Ideal Gas Law . If 3.3 g of a gas at 40°C and 1.15 atm pressure occupies a volume of 1.0 L, what is the mass of one mole of the gas?
Strategy : This problem is more complicated than previous ones. We are given grams of gas and P, T, and V values and asked to calculate the mass of one mole of the gas (g/mol). We can solve this problem in two steps.
(1) Use the ideal gas law to calculate the number of moles of gas present in the sample. (2) We are given the mass of gas (3.3 grams) and use the ratio grams/mole to determine the mass of one mole of the gas.
Step 1: Use the P, V, and T measurements and the ideal gas law to calculate
the number of moles of gas present in the sample. To use the ideal gas
law, we must first convert 40°C to kelvins: 40 + 273 = 313 K.
n=\frac{PV}{RT} =\frac{PV}{T} \times \frac{1}{R}=\frac{(1.15 \cancel{atm})(1.0\cancel{L})}{313 \cancel{K}} =0.0448 mol
Step 2: Calculate the mass of one mole of the gas by dividing grams by moles.
Mass of one mole = \frac{3.3g}{0.0448 mol} =74 g . mol^{-1}