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
4x
5x
16x
25x
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.
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