Question

A vessel is filled with a gas at a pressure of 76 cm of Hg at a certain temperature. The mass of the gas is increased by 50% by introducing more gas in the vessel at the same temperature. Find out the resultant pressure of the gas.

Answer 1

Here,

P1 = 76 mmHg

P2 = ?

T1 = T2 = T

Let initial mass of the gas be m1

Increase in mass ∆m/m1 = 0.5

Thus final mass m2 = m1 + 0.5m1 = 1.5m1

Let M be the molecular mass of the gas

Thus, number of moles in the original mass of gas n1 = m1/M

Final number of moles in the gas n2 = m2/M = 1.5n1

Now eqn. of state of the gas in the initial state

P1V= n1 RT ---1.

Eqn. of state in the final state

P2V = n2 RT ---2.

By eqn. 1 and 2

P1 /n1 = P2 /n2

=> P2  = P1 (n2 /n1)

=> P2 = 76 (1.5n1/n1 )

=> P2 = 76×1.5

=> P2 = 114 mm Hg

Answer 2

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