Question

what is the approximate volume of a gas in a 1.5 mol sample that exerts a pressure of 0.922 atm and has a temperature of 10.0°c? hint (pv=nrt) r=0.0821 (k = °c + 273.15)

Explanation:

Step1: Convert temperature to Kelvin

Given temperature \( T = 10.0^\circ\text{C} \), convert to Kelvin using \( K = ^\circ\text{C} + 273.15 \). So \( T = 10.0 + 273.15 = 283.15\,\text{K} \).

Step2: Use ideal gas law \( PV = nRT \) to find volume \( V \)

Rearrange the formula to \( V=\frac{nRT}{P} \). Given \( n = 1.5\,\text{mol} \), \( R = 0.0821\,\text{L·atm/(mol·K)} \), \( T = 283.15\,\text{K} \), \( P = 0.922\,\text{atm} \).
Substitute values: \( V=\frac{1.5\,\text{mol} \times 0.0821\,\text{L·atm/(mol·K)} \times 283.15\,\text{K}}{0.922\,\text{atm}} \)
Calculate numerator: \( 1.5 \times 0.0821 \times 283.15 \approx 1.5 \times 23.24 \approx 34.86 \)
Then \( V=\frac{34.86}{0.922} \approx 37.8\,\text{L} \) (close to 37.88L option)

Answer:

37.88L