Question

A one litre closed vessel was maintained at constant temperature, contains $5\times {10}^{12}$ molecules of an ideal gas. How many molecules remain if the volume of the vessel is reduced to 0.05 litres?

• A. $5$ x ${10}^{12}$
• B. $0.25$ x ${10}^{12}$
• C. $2.5$ x ${10}^{10}$
• D. $1$ x ${10}^{15}$

Answer 1

Answer: (B)

$0.25$ x ${10}^{12}$

Volume = 1 L

To contain $5\times {10}^{12}$ molecules of gas at constant temperature.

Since, $V\propto n$ (Avogadro's Law)

$\frac{V_1}{n_1}=\frac{V_2}{n_2}{V}_2=0.05L{V}_1=1L{n}_1=5\times {10}^{12}\therefore n_2=\frac{n_1\times V_2}{V_1}=\frac{5\times {10}^{12}\times 0.05L}{1L}=0.25\times {10}^{12}$