Questions: Calculate pressure, volume, moles of gas, or temperature using the ideal gas law (PV = nRT)

Solution Steps

The ideal gas law is given by: \[ PV = nRT \] where:

• \( P \) is the pressure,
• \( V \) is the volume,
• \( n \) is the number of moles of gas,
• \( R \) is the ideal gas constant (\( R = 0.0821 \, \text{L·atm·K}^{-1}\text{·mol}^{-1} \)),
• \( T \) is the temperature in Kelvin.

Let's assume we are given the following values:

• \( P = 2.00 \, \text{atm} \)
• \( V = 10.0 \, \text{L} \)
• \( T = 300 \, \text{K} \)

We need to find the number of moles of gas, \( n \).

Rearrange the ideal gas law to solve for \( n \): \[ n = \frac{PV}{RT} \]

Substitute the given values into the rearranged equation: \[ n = \frac{(2.00 \, \text{atm})(10.0 \, \text{L})}{(0.0821 \, \text{L·atm·K}^{-1}\text{·mol}^{-1})(300 \, \text{K})} \]

Calculate the number of moles of gas: \[ n = \frac{20.0 \, \text{atm·L}}{24.63 \, \text{L·atm·K}^{-1}\text{·mol}^{-1}} \] \[ n = 0.8120 \, \text{mol} \]

Final Answer