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
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
Solution and Explanation
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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Concepts Used:
States of Matter
The matter is made up of very tiny particles and these particles are so small that we cannot see them with naked eyes.
There are three States of Matter:
The three states of matter are as follows:
Solid State:
- The solid-state is one of the fundamental states of matter.
- Solids differ from liquids and gases by the characteristic of rigidity.
- The molecules of solids are tightly packed because of strong intermolecular forces; they only oscillate about their mean positions.
Liquid State:
- The molecules in a liquid are closely packed due to weak intermolecular forces.
- These forces are weaker than solids but stronger than that of gases.
- There is much space in between the molecules of liquids which makes their flowing ability easy.
Gaseous State:
- In this state of matter, distances between the molecules are large (intermolecular distance is in the range of 10-7-10-5 cm.
- The intermolecular forces experienced between them are negligible.
- Thus, translatory, rotatory and vibratory motions are observed prominently in gases.