Question

A sample of 5 litre gas in an open vessel is taken at $300K$ temperature and it is heated upto $450K$ then what fraction of gas will escape out with respect to final volume?
(A) $50\% $
(B) $25\% $
(C) $33.33\% $
(D) $100\% $

Answer 1

Hint: In this question we use the ideal gas equation of gases. In this equation after using open vessel condition, we will find the final volume after increase in temperature. After finding the ratio of final volume and initial volume we can easily find the percentage of escape out gas fraction.

Complete step by step solution:
In question the given values are
${V_1} = 5$ litre (Initial volume)
${T_1} = 300K$ (Initial temperature)
${T_2} = 450K$ (Final temperature)
We have to find out the fraction of gas escaped.
Now, by the ideal gas equation.
$PV = nRT$
There is an open vessel thus pressure remains constant and there will be no change in the volume of the vessel.
Which means,
$\dfrac{V}{T} = {\text{constant}}$
Which could be written as $\dfrac{{{V_1}}}{{{T_1}}} = \dfrac{{{V_2}}}{{{T_2}}}$ for initial and final condition.
$\Rightarrow \dfrac{{{V_1}}}{{{T_1}}} = \dfrac{{{V_2}}}{{{T_2}}}$ putting the values
$\Rightarrow \dfrac{5}{{300}} = \dfrac{{{V_2}}}{{450}} \Rightarrow {V_2} = 7.5{\text{ litre}}$
Thus, fraction of gas escaped $ = 1 - \dfrac{5}{{7.5}}$
$ = 0.333$
In percentage $ = 0.333 \times 100 $
$ = 33.3\% $
Therefore when it is heated upto then 33.3 percent of gas will escape out with respect to final volume.

Hence, the correct option is C.

Note: In an open vessel, pressure remains always constant. Thus there will be no change in volume of the vessel. It means that the ratio of volume and temperature will be constant.