An open vessel contains air at 27^@C. To what temperature should the vessel be heated so that the number of molecules in the vessel decreases by 25% ? (Neglect the expansion of the container).

An open vessel contains air at 27^@C. To what temperature should the v

1.	An open vessel contains air at 27^@C. To what temperature should the vessel be heated so that the number of molecules in the vessel decreases by 25% ? (Neglect the expansion of the container).
Answer» SOLUTION :Suppose, initially the container contains `n_1` moles of the gas. On heating the number of molecules decreases by 25%. Since number of moles is PROPORTIONAL to number of molecules, the number of moles left in the vessel `=(100 - 25)/100xx n_1 = 0.75 n_1` Since the vessel is open and does not expand on heating, the volume of the gas in the container and its pressure remain constant during heating. According to the gas equation, `PV = n_1 RT_1` (before heating) and `PV = 0.75 n_1 RT_2` (after heating) `:. "" n_1 T_1 = 0.75 n_1 T_2` or `T_2 =T_1/(0.75) =(273+27)/(0.75) = 400K(T_1 = 27^@C)` HENCE, the vessel should be heated to `400-273 = 127^@C`.