Questions: A gas sample contains 4.0 g of CH4 and 2.0 g of He. What is the volume of the sample at STP?

Transcript text: A gas sample contains 4.0 g of $\mathrm{CH}_{4}$ and 2.0 g of He. What is the volume of the sample at STP?

Solution

Solution Steps

Step 1: Determine the number of moles of each gas

First, we need to calculate the number of moles of each gas in the sample.

For methane ($\mathrm{CH}_4$):

Molar mass of $\mathrm{CH}_4$ is $12.01 + 4 \times 1.01 = 16.05 \, \text{g/mol}$.
Number of moles of $\mathrm{CH}_4$ is $\frac{4.0 \, \text{g}}{16.05 \, \text{g/mol}} = 0.2492 \, \text{mol}$.

For helium ($\mathrm{He}$):

Molar mass of $\mathrm{He}$ is $4.00 \, \text{g/mol}$.
Number of moles of $\mathrm{He}$ is $\frac{2.0 \, \text{g}}{4.00 \, \text{g/mol}} = 0.5000 \, \text{mol}$.

Step 2: Calculate the total number of moles

Add the moles of $\mathrm{CH}_4$ and $\mathrm{He}$ to find the total number of moles in the gas sample:

\[ \text{Total moles} = 0.2492 \, \text{mol} + 0.5000 \, \text{mol} = 0.7492 \, \text{mol} \]

Step 3: Calculate the volume at STP

At standard temperature and pressure (STP), 1 mole of an ideal gas occupies 22.4 liters. Therefore, the volume of the gas sample can be calculated as follows:

\[ \text{Volume} = 0.7492 \, \text{mol} \times 22.4 \, \text{L/mol} = 16.78 \, \text{L} \]