Question

A glass tube of volume $112ml$. containing a gas is partially evacuated till the pressure in it drops to $3.8\times {10}^{-5}torr$ at $0^{o}C$. The number of molecules of the gas remaining in the tube is?

• A. $3\times {10}^{17}$
• B. $1.5\times {10}^{14}$
• C. $4.5\times {10}^{18}$
• D. $6\times {10}^{18}$

Answer 1

Answer: (B)

$1.5\times {10}^{14}$

Pressure $=3.8\times {10}^{-5}torr$ and temperature $=0^{o}c+273k$

$R=62.36367LTorr|c^{-1}mo{|}^{-1}$

Volume $=112ml=112\times {10}^{-3}c$

number of mole $n=\frac{PV}{RT}$

$=\frac{3.8\times {10}^{-5}\times 112\times {10}^{-3}}{62.36367\times 273}$

$=2.5\times {10}^{-10}$

number of molecules of gas $=6.022\times {10}^{23}\times 2.5\times {10}^{-10}$

$=1.5\times {10}^{14}$

So, the correct option is $B$