Question

The density of air at N.T.P. is $1.293gm/lit$. If the pressure is tripled keeping its temperature constant its density becomes

• A. $3.87gm/ltr$
• B. $1.293gm/ltr$
• C. $2.586gm/ltr$
• D. $0.431gm/ltr$

Answer 1

The correct option is A $3.87gm/ltr$

First we derive an expression for density of a gas.
Density = $\frac{mass\left(w\right)}{volume\left(V\right)}$
but we know that PV = nRT
now n = $\frac{w}{M}$ where M is molecular weight
So, PV = $\frac{w}{M}RT$
this gives $\frac{w}{V}=\frac{PM}{RT}$ = density = d
Clearly at a constant temperature,
$\frac{d_1}{P_1}=\frac{d_2}{P_2}$
so since pressure is tripled, density also triples
new density = old density x 3
$=1.293\times 3$
$=3.87gm/ltr$