Question

One litre of a gas is at a pressure of ${10}^{-6}$ mm of mercury at $25{}^{\circ }C$ . How many molecules are present in the vessel?

• A. $3.2\times {10}^6$
• B. $3.2\times {10}^{10}$
• C. $3.2\times {10}^{13}$
• D. $3.2\times {10}^4$

Answer 1

Answer: (C)

According to question, $P_1={10}^{-6}mmHg$ $P_2=760mmHg$ (S.T.P. conditions) $T_1=298K$ $T_2=273K$ $V_1=1litre$ $V_2=?$ From gas equation, $\frac{P_1{V}_1}{T_1}=\frac{P_2{V}_2}{T_2}$ or $V_2=\frac{{10}^{-6}\times 1\times 273}{760\times 298}=1.205\times {10}^{-9}\text{litre}$ Hence, number of molecules in $1.205\times {10}^{-9}$ litre gas at S.T.P. $=\frac{6.023\times {10}^{23}\times 1.205\times {10}^{-9}}{22.4}$ $=3.24\times {10}^{13}$