Question

A sample of gas has a mass of 38.7 mg. Its volume is 220 mL at a temperature of 54 ∘C and a pressure of 897 torr. Find the molar mass of the gas. Express your answer in grams per mole to three significant figures. 

Answer 1

m=38.7 mg=$38.7 \times 10^{-3} \;g$

V=220 mL= 0.22 L

T = 54 + 273 = 327 K

p = 897 torr = 1.18 atm

Ideal Gas Law

pV = nRT

R= 0.08206 L×atm/mol×K

$n= \frac{pV}{RT} \\ = \frac{1.18 \times 0.22}{0.08206 \times 327} \\ = 0.00967 \;mol$

Molar mass $= \frac{m}{n}= \frac{38.7 \times 10^{-3}}{0.00967}=4.00 \;g/mol$

Answer: 4.00 g/mol