Gases Two More Laws Chapter 14

Dalton’s Law b The total pressure of a mixture of gases equals the sum of the partial pressures of the individual gases. P total = P 1 + P When a H 2 gas is collected by water displacement, the gas in the collection bottle is actually a mixture of H 2 and water vapor.

GIVEN: P total = ? P O2 = 20.0 kPa P N2 = 46.7 kPa P He = 26.7 kPa WORK: P total = P o2 + P N2 + P He P total = P total = 93.4 kPa Dalton’s Law b Determine the total pressure of a gas mixture that contains O 2, N 2, and He if the partial pressures of the gases are as listed below.

GIVEN: P gas = ? P total = torr P H2O = 42.2 torr WORK: P total = P gas + P H2O torr = P H torr P gas = torr b A gas is collected over water at a temp of 35.0°C when the barometric pressure is torr. What is the partial pressure of the dry gas? Given: water-vapor pressure for 35.0°C. Dalton’s Law The total pressure in the collection bottle is equal to barometric pressure and is a mixture of the “gas” and water vapor.

Graham’s Law b Diffusion Spreading of gas molecules throughout a container until evenly distributed. b Effusion Passing of gas molecules through a tiny opening in a container

Graham’s Law KE = ½mv 2 b Speed of diffusion/effusion Kinetic energy is determined by the temperature of the gas. At the same temp & KE, heavier molecules move more slowly.  Larger m  smaller v

Graham’s Law b Graham’s Law Rate of diffusion of a gas is inversely related to the square root of its molar mass. The equation shows the ratio of Gas A’s speed to Gas B’s speed.

b Determine the relative rate of diffusion for krypton and bromine. Kr diffuses times faster than Br 2. Graham’s Law The first gas is “Gas A” and the second gas is “Gas B”. Relative rate means find the ratio “v A /v B ”.

b A molecule of oxygen gas has an average speed of 12.3 m/s at a given temp and pressure. What is the average speed of hydrogen molecules at the same conditions? Graham’s Law Put the gas with the unknown speed as “Gas A”.

b An unknown gas diffuses 4.0 times faster than O 2. Find its molar mass. Graham’s Law The first gas is “Gas A” and the second gas is “Gas B”. The ratio “v A /v B ” is 4.0. Square both sides to get rid of the square root sign.

Questions!Questions! 1) How is the partial pressure of a gas in a mixture calculated? How is the rate of effusion of a gas calculated?

Questions!Questions! 2) At the same temperature, the rates of diffusion of carbon monoxide and nitrogen gas are virtually identical. Explain.

CalculationsCalculations 3) Determine the relative rate of diffusion for helium atoms to fluorine molecules at the same temperature.

Calculations!Calculations! 4) Carbon dioxide molecules have an average speed of 25.0 m/s at a given temperature and pressure. What is the average speed of carbon monoxide molecules at the same conditions?

Calculations!Calculations! 5) Argon is collected over water at 30  C. Find the pressure of the dry gas if the barometric pressure is atm. Water-vapor pressure for 30  C is atm.