Question

The number of oxygen molecules in a cylinder of volume $1 \,m ^{3}$ at a temperature of $27^{\circ} C$ and pressure of $13.8 \,Pa$ is: (Boltzmann's constant $k=1.38 \times 10^{-23} J\, K^{-1}$ )

• A. $ 6.23\times 10^{26} $
• B. $ 0.33\times 10^{28} $
• C. $ 3.3\times 10^{21} $
• D. none of these

Answer 1

Answer: (C)

From ideal gas equation $P V=n k T$
$ \Rightarrow n=\frac{P V}{k T}$
Putting $P=13.8 \,P a, V=1 \,m^{3} $
$k=1.38 \times 10^{-23} J \,K^{-1}, $
$T=300\, K$
$ \therefore n=\frac{13.8 \times 1}{1.38 \times 10^{-23} \times 300} n$
$=3.3 \times 10^{21}$