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Using the equation of state, \(\mathrm{PV}=\mathrm{n} \mathrm{RT}\), show that at a given temperature, density of a gas is proportional to gas pressure, \(P\).
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Using PV \(=\mathrm{nRT}\)
\(\begin{aligned}
&\text { PV }=\frac{\text { wRT }}{M}, \text { where } n=\text { No. of moles }=\frac{\text { weight }(w)}{\text { Mol.Mass }(M)} \\
&\therefore P=\frac{w R T}{V M}
\end{aligned}\)
\(\mathrm{P}=\mathrm{d} \frac{\mathrm{RT}}{\mathrm{M}}\), where density \(\mathrm{d}=\) weight \(/\) Volume
or \(\mathrm{d}=\frac{\mathrm{MP}}{\mathrm{RT}}\)
Thus, for a given temperature ( \(M\) and \(R\) are constant) , the density of gas is proportional to gas pressure i.e. \(d \propto P\).
\(\begin{aligned}
&\text { PV }=\frac{\text { wRT }}{M}, \text { where } n=\text { No. of moles }=\frac{\text { weight }(w)}{\text { Mol.Mass }(M)} \\
&\therefore P=\frac{w R T}{V M}
\end{aligned}\)
\(\mathrm{P}=\mathrm{d} \frac{\mathrm{RT}}{\mathrm{M}}\), where density \(\mathrm{d}=\) weight \(/\) Volume
or \(\mathrm{d}=\frac{\mathrm{MP}}{\mathrm{RT}}\)
Thus, for a given temperature ( \(M\) and \(R\) are constant) , the density of gas is proportional to gas pressure i.e. \(d \propto P\).
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