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}}mm\,Hg $ $ {{P}_{2}}=760\,mm\,Hg $ (S.T.P. conditions) $ {{T}_{1}}=298\,K $ $ {{T}_{2}}=273\,K $ $ {{V}_{1}}=1\,\,litre $ $ {{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}} $