What is the pressure, in atm, of a sample of CH_4 gas (6.022 g) contained in a 30.0 L vessel at 402 K? (R = 0.0821 L·atm·mol^{-1}·K^{-1})

• A. 0.164 atm
• B. 0.0412 atm
• C. 0.0821 atm
• D. 0.041 atm

Answer: (B)

Verified step by step guidance

1. First, calculate the number of moles of CH_4 gas using its molar mass. The molar mass of CH_4 is calculated by adding the atomic masses: Carbon (12.01 g/mol) + 4 × Hydrogen (1.008 g/mol). Then, use the formula: \(n = \frac{\text{mass}}{\text{molar mass}}\).
2. Next, write down the Ideal Gas Law equation: \(P V = n R T\), where \(P\) is pressure, \(V\) is volume, \(n\) is moles, \(R\) is the gas constant, and \(T\) is temperature in Kelvin.
3. Rearrange the Ideal Gas Law to solve for pressure \(P\): \(P = \frac{n R T}{V}\).
4. Substitute the known values into the equation: number of moles \(n\) from step 1, gas constant \(R = 0.0821\ \text{L} \cdot \text{atm} \cdot \text{mol}^{-1} \cdot \text{K}^{-1}\), temperature \(T = 402\ \text{K}\), and volume \(V = 30.0\ \text{L}\).
5. Finally, perform the calculation to find the pressure \(P\) in atm.