The number of oxygen molecules in a cylinder of volume 1 m 3 at a temperature of 27° C and pressure of 13.8 Pa is: (Boltzmann's constant k=1.38 × 10-23 J K-1 )

Question

The number of oxygen molecules in a cylinder of volume 1 m 3 at a temperature of 27° C and pressure of 13.8 Pa is: (Boltzmann's constant k=1.38 × 10-23 J K-1 ) (A)  6.23× 1026  (B)  0.33× 1028  (C)  3.3× 1021  (D) none of these

Tardigrade Admin · Accepted Answer

From ideal gas equation P V=n k T ⇒ n=(P V/k T) Putting P=13.8 P a, V=1 m3 k=1.38 × 10-23 J K-1, T=300 K ∴ n=(13.8 × 1/1.38 × 10-23 × 300) n =3.3 × 1021

Q. The number of oxygen molecules in a cylinder of volume $1 m^{3}$ at a temperature of $2 7^{\circ} C$ and pressure of $13.8 P a$ is: (Boltzmann's constant $k = 1.38 \times 1 0^{- 23} J K^{- 1}$ )

$6.23 \times 1 0^{26}$

$0.33 \times 1 0^{28}$

$3.3 \times 1 0^{21}$

none of these

From ideal gas equation $P V = nk T$
$\Rightarrow n = \frac{P V}{k T}$
Putting $P = 13.8 P a, V = 1 m^{3}$
$k = 1.38 \times 1 0^{- 23} J K^{- 1},$
$T = 300 K$
$∴ n = \frac{13.8 \times 1}{1.38 \times 1 0 ^{- 23} \times 300} n$
$= 3.3 \times 1 0^{21}$

Q. The number of oxygen molecules in a cylinder of volume 1m3 at a temperature of 27∘C and pressure of 13.8Pa is: (Boltzmann's constant k=1.38×10−23JK−1 )

6.23×1026

0.33×1028

3.3×1021