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## Q. 5.12

Consider the two boxes A and B shown below. Box B has a volume exactly twice that of box A. The circles and represent one mole of HCl and He, respectively. The two boxes are at the same temperature.

(a) Compare the pressures of the gases in the two containers.

(b) Compare the densities of the two gases.

(c) Compare the number of atoms in the two boxes.

(d) If the HCl in box A were transferred to box B, what would be the mole fraction of HCl in the mixture?

(e) Which of the two gases effuses faster?

## Verified Solution

(a) Since n/V and T are the same in both cases, P = nRT/V is the same for the two gases.
(b) The mass of HCl is 2(36.5 g) = 73.0 g; that of He is 4(4.00 g) = 16.0 g. Since 73.0 g/V > 16.0 g/2V, HCl has the higher density.
(c) Two moles of diatomic HCl contain the same number of atoms as four moles of He.
(d) $X_{HCl}$ = 2/6 = 1/3
(e) Because HCl and He are at the same pressure, the lighter gas, He, effuses faster.