Question

What is the total number of moles of gas in a 5 L container at 300 K and 2 atm pressure (Use the ideal gas law)?

• A. 0.4 mol
• B. 0.6 mol
• C. 1.0 mol
• D. 2.0 mol

Hint:

Remember: The ideal gas law is a useful tool for relating pressure, volume, temperature, and moles of gas. Ensure that units are consistent with the gas constant used.

Answer 1

The Correct Option is A

Step 1: Use the ideal gas law The ideal gas law is: \[ PV = nRT \] where: - \( P \) is the pressure (in atm), - \( V \) is the volume (in liters), - \( n \) is the number of moles of gas, - \( R \) is the ideal gas constant (\( 0.0821 \, \text{L} \cdot \text{atm} / \text{mol} \cdot \text{K} \)), - \( T \) is the temperature (in Kelvin). Step 2: Substitute the given values Given: - Pressure \( P = 2 \, \text{atm} \), - Volume \( V = 5 \, \text{L} \), - Temperature \( T = 300 \, \text{K} \), - \( R = 0.0821 \, \text{L} \cdot \text{atm} / \text{mol} \cdot \text{K} \). Now, solve for \( n \): \[ n = \frac{PV}{RT} \] Substitute the known values: \[ n = \frac{(2 \, \text{atm}) \times (5 \, \text{L})}{(0.0821 \, \text{L} \cdot \text{atm} / \text{mol} \cdot \text{K}) \times (300 \, \text{K})} \] \[ n = \frac{10}{24.63} = 0.406 \, \text{mol} \] Answer: Therefore, the total number of moles of gas in the container is approximately \( 0.4 \, \text{mol} \). So, the correct answer is option (1).