Chapter 14 Gas Laws

Standards Students know how to apply the gas laws to relations between the pressure, temperature, and volume of any amount of an ideal gas or any mixture of ideal gases.

Dalton’s Law of Partial Pressures For a mixture of gases in a container, PTotal = P1 + P2 + P3 + . . . This is particularly useful in calculating the pressure of gases collected over water.

Dalton’s Law of Partial Pressure The total pressure in a container is the sum of the pressure each gas would exert if it were alone in the container. The total pressure is the sum of the partial pressures. PTotal = P1 + P2 + P3 + P4 + P5 ... For each P = nRT/V

Dalton’s Law Continued In the same container R, T and V are the same. PTotal = n1RT + n2RT + n3RT +... V V V

The Mole Fraction Ratio of moles of the substance to the total moles. symbol is Greek letter chi c c1 = n1 = P1 nTotal PTotal

Examples The partial pressure of nitrogen in air is 592 torr. Air pressure is 752 torr, what is the mole fraction of nitrogen? What is the partial pressure of nitrogen if the container holding the air is compressed to 5.25 atm? .

Gas Density and Molar Mass D = m/V Let M stand for molar mass M = m/n n= PV/RT M = m PV/RT M = mRT = m RT = DRT PV V P P PTotal = (n1+ n2 + n3+...)RT V PTotal = (nTotal)RT V

Examples What is the density of ammonia at 23ºC and 735 torr? A compound has the empirical formula CHCl. A 256 mL flask at 100.ºC and 750 torr contains .80 g of the gaseous compound. What is the molecular formula? .

Boyle’s Law Pressure is inversely proportional to volume when temperature is held constant.

Examples 1. 20.5 L of nitrogen at 25ºC and 742 torr are compressed to 9.8 atm at constant T. What is the new volume? 2. 30.6 mL of carbon dioxide at 740 torr is expanded at constant temperature to 750 mL. What is the final pressure in kPa?

A Graph of Boyle’s Law

Charles’s Law The volume of a gas is directly proportional to temperature, and extrapolates to zero at zero Kelvin. (P = constant) Temperature MUST be in KELVINS!

Examples 1.What would the final volume be if 247 mL of gas at 22ºC is heated to 98ºC , if the pressure is held constant? 2. At what temperature would 40.5 L of gas at 23.4ºC have a volume of 81.0 L at constant pressure?

A Graph of Charles’ Law

Gay Lussac’s Law The pressure and temperature of a gas are directly related, provided that the volume remains constant. Temperature MUST be in KELVINS!

Examples A sample of nitrogen gas has a pressure of 6.58 kPa at 539 K. If the volume does not change, what will the pressure be at 211 K ? The pressure in a car tire is 198 kPa at 27°C. After a long drive, the pressure is 225 kPa. What is the temperature of the air in the tire? Assume that the volume is constant.

A Graph of Gay-Lussac’s Law

The Combined Gas Law The combined gas law expresses the relationship between pressure, volume and temperature of a fixed amount of gas.

Examples A deodorant can has a volume of 175 mL and a pressure of 3.8 atm at 22ºC. What volume of gas could the can release at 22ºC and 743 torr?

No kinetic energy is lost in elastic collisions Ideal Gases Ideal gases are imaginary gases that perfectly fit all of the assumptions of the kinetic molecular theory. Gases consist of tiny particles that are far apart relative to their size. Collisions between gas particles and between particles and the walls of the container are elastic collisions No kinetic energy is lost in elastic collisions

Ideal Gases (continued) Gas particles are in constant, rapid motion. They therefore possess kinetic energy, the energy of motion There are no forces of attraction between gas particles The average kinetic energy of gas particles depends on temperature, not on the identity of the particle.

Real Gases Do Not Behave Ideally Real gases DO experience inter-molecular attractions Real gases DO have volume Real gases DO NOT have elastic collisions

Deviations from Ideal Behavior Likely to behave nearly ideally Gases at high temperature and low pressure Small non-polar gas molecules Likely not to behave ideally Gases at low temperature and high pressure Large, polar gas molecules

IDEAL GAS LAW PV = nRT P = pressure in atm, kPa, mm Hg  n = number of moles  V = volume in Liters  R is the ideal gas constant; depends on the pressure unit  R = 0.0821 Latm/ Kmol or R = 8.314 LkPa/ Kmol or R = 62.36 LmmHg/ Kmol

Examples 1.A 47.3 L container containing 1.62 mol of He is heated until the pressure reaches 1.85 atm. What is the temperature? 2.Kr gas in a 18.5 L cylinder exerts a pressure of 8.61 atm at 24.8ºC What is the mass of Kr? 3.A sample of gas has a volume of 4.18 L at 29ºC and 732 torr. What would its volume be at 24.8ºC and 756 torr?

Diffusion Diffusion describes the mixing of gases. The rate of diffusion is the rate of gas mixing. Diffusion is the result of random movement of gas molecules The rate of diffusion increases with temperature Small molecules diffuse faster than large molecules

Graham’s Law of Diffusion M1 = Molar Mass of gas 1 M2 = Molar Mass of gas 2

Examples Which gas effuses faster: hydrogen or chlorine, and by what factor? 2. Calculate the ratio of the velocity of helium atoms to fluorine molecules at the same temperature.