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A vessel containing 1 g of oxygen at a p...

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.

Text Solution

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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`
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