GAS LAWS

Ideal Gases Solid carbon dioxide, or dry ice, doesn’t melt. It sublimes. Dry ice can exist because gases don’t obey the assumptions of kinetic theory under all conditions. You will learn how real gases differ from the ideal gases on which the gas laws are based.

Ideal Gases and Real Gases There are attractions between the particles in an ideal gas. Because of these attractions, a gas can condense,or even solidify, when it is compressed or cooled. In this flask used to store liquid nitrogen, there are two walls with a vacuum in between.

Ideal Gases and Real Gases Under what conditions are real gases most likely to differ from ideal gases?

Ideal Gases and Real Gases Real gases differ most from an ideal gas at low temperatures and high pressures.

Ideal Gases and Real Gases This graph shows how real gases deviate from the ideal gas law at high pressures. INTERPRETING GRAPHS a. Observing What are the values of (PV)/(nRT) for an ideal gas at 20,000 and 60,000 kPa? b. Comparing What variable is responsible for the differences between the two (CH4) curves? c. Making Generalizations How does an increase in pressure affect the (PV)/(nRT ) ratio for real gases?

Lorenzo Romano Amedeo Carlo Avogadro di Quareqa e di Carreto - Avogadro for short Born in Turin, Italy in 1776, Avogadro's Hypothesis

Avogrado’s Hypothesis Equal volume of gases at the same temperature and pressure contain equal numbers of particles (molecules)

Molar Volume The number of molecules in 22.4 L of any gas at STP has been chosen as a standard unit called 1 mole 1mole = 6.02 x 1023 particles 1 mole = 22.4 L of any gas STP 22.4 L of any gas at STP contains 6.02x1023 particles

Gas Laws How are the pressure, volume, and temperature of a gas related? Pressure atm or kPa Volume ml or L Temperature Kelvin

Boyle’s Law: Pressure and Volume If the temperature is constant, as the pressure of a gas increases, the volume decreases.

Boyle’s Law: Pressure and Volume Boyle’s law states that for a given mass of gas at constant temperature, the volume of the gas varies inversely with pressure.

Boyle’s Law: Pressure and Volume The pressure of a gas changes as the volume changes. INTERPRETING GRAPHS a. Observing When the volume is 2.0 L, what is the pressure? b. Predicting What would the pressure be if the volume were increased to 3.0 L? c. Drawing Conclusions Based on the shape of the graph, describe the general pressure-volume relationship.

Charles’s Law: Temperature and Volume As the temperature of an enclosed gas increases, the volume increases, if the pressure is constant.

Charles’s Law: Temperature and Volume As the temperature of the water increases, the volume of the balloon increases. When the gas in the blue balloon is cooled at constant pressure, the volume of the gas decreases. When the gas is heated at constant pressure, the volume increases. Calculating What is the ratio of volume to temperature for each set of conditions? Round your answer to two significant figures.

Charles’s Law: Temperature and Volume Charles’s law states that the volume of a fixed mass of gas is directly proportional to its Kelvin temperature if the pressure is kept constant.

Charles’s Law: Temperature and Volume This graph shows how the volume changes as the temperature of a gas changes. INTERPRETING GRAPHS a. Observing What is the unit of temperature? b. Drawing Conclusions What happens to the volume as the temperature rises? c. Predicting If the temperature of a gas were 0 K, what would the volume of the gas be?

Gay-Lussac’s Law: Pressure and Temperature As the temperature of an enclosed gas increases, the pressure increases, if the volume is constant.

Gay-Lussac’s Law: Pressure and Temperature When a gas is heated at constant volume, the pressure increases. When a gas is heated at constant volume, the pressure increases. Interpreting Diagrams How can you tell from the drawings that there is a fixed amount of gas in the cylinders?

Gay-Lussac’s Law: Pressure and Temperature Gay-Lussac’s law states that the pressure of a gas is directly proportional to the Kelvin temperature if the volume remains constant.

Gay-Lussac’s Law: Pressure and Temperature A pressure cooker demonstrates Gay-Lussac’s Law. In a pressure cooker, food cooks faster than in an ordinary pot with a lid.

Gay-Lussac’s Law: Pressure and Temperature Simulation 17 Examine the relationship between gas pressure and temperature.

The Combined Gas Law The combined gas law allows you to do calculations for situations in which only the amount of gas is constant.

14.2 Section Quiz. 1. If the volume of a gas in a container were reduced to one fifth the original volume at constant temperature, the pressure of the gas in the new volume would be one and one fifth times the original pressure. one fifth of the original pressure. four fifths of the original pressure. five times the original pressure.

