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

Question

The density of air at N.T.P. is 1.293 gm/lit. If the pressure is tripled keeping its temperature constant its density becomes (A) 3.87 gm/Itr (B) 1.293 gm/Itr (C) 2.586 gm/Itr (D) 0.431 gm/Itr

Tardigrade Admin · Accepted Answer

First we derive an expression for density of a gas.
Density

= \frac{mass ( w )}{volume ( V )}

but we know that PV = nRT
now

n = \frac{w}{M}

where

M

is molecular weight
So,

P V = \frac{w}{M} RT

this gives

\frac{w}{V} = \frac{PM}{RT} =

density

= d

Clearly at a constant temperature,

< b r / > \frac{d _{1}}{P _{1}} = \frac{d _{2}}{P _{2}} < b r / >

so since pressure is tripled, density also triples new density

=

old density

x_{3}

= 1.293 \times 3

= 3.87 g m / lt r

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

3.87 gm/Itr

1.293 gm/Itr

2.586 gm/Itr

0.431 gm/Itr