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.

Options

A. `1/3 g`
B. `1/48 g`
C. 1 g
D. `2/3` g

Answer

A

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)))`
`rArr 10/((1//32) xx 320) = (5/8 xx 10)/(n_(2) xx 300)`
`rArr n_(2) = 320/300 xx 5/8 xx 1/32 = 1/48` moles.
Mass leaking out = `1- n_(2) (32) = 1 - (2//3) = 1/3` g