Applications of the Ideal Gas Law

Density, Molar Mass, Molar Volume Molar volumeDensityMolar mass UnitL/molg/Lg/mol Meaning Volume/amountMass/volumeMass/amount Calculations MV = V/nD= m/VM = m/n

1. Finding the density of a gas Example: Nitrogen gas makes up almost 80% of our atmosphere. What is the density of pure nitrogen gas, in g/L, at 12.50°C and kPa?

Step 1: Convert temperature to K T = (12.50°C ) = K Step 2: Calculate the molar mass of Nitrogen gas, N 2 M = g/mol x 2 = g/mol Step 3: Since the volume is not given, set it as 1.00 L PV = nRT n = (126.63)(1.00L) (285.65) = X mol

Step 4: Convert moles to mass. m = nM = X mol (28.02 g/mol) = g Step 5: Find the density. D = m/V = g/1.00 L = g/L

2. Using Molar Mass to Identify an Unknown Gas Example: A Scientist isolates g of a gas. The sample occupies a volume of 800 mL at 78.0°C and 103 kPa. Calculate the molar mass of the gas. Is the gas most likely to be bromine, krypton, neon or fluorine?

Step 1: What is given? P = 103 kPa m = g V = 800 mL R = = L T = 78.0°C = = 351 K Step 2 Use the ideal gas law to solve for n PV = nRT n = (103)(0.800L) (351K) = mol

Step 3. Solve for M using mass and moles M = m n = g mol = 83.9 g/mol

To identify the gas, compare the molar masses of the four gases mentioned. Bromine = 2 x 79.9 g/mol = g/mol Krypton = 83.8 g/mol Neon = 20.2 g/mol Fluorine = 2 x 18.9 g/mol = 38.0 g/mol Therefore, the gas must be krypton

3. Calculating the volume of a gas collected over water Example: A student reacts magnesium with excess dilute hydrochloric acid to produce hydrogen gas.What volume of dry hydrogen does she collect over water at 28°C and kPa

Step 1: Use Dalton’s Law of Partial Pressures. P total = P H + P water vapour = P H P H = 98.0 kPa Temperature °C Pressure (kPa)