A student forgot to add the reaction mixture to the round bottomed flask at `27 ^(@)C` but instead he/she placed the flask on the flame. After a lapse of time, he realized his mistake, and using a pyrometer he found the temperature of the flask was `477 ^(@)C.` What fraction of air would have been expelled out?

Explanation

When an open flask is heated, its volume and pressure may be regarded as constant. Suppose the number of moles of air in the flask before and after heating are `n_1 and n_2` respectively. According to the ideal gas equation,
`PV =n_1 RT_1 = n_1 xx R xx (273+27)`
(before heating ) ...(i)
and `PV =n_2 RT_2 = n_2 xx R xx (273+477)`
(after heating) ...(ii)
Dividing eq. (i) by (ii), we have
`1 = (n_1 xx 300)/(n_2 xx 750)`
`:. " " n_2 = 300/750 xx n_1 = 2/5 n_1`
Hence, number of moles of air expelled on heating
`=n_1 - n_2 =n_1 - 2/5 n_1 = 3/5 n_1`
Therefore, the fraction of air expelled `=(3/5 n_1)/n_1=3/5`