# Problem: The mass of a sample of gas is 827 mg. Its volume is 0.270 L at a temperature of 88°C and a pressure of 975 mmHg. Find its molar mass.

###### FREE Expert Solution

Molar mass:

First, we have to calculate the amount of gas in moles using the ideal gas equation.

$\overline{){\mathbf{P}}{\mathbf{V}}{\mathbf{=}}{\mathbf{n}}{\mathbf{R}}{\mathbf{T}}}$

P = pressure, atm
V = volume, L
n = moles, mol
R = gas constant = 0.08206 (L·atm)/(mol·K)
T = temperature, K

Isolate n (number of moles of gas):

$\frac{\mathbf{P}\mathbf{V}}{\mathbf{R}\mathbf{T}}\mathbf{=}\frac{\mathbf{n}\overline{)\mathbf{R}\mathbf{T}}}{\overline{)\mathbf{R}\mathbf{T}}}\phantom{\rule{0ex}{0ex}}\overline{){\mathbf{n}}{\mathbf{=}}\frac{\mathbf{P}\mathbf{V}}{\mathbf{R}\mathbf{T}}}$

Given:

P = 1.2829 atm

V = 0.270 L
T = 88°C + 273.15 = 361.15 K
R = 0.08206 (L·atm)/(mol·K)

Calculate for n: ###### Problem Details

The mass of a sample of gas is 827 mg. Its volume is 0.270 L at a temperature of 88°C and a pressure of 975 mmHg. Find its molar mass.