Density, Dalton Avogadro & Graham

Density of Gas The density of a gas varies widely depending on temperature and pressure Remains the same D = m/v

Hints to Density problems Write down everything known and unknown in the problem Before you find D you must find V2 If D is given, immediately find mass to volume ratio

Dalton’s Law PTotal = P1 + P2 + P3 . . . and In a rigid container (same volume) where a mixture of different gases is present, the total pressure of the mixture is equal to the sum of the pressures for each of the gases PTotal = P1 + P2 + P3 . . . and

Number of moles is proportional to pressure… Number of moles is proportional to pressure…. if they are in the same system. 2 mol of a gas exerts twice as much pressure as 1 mol

Practice In a fixed container, 3 mol of CO2 and 2 mol of O2 exist at a temp of 298K and a pressure of 45kPa. What is the partial pressure exerted by the oxygen?

Answer 3 mol CO2 + 2mol O2 = 5 mol of gas 5 mol gas = total pressure 45kPa If 5x = 45 then X = 9 Then 2 mol O2 = 18kPa And 3 mol CO2 = 27kPa

Avogadro’s Law Equal volumes of gases under the same conditions of temperature and pressure contain the same number of molecules.

CO2 and CH4 are in separate containers. CO2 occupies a volume of 3 CO2 and CH4 are in separate containers. CO2 occupies a volume of 3.5L at 298K and 105kPa. CH4 (methane) occupies a volume of 3.2L at 273K and 120kPa. Which container contains more gas molecules?

CO2 V1 = 3.5L T1 = 298K P1 = 105kPa T2 = 273K P2 = 120kPa Set the second temperature and pressure the same as the CH4. Use combined gas law to calculate V2 of CO2 The greater volume has more molecules. V2 of CO2 = 2.81L so CH4 has more molecules CH4 V= 3.2L T = 273K P = 120kPa

Another way to solve the problem . . . Use the ideal gas law to determine the number of moles for each. Greater number of moles = greater number of molecules. PV = nRT for carbon dioxide (105kPa)(3.5L) = n(0.0821)(298) n= 15.02 mol PV = nRT for methane (120kPa)(3.2L) = n(0.0821)(273) n= 17.13 mol

Graham’s Law Molecules of higher molecular mass undergo diffusion & effusion more slowly as compared to molecules of lower molecular mass.

Diffusion Movement of particles from an area of high concentration to low concentration until the concentration is uniform Effusion Escape of a gas through pores of its container

Graham’s Equation Suppose you have two balloons, one filled with helium and one balloon filled with CO2. Which will deflate faster? How much faster will it deflate?

The End