(A) : Most probable velocity of nitrogen is greater than most probable velocity of Cl2 at any given temperature(R) : Molecular weight of N2 < Molecular weight of Cl2

The most probable velocity of gas molecules is given by the formula: Vmp=2kTmVmp is the most probable velocity, k is the Boltzmann constant, T is the absolute temperature of the gas, and m is the mass of the gas molecule.According to this formula, the most probable velocity of a gas molecule is inversely proportional to the square root of its mass. This means that, at any given temperature, the most probable velocity of a gas with a lower molecular weight will be greater than that of a gas with a higher molecular weight.The molecular weight of nitrogen (N2) is 28.02 g/mol, while the molecular weight of chlorine gas (Cl2) is 70.90 g/mol. Therefore, the molecular weight of Cl2 is higher than that of N2. This means that, at any given temperature, the most probable velocity of nitrogen gas molecules will be greater than that of chlorine gas molecules.

(A) : Most probable velocity of nitrogen is greater than most probable velocity of Cl2 at any given temperature(R) : Molecular weight of N2 < Molecular weight of Cl2

The most probable velocity of gas molecules is given by the formula: Vmp=2kTmVmp is the most probable velocity, k is the Boltzmann constant, T is the absolute temperature of the gas, and m is the mass of the gas molecule.According to this formula, the most probable velocity of a gas molecule is inversely proportional to the square root of its mass. This means that, at any given temperature, the most probable velocity of a gas with a lower molecular weight will be greater than that of a gas with a higher molecular weight.The molecular weight of nitrogen (N2) is 28.02 g/mol, while the molecular weight of chlorine gas (Cl2) is 70.90 g/mol. Therefore, the molecular weight of Cl2 is higher than that of N2. This means that, at any given temperature, the most probable velocity of nitrogen gas molecules will be greater than that of chlorine gas molecules.

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(A) : Most probable velocity of nitrogen is greater than most probable velocity of Cl₂ at any given temperature
(R) : Molecular weight of N₂ < Molecular weight of Cl₂

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(A) is true but (R) is false

Both (A) and (R) are correct and (R) is the correct explanation of (A)

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Both (A) and (R) are correct but (R) is not the correct explanation of (A)

answer is A.

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Detailed Solution

The most probable velocity of gas molecules is given by the formula: $V_{mp} = \sqrt{\frac{2 kT}{m}}$
V_mp is the most probable velocity, k is the Boltzmann constant, T is the absolute temperature of the gas, and m is the mass of the gas molecule.
According to this formula, the most probable velocity of a gas molecule is inversely proportional to the square root of its mass.
This means that, at any given temperature, the most probable velocity of a gas with a lower molecular weight will be greater than that of a gas with a higher molecular weight.
The molecular weight of nitrogen (N₂) is 28.02 g/mol, while the molecular weight of chlorine gas (Cl₂) is 70.90 g/mol.
Therefore, the molecular weight of Cl₂ is higher than that of N₂.
This means that, at any given temperature, the most probable velocity of nitrogen gas molecules will be greater than that of chlorine gas molecules.