Question

an unknown gas occupies a volume of 1250 ml at 26 °c and 705 torr. if the mass is 2.37 g, what is the molar mass of the gas? (r = 0.0821 atm·l/mol·k)

50.2 g/mol

67.5 g/mol

78.4 g/mol

14.0 g/mol

43.2 g/mol

Explanation:

Step1: Convert units

Convert volume from mL to L: \( V = 1250\space mL = 1.25\space L \)
Convert temperature from \( ^\circ C \) to K: \( T = 26 + 273.15 = 299.15\space K \)
Convert pressure from torr to atm: \( P = 705\space torr \times \frac{1\space atm}{760\space torr} \approx 0.9276\space atm \)

Step2: Use ideal gas law \( PV = nRT \) to find moles \( n \)

Rearrange the formula: \( n = \frac{PV}{RT} \)
Substitute values: \( n = \frac{0.9276\space atm \times 1.25\space L}{0.0821\space atm\cdot L/mol\cdot K \times 299.15\space K} \)
Calculate denominator: \( 0.0821 \times 299.15 \approx 24.56 \)
Calculate numerator: \( 0.9276 \times 1.25 \approx 1.1595 \)
So, \( n \approx \frac{1.1595}{24.56} \approx 0.0472\space mol \)

Step3: Calculate molar mass \( M \)

Molar mass \( M = \frac{mass}{moles} = \frac{2.37\space g}{0.0472\space mol} \approx 50.2\space g/mol \)

Answer:

50.2 g/mol