Molar Mass (M) and Density (d) of Gases

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Presentation transcript:

Molar Mass (M) and Density (d) of Gases PV = nRT Density of CO2: 44.0 g/mol 22.4 L/mol = 1.96 g/L

Which gas would be the most dense? N2, CO2, He, or O2 x g/mol 22.4 L/mol d =

PV = nRT P n = RT V MP nM = RT V = d How Molar Mass (M) and Density (d) are Related: PV = nRT P n RT V = MP nM RT V = = d Hint: always use PV = nRT first and watch your units!

Practice An experiment shows that a 0.495 g sample of an unknown gas occupies 127 mL at 98°C and 754 torr pressure. Calculate the molar mass of the gas.

Solution (PV = nRT)

Another Example PV = nRT The density of a gas containing chlorine and oxygen has a density of 2.875 g/L at 756 mmHg and 11oC. What is the most likely formula of the gas? 756 mmHg = 0.995 atm 11oC = 284 K 2.875 g/L = 67.3g/mol 0.0427mol/L PV = nRT (0.995atm) (V) = n (0.08206L.atm/mol.K) (284K) (0.995atm) n = = 0.0427mol/L (0.08206L.atm/mol.K) (284K) (V)

Dalton’s Law Gas identity is not important Mixture of gases obeys ideal gas law Dependent only on total number of moles Ptot = P1 + P2 + P3 + …

Dalton’s Law of Partial Pressures For a mixture of gases in a container PTotal = P1 + P2 + P3 + …

Mole Fraction Percentage of moles in a mixture Xi = ni / ntot Pi = XiPtot (partial pressure = mole fraction x total pressure)

Mole Fraction and Partial Pressure C1 = P1 = P1 P1 + P2 + P3 + … PTOTAL C1 = n1 = P1 nTOTAL PTOTAL

Mole Fraction Example At 25°C, a 1.0 L flask contains 0.030 moles of nitrogen, 150.0 mg of oxygen, and 4 x 1021 molecules of ammonia. What is the partial pressure of each gas? What is the total pressure in the flask? What is the mole fraction of each?

Partial Pressures

Total Pressure

Mole Fractions

Mole Fractions

Practice A sample of KClO3 is heated and decomposes to produce O2 gas. The gas is collected by water displacement at 25°C. The total volume of the collected gas is 229 mL at a pressure of 754 torr. How many moles of oxygen formed? Hint: The gas collected is a mixture so use Dalton’s Law to calculate the pressure of oxygen then the ideal gas law to find the number of moles oxygen. PT = PO2 + PH2O

Solution