Question

The rate of diffusion of a gas A is √5 times more than of gas B. If the molar mass of A is x gmol-1, the molar mass of B ( in g mole-1) is

• A. 4x
• B. 5x
• C. 16x
• D. 25x

Answer 1

Answer: (B)

5x

Answer 2

The correct option is: (B): 5x.

The rate of diffusion of a gas is inversely proportional to the square root of its molar mass. Mathematically, this relationship is given by Graham's law of diffusion:

Rate A / Rate B = √(Molar mass B / Molar mass A)

Given that the rate of diffusion of gas A is √5 times more than that of gas B, we can write:

Rate A / Rate B = √5

Using Graham's law, we can set up the following equation:

√5 = √(Molar mass B / Molar mass A)

Squaring both sides of the equation to solve for the ratio of molar masses:

5 = Molar mass B / Molar mass A

Given that the molar mass of gas A is x g/mol, we can substitute this value into the equation:

5 = Molar mass B / x

Solving for the molar mass of gas B (Molar mass B):

Molar mass B = 5 * x

So, the molar mass of gas B is 5 times the molar mass of gas A, which is consistent with the provided answer of 5x g/mol.