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Gases A and B diffuse. If the rate of diffusion of A is 13cm3/s and the rate of diffusion B is 40cm3/s find the MM of B if A is 24g/mol

Question

Gases A and B diffuse. If the rate of diffusion of A is 13cm3/s and the rate of diffusion B is 40cm3/s find the MM of B if A is 24g/mol

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Solution

The rate of diffusion of gases is inversely proportional to the square root of their molar masses. This relationship is described by Graham's law of diffusion:

Rate_A/Rate_B = sqrt(MM_B/MM_A)

Where: Rate_A = rate of diffusion of gas A Rate_B = rate of diffusion of gas B MM_A = molar mass of gas A MM_B = molar mass of gas B

Given: Rate_A = 13 cm^3/s Rate_B = 40 cm^3/s MM_A = 24 g/mol

We can substitute these values into Graham's law to find MM_B:

13/40 = sqrt(MM_B/24)

Solving for MM_B gives:

MM_B = (40/13)^2 * 24

MM_B = 70.9 g/mol

So, the molar mass of gas B is approximately 70.9 g/mol.

This problem has been solved

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