14.2 Section Quiz. 2. A balloon appears slightly smaller when it is moved from the mountains to the seashore at constant temperature. The best gas law to explain this observation would be Gay-Lussacs's Law. Graham's Law. Charles's Law. Boyle's Law.

14.2 Section Quiz. 3. At 46°C and 89 kPa pressure, a gas occupies a volume of 0.600 L. How many liters will it occupy at 0°C and 20.8 kPa? 0.600 L 2.58 L 0.140 L 2.20 L

14.3 Section Quiz. 3. An ideal gas differs from a real gas in that the molecules of an ideal gas have no attraction for one another. have a significant volume. have a molar mass of zero. have no kinetic energy.

Dalton’s Law Dalton’s Law How is the total pressure of a mixture of gases related to the partial pressures of the component gases?

Dalton’s Law The contribution each gas in a mixture makes to the total pressure is called the partial pressure exerted by that gas.

Dalton’s Law Gas pressure depends # of gas particles in a given volume Average KE In a mixture of gases, the total pressure is the sum of the partial pressures of the gases.

Dalton’s Law Dalton’s law of partial pressures states that, at constant volume and temperature, the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures of the component gases.

Dalton’s Law Three gases are combined in container T. Three gases are combined in container T. The pressure that each gas exerts is independent of the pressure exerted by the other two gases. The pressure in container T is the sum of the pressures in containers A, B, and C. Interpreting Diagrams What is the relationship between the number of particles in containers A and C and the partial pressures of the gases in A and C?

Molar Volume The number of molecules in 22.4 L of any gas at STP has been chosen as a standard unit called 1 mole 1mole = 6.02 x 1023 particles 1 mole = 22.4 L of any gas STP 22.4 L of any gas at STP contains 6.02x1023 particles

Graham’s Law Graham’s Law How does the molar mass of a gas affect the rate at which the gas effuses or diffuses?

Graham’s Law Diffusion is the tendency of molecules to move toward areas of lower concentration until the concentration is uniform throughout.

Graham’s Law Bromine vapor is diffusing upward through the air in a graduated cylinder. The diffusion of one substance through another is a relatively slow process. a) Bromine vapor is diffusing upward through the air in a graduated cylinder. b) After several hours, bromine vapors are near the top of the cylinder. Predicting What will happen as the bromine continues to diffuse?

Graham’s Law After several hours, the bromine has diffused almost to the top of the cylinder. The diffusion of one substance through another is a relatively slow process. a) Bromine vapor is diffusing upward through the air in a graduated cylinder. b) After several hours, bromine vapors are near the top of the cylinder. Predicting What will happen as the bromine continues to diffuse?

Graham’s Law During effusion, a gas escapes through a tiny hole in its container. Gases of lower molar mass diffuse and effuse faster than gases of higher molar mass.

Graham’s Law Thomas Graham’s Contribution Graham’s law of effusion states that the rate of effusion of a gas is inversely proportional to the square root of the gas’s molar mass. This law can also be applied to the diffusion of gases.

Graham’s Law Comparing Effusion Rates A helium filled balloon will deflate sooner than an air-filled balloon. The character balloons used in parades are filled with helium gas so that they will float.

Graham’s Law Helium atoms are less massive than oxygen or nitrogen molecules. So the molecules in air move more slowly than helium atoms with the same kinetic energy. KE = ½ mv2 25 = ½ 2g (5 m/s)2 25 = ½ (.1g) (v)2

25 = ½ .1 (v)2 V= 22.4 m/s

Graham’s Law Because the rate of effusion is related only to a particle’s speed, Graham’s law can be written as follows for two gases, A and B.

Graham’s Law Helium effuses (and diffuses) nearly three times faster than nitrogen at the same temperature.

Graham’s Law Animation 18 Observe the processes of gas effusion and diffusion.

14.4 Section Quiz. 1. What is the partial pressure of oxygen in a diving tank containing oxygen and helium if the total pressure is 800 kPa and the partial pressure of helium is 600 kPa? 200 kPa 0.75 kPa 1.40 104 kPa 1.33 kPa

14.4 Section Quiz. 2. A mixture of three gases exerts a pressure of 448 kPa, and the gases are present in the mole ratio 1 : 2 : 5. What are the individual gas pressures? 44 kPa, 88 kPa, and 316 kPa 52 kPa, 104 kPa, and 292 kPa 56 kPa, 112 kPa, and 280 kPa 84 kPa, 168 kPa, and 196 kPa

14.4 Section Quiz. 3. Choose the correct words for the spaces. Graham's Law says that the rate of diffusion of a gas is __________ proportional to the square root of its _________ mass. directly, atomic inversely, atomic inversely, molar directly, molar

Concept Map 14 Concept Map 14 Solve the Concept Map with the help of an interactive guided tutorial.