Question

a sample of nitrogen gas kept in a container of volume 2.52 l and at a temperature of 29. °c exerts a pressure of 4.95 atm. calculate the number of moles of gas present. round your answer to 3 significant digits. note: reference the fundamental constants table for additional information.

Explanation:

Step1: List given values and ideal gas law

Given: \( P=4.95\ \text{atm} \), \( V=2.52\ \text{L} \), \( T=29^\circ\text{C}=302.15\ \text{K} \), \( R=0.0821\ \frac{\text{L·atm}}{\text{mol·K}} \).
Ideal gas law: \( PV=nRT \Rightarrow n=\frac{PV}{RT} \).

Step2: Substitute values into formula

\( n=\frac{4.95 \times 2.52}{0.0821 \times 302.15} \).

Step3: Calculate numerator and denominator

Numerator: \( 4.95 \times 2.52 = 12.474 \).
Denominator: \( 0.0821 \times 302.15 \approx 24.806 \).

Step4: Compute moles and round

\( n \approx \frac{12.474}{24.806} \approx 0.503 \).

Answer:

0.503