What will be the number of molecules in 1 cm3 of a gas at a pressure of 1.38 atm and temperature 27°C ?

Question

What will be the number of molecules in 1 cm3 of a gas at a pressure of 1.38 atm and temperature 27°C ? (A) 3.3×1023 (B) 3.3×1019 (C) 3.3×1016 (D) 3.3×109

Tardigrade Admin · Accepted Answer

pV=n RT ⇒ n=(pV/RT).Here nR=nNA kwhere n NA is the number of molecules in the sample.Hence N=n NA=(pV/kT) =(1.38 × 10-5 ×10-6/1.38 × 10-23× 300)=3.3 × 109

Q. What will be the number of molecules in $1 c m^{3}$ of a gas at a pressure of 1.38 atm and temperature $2 7^{\circ}$ C ?

$3.3 \times 1 0^{23}$

$3.3 \times 1 0^{19}$

$3.3 \times 1 0^{16}$

$3.3 \times 1 0^{9}$

$p V = n RT \Rightarrow n = \frac{p V}{RT} . Here n R = n N_{A} k$ where $n N_{A}$ is the number of molecules in the sample. $He n ce N = n N_{A} = \frac{p V}{k T} = \frac{1.38 \times 1 0 ^{- 5} \times 1 0 ^{- 6}}{1.38 \times 1 0 ^{-} 23 \times 300} = 3.3 \times 1 0^{9}$

Q. What will be the number of molecules in 1cm3 of a gas at a pressure of 1.38 atm and temperature 27∘C ?

3.3×1023

3.3×1019

3.3×1016

3.3×109