Question

An electron tube was sealed off during manufacture at a pressure of $ 1.2\times {{10}^{-7}}mm $ of mercury at $ 27{}^\circ C $ . Its volume is 100 cm3. The number of molecules that remain in the tube is:

• A. $ 2\times {{10}^{16}} $
• B. $ 3\times {{10}^{15}} $
• C. $ 3.86\times {{10}^{11}} $
• D. $ 5\times {{10}^{11}} $
• E. $ 2.5\times {{10}^{12}} $

Answer 1

Answer: (C)

$ PV=nRT $ $ \Rightarrow $ $ (1.2\times {{10}^{-10}}\times 13.6\times {{10}^{3}}\times 9.8)\times {{10}^{-4}} $ $ =n\times 8.31\times (273+27) $ $ \therefore $ number of moles $ n=6.42\times {{10}^{-13}} $ Hence, number of molecules $ =6.42\times {{10}^{-13}}\times 6.02\times {{10}^{23}} $ $ =3.86\times {{10}^{11}} $