Question
Derive the relation between density, molar mass and pressure.
✓
Answer
Relation between density, molar mass and pressure:
According to ideal gas equation,
$PV = nRT....(1)$
On rearranging equation $(1)$,
we get$\frac{ n }{ V }=\frac{ P }{ RT}......(2)$
Now, $n =\frac{ m }{ M }$
On substituting the value of $n$, equation $(2)$ becomes
$\frac{ m }{ MV }=\frac{ P }{ RT}$
$\frac{ d }{ M }=\frac{ P }{ RT }.......(3)$
where $d=\frac{m}{V}=$ density of the gas
On rearranging the equation, we get
$M=\frac{ dRT }{ P }........(4)$
This equation can be used to calculate molar mass of a gas in terms of its density.
According to ideal gas equation,
$PV = nRT....(1)$
On rearranging equation $(1)$,
we get$\frac{ n }{ V }=\frac{ P }{ RT}......(2)$
Now, $n =\frac{ m }{ M }$
On substituting the value of $n$, equation $(2)$ becomes
$\frac{ m }{ MV }=\frac{ P }{ RT}$
$\frac{ d }{ M }=\frac{ P }{ RT }.......(3)$
where $d=\frac{m}{V}=$ density of the gas
On rearranging the equation, we get
$M=\frac{ dRT }{ P }........(4)$
This equation can be used to calculate molar mass of a gas in terms of its density.
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