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Gas v takes 10seconds to diffuse through a distance of one fifth of a meter. Another gas w takes the same time to diffuse through a distance of 10cm,if the relative molecular mass of gas v is 16.0, calculate the molecular mass of w

Question

Gas v takes 10seconds to diffuse through a distance of one fifth of a meter. Another gas w takes the same time to diffuse through a distance of 10cm,if the relative molecular mass of gas v is 16.0, calculate the molecular mass of w

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Solution

The problem can be solved using Graham's law of diffusion, which states that the rate of diffusion of a gas is inversely proportional to the square root of its molar mass.

Let's denote:

  • the rate of diffusion of gas v as Rv,
  • the rate of diffusion of gas w as Rw,
  • the molar mass of gas v as Mv, and
  • the molar mass of gas w as Mw.

According to the problem, Rv = 1/5 m / 10 s = 0.02 m/s and Rw = 0.1 m / 10 s = 0.01 m/s. Also, we know that Mv = 16 g/mol.

From Graham's law, we have Rv / Rw = sqrt(Mw / Mv). Substituting the known values, we get 0.02 / 0.01 = sqrt(Mw / 16). Simplifying, we get 2 = sqrt(Mw / 16).

Squaring both sides to get rid of the square root, we get 4 = Mw / 16. Solving for Mw, we find that Mw = 4 * 16 = 64 g/mol.

So, the molar mass of gas w is 64 g/mol.

This problem has been solved

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