From the equation of Graham's law of diffusion of gases, it would take the same number of moles of Ar(g) 23 minutes to effuse through the same membrane.
The rate of diffusion or effusion of gases is affected by temperature, concentration, pressure, and the molecular weight of the gas.
The gas law that describes how the molecular weight or vapor density of a gas affects the rate of diffusion is Graham's law of diffusion of gases.
Mathematically, Graha's law of diffusion of gases is given below as follows:
R₁ / R₂ = √(M₂ / M₁) or T₁ / T₂ = √(M₁ / M₂)
where;
R₁ is the rate of diffusion of gas 1
T₁ is the time of diffusion of gas 1
M₁ is the molecular weight of gas 1
R₂ is the rate of diffusion of gas 2
T₂ is the time of diffusion of gas 2
M₂ is the molecular weight of gas 2
Substituting the values in the second equation:
The molecular weight of Br₂ = 160 g/mol
The molecular weight of Ar = 40 g/mol
46 / T₂ = √(160 / 40)
T₂= 46 / 2
T₂ = 23 mins
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