1. Applications of the Ideal Gas Law

2. 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

3. 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 126.63 kPa?

4. Step 1: Convert temperature to K T = (12.50°C + 273.15) = 285.65K Step 2: Calculate the molar mass of Nitrogen gas, N 2 M = 14.01 g/mol x 2 = 28.02 g/mol Step 3: Since the volume is not given, set it as 1.00 L PV = nRT n = (126.63)(1.00L) 8.314 (285.65) = 5.3320 X 10 -2 mol

5. Step 4: Convert moles to mass. m = nM = 5.3320 X 10 -2 mol (28.02 g/mol) = 1.4940 g Step 5: Find the density. D = m/V = 1.4940 g/1.00 L = 1.494 g/L

6. 2. Using Molar Mass to Identify an Unknown Gas Example: A Scientist isolates 2.366 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?

7. Step 1: What is given? P = 103 kPa m = 2.366 g V = 800 mL R = 8.314 = 0.800 L T = 78.0°C = 78 + 273 = 351 K Step 2 Use the ideal gas law to solve for n PV = nRT n = (103)(0.800L) 8.314 (351K) = 0.0282 mol

8. Step 3. Solve for M using mass and moles M = m n = 2.366 g 0.0282 mol = 83.9 g/mol

9. To identify the gas, compare the molar masses of the four gases mentioned. Bromine = 2 x 79.9 g/mol = 141.8 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

10. 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 101.8 kPa

11. Step 1: Use Dalton’s Law of Partial Pressures. P total = P H + P water vapour 101.8 = P H + 3.78 P H = 98.0 kPa Temperature °C Pressure (kPa) 192.20 202.34 212.49 222.64 232.81 242.98 253.17 263.36 273.56 283.78