A gas X diffused through a porous partition the rate of 3 cm per second. Under the same condition hydrogen diffused at the rate of 15 cm' per second. What is the relative molecular mass of X.

 A gas X diffused through a porous partition the rate of 3 cm per second. Under the same condition hydrogen diffused at the rate of 15 cm' per second. What is the relative molecular mass of X.

A. 5

B. 12

C. 18

D. 45

E. 50

The correct answer is E. 50

Explanation:

To determine the relative molecular mass of gas X, we make use of Graham Law of Diffusion. The law states that the rate of diffusion of a gas is inversely proportional to the square root of its molar mass. 

Mathematically

rate1 / rate2 = √(M2/ M1)

where rate1 and rate2 are the diffusion rates of gas 1 and gas 2, while M1 and M2 are their molar masses.

In this case, gas X is gas 1 and hydrogen is gas 2. We know the rates of diffusion for both gases: 3 cm³/s for gas X and 15 cm³/s for hydrogen. The molar mass of hydrogen (H₂) is 2 g/mol.

Now let's substitute the values into the equation and solve it mathematically:

3 / 15 = √(2 / M1)

1 / 5 = √(2 / M1)

(1 / 5)² = 2 / M1

1 / 25 = 2 / M1

M1= 2 * 25 = 50 g/mol

So, the relative molecular mass of gas X is 50 making option E the chosen one.

SOURCE: NECO CHEMISTRY 2001 QUESTION 30.