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