Question
Derive the relation between density of a gas and its molar mass.
✓
Answer
Relation between density of a gas and its molar mass:
According to Avogadro's law, $V \propto n$
Now, $n =\frac{ m }{ M } ($where, $m$ is the mass of the gas and $M$ is the molar mass of the gas$)$
$\therefore V \propto \frac{ m }{ M }$
$M \propto \frac{ m }{ V }$
But, $\frac{ m }{ V }= d ($where, $d$ is the density of the gas $)$
$\therefore d \propto M$
Thus, density of a gas is directly proportional to its molar mass.
According to Avogadro's law, $V \propto n$
Now, $n =\frac{ m }{ M } ($where, $m$ is the mass of the gas and $M$ is the molar mass of the gas$)$
$\therefore V \propto \frac{ m }{ M }$
$M \propto \frac{ m }{ V }$
But, $\frac{ m }{ V }= d ($where, $d$ is the density of the gas $)$
$\therefore d \propto M$
Thus, density of a gas is directly proportional to its molar mass.
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