 8. • At constant pressure, the volume of a fixed quantity of a gas is directly proportional to the absolute temperature. This means that provided the pressure on the gas remains constant, the volume will increase proportionally to the absolute temperature, that is, the volume of the gas will double if the absolute temperature (NOT the temperature in the Celsius or Fahrenheit scale!) is doubled. The direct relationship between volume and absolute temperature at constant pressure is described in a plot called an isobar). Mathematically, the law may be expressed. Charles’ Law
- 9. Jacques Charles (1746-1823) was the proponent of Charles’ law (1787). Charles was a French-born balloonist who flew the firrst hydrogen balloon in 1783. Charles did an experiment where he filled five different balloons with the same volume of five different gases. He observed that the balloons expanded uniformly when heated uniformly. This observation was not published until 1802, by Gay-Lussac, but was named for the original observer, Charles.
- 10. Sample Problem: ▪ A gas sample is observed to occupy 12.0 L under a pressure of 101.325 kPa (also 1 atm) at 27oC. What will be the volume of the gas if it is heated to 57oC under the same pressure? Given: P1 = 101.325 kPa P2 = 101.325 kPa V1 = 12.0 L V2 = unknown T1 = 27 + 273 = 300 K T2 = 57 + 273 = 330 K Solution: Since pressure is constant, Charles’ law will be applied.
- 11. Practical Applications of Charles’ Law ➢ A balloon that has been inflated inside a cool building expands when it is carried to a warmer area like the outdoors. This is why we often see balloons just bursting even when nobody is near it. ➢ The capacity of the human lungs is reduced in colder weather. This is why athletes who come from countries with warm climates like the Philippines may find it difficult to perform well in countries with severely cold weather due to difficulty in breathing. For the same reason, asthmatic people usually experience asthma attacks when there is a sudden change in temperature. ➢ Charles’ law, along with other gas laws, can explain the process of leavening for the or rising of bread and other baked goods during baking. Small pockets of CO2 gas produced by the action of yeast or leavening ingredients expand when heated. This causes the dough to rise (expand) which results in lighter finished baked goods ➢ Car (combustion) engines work by this principle. The heat of combustion of the fuel causes the combustion gases in the cylinder to expand thereby pushing the piston, causing the crankshaft to turn.
- 12. • Two gases that occupy equal volumes under the same temperature and pressure contain the same number of moles (or the same number of molecules). At standard temperature (0oC or 273 K) and pressure (1 atm or 101.3 kPa), one mole of any ideal gas will occupy 22.413 L and contain 6.02 x 10 23 molecules. Avogadro’s Law
- 13. More than 200 years ago, a paper proposing the idea that equal volumes of different gases, at the same temperature and pressure, contain an equal number of molecules—was published in the Journal de Physique. The paper’s author was Italian mathematical physicist Amedeo Avogadro, and his idea became known as Avogadro’s law, which is now a fundamental concept in the physical sciences.
- 14. Practical Applications of Avogadro’s Law ➢ Avogadro’s law, with other gas laws, explains why bread and other baked goods rise. Yeast or other leavening agents cause the production of carbon dioxide gas and ethanol. The carbon dioxide forms bubbles which appear as holes in the dough. As the yeast continues the leavening process, the number of particles of carbon dioxide increases, hence causing an increase in the number, or volume, of bubbles and in the size of the dough. ➢ Inflation of a balloon demonstrates of Avogadro’s law. When a person inflates a balloon, he places more gas particles inside the balloon, so as the number of gas particles increases, volume of the balloon increases. ➢ We demonstrate Avogadro’s law when we breathe. As the lungs expand when we inhale, more oxygen molecules from the air enter the lungs. When the lungs contract, carbon dioxide gas molecules are expelled (exhaling).
- 15. The Ideal Gas Equation of State Taking into account Boyle’s Law, Charles’ Law, and Avogadro’s Law and combining the effect of each law on the volume of a gas, we get the following expressions: V ∞1 since volume is inversely proportional to pressure; P V ∞1 since volume is directly proportional to absolute P temperature; and V ∞1 or PV ∞ nT since V is directly proportional to the P number of moles of the gas. We finally arrive at the relationship called the Ideal Gas Equation written as: PV = nRT
- 16. The Ideal Gas Equation of State where R is the universal gas constant whose value depends on the units for V, P and T. If we use standard conditions and apply the values to the ideal gas equation, we get Sample Problem ▪ Calculate the volume of 22.0 g of CO2 gas at 40oC and 2.0 atm. ▪ Given: m = 22.0 g P = 2.0 atm T = 40 + 273 = 313 K
- 17. Solution: ▪ First, we solve for the number of mols of CO2: n = mass/molar mass = 22.0 g/ (44.0 g/mol) = 0.500 mol ▪ We can now substitute the values in the Ideal Gas Equation of State: ▪ For the two gases, 1 and 2, we can write P1V1 = n1RT1 and P2V2 = n2RT2 ▪ If we take equal number of moles of the two gases, we get the combined gas equation.
- 18. Solution: ▪ We can also use the ideal gas equation to determine gas density from pressure and temperature. ▪ Using the definitions of density, (density) = mass/volume, mass = n x M, and gas volume from the ideal gas equation, , we get the following equation for density of an ideal gas.
- 19. Section Assessment 1. Which of the following conditions should be done to cause the density of a gas to increase? A. Increase the pressure and increase the temperature B. Increase the pressure and decrease the temperature C. Decrease the pressure and increase the temperature D. Decrease the pressure and Decrease the temperature 2. A sample of methane gas is kept in a 15.0 – liter container fitted with a piston that keeps the gas inside the tank under a pressure of 740 mmHg at 20°C. How much pressure must be exerted on the gas to reduce its volume to 12.0 L without changing the temperature? A. 925 mm Hg C. 760 mm Hg B. 592 mm Hg D. 750 mm Hg
- 20. Section Assessment 3. A sample of H2 gas is kept in container fitted with a movable piston set at the 8.0-liter mark at 50°C and 110 kPa. At what temperature will the piston to move to the 9.0-liter mark without a change in the pressure reading? A. 14°C C. 34°C B. 27°C D. 90°C 4. If 1.0 g of each of the following gases is taken and kept under the same conditions of temperature and pressure, which gas will occupy the smallest volume? A. H2 C. N2 B. CH4 D. CO2 5. An LPG tank contains 11.0 kg of butane gas, (C4H10), in a 20.0- liter gas tank. What must be the pressure of the gas inside the tank when the temperature is 27°C?