First slide

laws

Question

A given sample of an ideal gas occupies a volume V at a pressure p and absolute temperature T. The mass of each molecule of the gas is m. Which of the following gives the density of the gas?

Easy

A

$\frac{p}{K T}$
B

$\frac{p m}{K T}$
C

$\frac{p}{K T V}$
D

mkT

Solution

We know that, $p V = R T \Rightarrow V = \frac{R T}{p}$ …(i)
$∴$ Density, $ρ = \frac{M}{V} = \frac{m N_{A}}{\frac{R T}{p}}$ [From Eq. (i)]
$= \frac{m p N_{A}}{k N_{A} T}$ ( $∵$ R = kN_A)
$\Rightarrow$ $ρ = \frac{p m}{k T}$

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