Gases Chapter 5

Things to know about gases Have no specific volume-volume of the gas is the volume of the container Temperature must be in Kelvin Barometers measure atmospheric pressure 760 mm Hg 1 atm 101.3 kPa STP

Charles’ Law Volume is directly proportional to absolute temperature

Boyle’s Law Volume is inversely proportional to pressure P1V1 = P2V2 http://www.grc.nasa.gov/WWW/K-12/airplane/Animation/frglab2.html

Gay-Lussac’s Law Pressure is directly proportional to absolute temperature

Ideal Gas Law P = pressure (atm) V = volume (L) n = moles R = 0.0821 T =temperature (K) PV = nRT

What is the pressure exerted by 15. 0 mol of O2 in a 50 What is the pressure exerted by 15.0 mol of O2 in a 50.0 L tank at 50 C?

GMM = molar mass d = density = mass/volume (g/L) R = 0.0821 T = temperature (K)

Determine the density of O2 at 27 C and 735 mm Hg

Density of a gas Compressing a gas increases its density Increasing temperature decreases density--hot air rises Hydrogen is the least dense gas of all because it has the lowest GMM--greatest lifting power

A flask weighs 52. 693 g empty and 53 A flask weighs 52.693 g empty and 53.117 g when filled with acetone vapor at 100 C and 752 mm Hg. Taking the volume of the flask to be 226.2 mL calculate the molar mass of acetone.

Gases in reactions First law of Gases. . .Gas Laws only work for Gases!

Determine the mass of zinc metal required to react with HCl to form 16 Determine the mass of zinc metal required to react with HCl to form 16.0 L H2 (g) at 20 C and 735 mm Hg

Dalton’s Law of Partial Pressures The total pressure of a gas mixture is the sum of partial pressures of the components of the mixture. Ptotal = P1 + P2 +. . . Used when gases are collected over water Pgas =Ptotal - Pwater vapor Pwater vapor is the vapor pressure of water at the specified temperature.

A student prepares a sample of hydrogen gas by electrolyzing water at 25 C. She collects 152 ml of hydrogen over water at a pressure of 758 mm Hg, calculate the moles of hydrogen collected. Look up the vapor pressure of water at 25 C from appendix 1. Pwater = 23.76 mm Hg. 758 mm Hg – 23.76 mmHg = 734 mm Hg

Now solve for moles of hydrogen with the ideal gas law.

Partial pressure and mole fractions Mole fraction = X Xa = na/ntotal Partial pressure of a gas in a mixture is equal to its mole fraction multiplied by the total pressure Pa = XaPtotal

Find the partial pressure of oxygen in air when the barometric pressure is 734 mm Hg and the mole fraction of oxygen is 0.2095.

Kinetic theory of Gases Gases are mostly empty space Gas molecules are in constant random motion They collide with each other and the sides of the container Collisions are elastic Gas pressure is caused by the collisions with the walls of the container Increase P increases the number of collisions

Expression for pressure The ratio N/V is the concentration of gas mc in the container. The more mc, the more collisions, the more P. mu2 is the measure of the energy of the collisions.

Average kinetic energy of translational motion Et At a given T molecules of different gases must all have the same Et Et of a molecule is directly proportional to the T in Kelvin T is the only variable! R = 0.0821 NA = 6.022 X 1023

Average speed, u

Constant GMM aka the same gas

At constant temperature

Graham’s Law Effusion The flow of gas molecules at low pressures through tiny pores or pinholes. At a given temperature the rate of effusion of a gas is inversely proportional to the square root of its molar mass

What does this mean? A lighter gas will have a faster rate. Can be used to separate isotopes

Real gases The closer a gas is to the liquid state (high P low T) the more it will deviate from the ideal gas law because Of the attractive forces between gas molecules Gives a smaller molar volume (<22.4 L/mol) than predicted The larger the attractive forces the bigger the deviation The finite volume of gas particles Gives a larger molar volume (>22.4 L/mol) predicted because gases can only get so close