# Problem: The density of a gas is 1.42 g/L at a temperature of 23 oC and a pressure of 0.786 atm . Calculate the molar mass of the gas.

###### FREE Expert Solution

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

$\mathbit{P}\mathbf{=}\frac{{\mathbf{m}}\mathbf{R}\mathbf{T}}{\mathbf{M}{\mathbf{V}}}$

$\frac{\mathbf{m}}{\mathbf{V}}{\mathbf{=}}\frac{\mathbf{g}}{\mathbf{L}}{\mathbf{=}}{\mathbit{d}}{\mathbit{e}}{\mathbit{n}}{\mathbit{s}}{\mathbit{i}}{\mathbit{t}}{\mathbit{y}}\left(\mathbf{d}\right)$

$\mathbit{P}\left(\mathbf{M}\right)\mathbf{=}\frac{{\mathbf{d}}\mathbf{R}\mathbf{T}}{\overline{)\mathbf{M}}}\left(\overline{)\mathbf{M}}\right)\phantom{\rule{0ex}{0ex}}\frac{\mathbf{P}\mathbf{M}}{\mathbf{R}\mathbf{T}}\mathbf{=}\frac{\mathbf{d}\overline{)\mathbf{R}\mathbf{T}}}{\overline{)\mathbf{R}\mathbf{T}}}\phantom{\rule{0ex}{0ex}}\overline{){\mathbf{d}}{\mathbf{=}}\frac{\mathbf{P}\mathbf{M}}{\mathbf{R}\mathbf{T}}}$

Calculating the molar mass of the gas:

92% (150 ratings) ###### Problem Details

The density of a gas is 1.42 g/L at a temperature of 23 oC and a pressure of 0.786 atm . Calculate the molar mass of the gas.