2 Answers

Drunkdolphin · Answer 1 · 2022-02-18T19:21:09+0000

Answer: The molar mass of the gas is 9.878 g/mol.

Step-by-step explanation:

According to Graham's law, the rate of diffusion is inversely proportional to square root of molar mass of gas.

Rate = (1)/(√(M))

where,

M = molar mass of gas

As given gas diffuses 1/7 times faster than hydrogen gas. So, its molar mass is calculated as follows.

$(R_(1))/(R_(2)) = \sqrt{(M_(2))/(M_(1))}\\$

where,

M_(1) = molar mass of hydrogen gas

M_(2) = molar mass of another given gas

R_(1) = rate of diffusion of hydrogen

R_(2) = rate of diffusion of another given gas =
(1)/(7)R_(1)

Substitute the values into above formula as follows.

$(R_(1))/(R_(2)) = \sqrt{(M_(2))/(M_(1))}\\(R_(1))/((1)/(7)R_(1)) = \sqrt{(M_(2))/(2)}\\7 * 1.414 = M_(2)\\M_(2) = 9.878 g/mol$

Thus, we can conclude that the molar mass of the gas is 9.878 g/mol.

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