A vessel containing 1 g of oxygen at a pressure of 10 atm a temperature of `47^(@)C`. It is found that because of a leak, the pressure drops to `5//8th` of its original value and the temperature falls to `27^(@)C`. Find the volume of the vessel and the mass of oxygen that is leaked out.

Explanation

The pressure, temperature and the number of moles of oxygen in the vessel change due to leak, while the volume remains fixed. Hence using PV = nRT, we have
`((P_(1))/(n_(1) T_(1))) = ((P_(2))/(n_(2) T_(2))) implies n_(2) = (320)/(300) xx (5)/(8) xx (1)/(32) = (1)/(48)` moles
Mass leaking out `= - n_(2) (32) = 1 - (2//3) = (1)/(3) g`
Volume of vessel `= V = (n_(1) RT_(1))/(P_(1))`
`implies V = (1 xx 0.082 xx 320)/(32 xx 10) = 0.082 L`