A gas at 300 K has pressure 4 × 10-10 N m-2. If kB = 1.38 × 10-23 J K-1, the number of molecules per cm3 is of the order of

Question

A gas at 300 K has pressure 4 × 10-10 N m-2. If kB = 1.38 × 10-23 J K-1, the number of molecules per cm3 is of the order of (A) 103 (B) 105 (C) 106 (D) 109

Tardigrade Admin · Accepted Answer

Using, PV = nRT = nN((R/N)) T = nNkBT (nN/V) = (P/kBT) = number of molecules per m3 ∴ Number of molecules/cm3 = (P/kBT)×10-6 = (4 × 10-10 × 10-6/1.38 × 10-23 × 300) = 105

Q. A gas at $300 K$ has pressure $4 \times 1 0^{- 10} N m^{- 2}$ . If $k_{B} = 1.38 \times 1 0^{- 23} J K^{- 1}$ , the number of molecules per $c m^{3}$ is of the order of

$1 0^{3}$

$1 0^{5}$

$1 0^{6}$

$1 0^{9}$

Using, $P V = n RT = n N (\frac{R}{N}) T = n N k_{B} T$
$\frac{n N}{V} = \frac{P}{k _{B} T} =$ number of molecules per $m^{3}$
$∴$ Number of molecules/cm $^{3} = \frac{P}{k _{B} T} \times 1 0^{- 6}$
$= \frac{4 \times 1 0 ^{- 10} \times 1 0 ^{- 6}}{1.38 \times 1 0 ^{- 23} \times 300} = 1 0^{5}$

Q. A gas at 300K has pressure 4×10−10Nm−2. If kB​=1.38×10−23JK−1, the number of molecules per cm3 is of the order of

103

105

106

109