Question
Derive the following expression: $M =\frac{ mRT }{ PV }$
✓
Answer
According to ideal gas equation,
$ PV = nRT$
$n =\frac{ PV }{ RT }$
Now, for a known mass $'m '$ of gas having molar mass $'M\ ',$ number of moles $' n\ '$ is given as:
$n =\frac{ m }{ M }$
Therefore, $\frac{m}{M}=\frac{P V}{R T}$
On rearranging the equation, we get $M=\frac{m R T}{P V}$
$ PV = nRT$
$n =\frac{ PV }{ RT }$
Now, for a known mass $'m '$ of gas having molar mass $'M\ ',$ number of moles $' n\ '$ is given as:
$n =\frac{ m }{ M }$
Therefore, $\frac{m}{M}=\frac{P V}{R T}$
On rearranging the equation, we get $M=\frac{m R T}{P V}$
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