Question

If X diffuses 10 times faster than Y, what will be the molecular weight ratio X : Y?

• A. 10
• B. 1/10
• C. 100
• D. 1/100

Answer 1

Answer:

D. 1/100

• To solve the problem of finding the ratio of the molecular weight of two gases X and Y, given that gas X diffuses 10 times faster than gas Y.

• The rate of diffusion of a gas is inversely proportional to the square root of its density.

• This relationship can be expressed mathematically as:

Rate ∝ 1/√D

Therefore, we can write:

Rate of X / Rate of Y = √D_Y/√D_X

Rate of diffusion of gas Y be R_Y and the rate of diffusion of gas X be R_X.

According to the problem, gas X diffuses 10 times faster than gas Y:

R_X = 10 R_Y

Substituting

10R_Y / R_Y = √D_Y / √D_X

10 = √D_Y / √D_X

To eliminate the square root, we square both sides of the equation:

10² = (√D_Y / √D_X⁾²

100 = D_Y/D_X

(D = M/V where, D is density, M is mass, V is volume)

So,

• D_Y/D_X = 100

• D_X/D_Y = 1/100

• M_X/M_Y = 1/100