Questions: Calculate the volume occupied by 0.627 mol of nitrogen gas at a pressure of 1.06 atm and a temperature of 287 K .

Solution Steps

The Ideal Gas Law is given by the equation: \[ PV = nRT \] where:

• \( P \) is the pressure,
• \( V \) is the volume,
• \( n \) is the number of moles,
• \( R \) is the ideal gas constant,
• \( T \) is the temperature in Kelvin.

From the problem, we have:

• \( n = 0.627 \) mol,
• \( P = 1.06 \) atm,
• \( T = 287 \) K.

The ideal gas constant \( R \) is \( 0.0821 \) L·atm/(mol·K).

Rearrange the equation to solve for \( V \): \[ V = \frac{nRT}{P} \]

Substitute the values into the equation: \[ V = \frac{(0.627 \, \text{mol}) (0.0821 \, \text{L·atm/(mol·K)}) (287 \, \text{K})}{1.06 \, \text{atm}} \]

Perform the calculation: \[ V = \frac{(0.627) (0.0821) (287)}{1.06} \] \[ V = \frac{14.7357}{1.06} \] \[ V \approx 13.9007 \, \text{L} \]

Final Answer