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The densities of two gases are in the ratio of 1:16. The ratio of their rates of diffusion is
- a)16:1
- b)4:1
- c)1:4
- d)1:16
Correct answer is option 'B'. Can you explain this answer?
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Given: The ratio of densities of two gases is 1:16
To find: The ratio of their rates of diffusion
Diffusion is the process by which molecules move from an area of high concentration to an area of low concentration. The rate of diffusion of a gas is directly proportional to its density, i.e., denser gases diffuse slower than lighter gases.
Let the densities of the two gases be d1 and d2, and their rates of diffusion be r1 and r2, respectively.
Given, d1:d2 = 1:16
Let us assume that the molecular masses of the two gases are M1 and M2, respectively. Then, the formula for density is given by:
Density = (Molecular mass × Pressure) / (RT)
where R is the universal gas constant and T is the temperature.
We can write the ratio of densities as:
d1/d2 = (M1/M2) × (P1/P2) × (T2/T1) --(1)
where P1 and P2 are the pressures of the two gases at the same temperature T1 = T2.
Since the two gases are diffusing at the same temperature and pressure, their diffusion rates can be expressed as:
r1 ∝ 1/√d1 and r2 ∝ 1/√d2
Taking the ratio of these two rates, we get:
r1/r2 = √(d2/d1)
Substituting the given ratio of densities from equation (1), we get:
r1/r2 = √(16) = 4
Therefore, the ratio of the rates of diffusion of the two gases is 4:1. Hence, option (b) is the correct answer.
To find: The ratio of their rates of diffusion
Diffusion is the process by which molecules move from an area of high concentration to an area of low concentration. The rate of diffusion of a gas is directly proportional to its density, i.e., denser gases diffuse slower than lighter gases.
Let the densities of the two gases be d1 and d2, and their rates of diffusion be r1 and r2, respectively.
Given, d1:d2 = 1:16
Let us assume that the molecular masses of the two gases are M1 and M2, respectively. Then, the formula for density is given by:
Density = (Molecular mass × Pressure) / (RT)
where R is the universal gas constant and T is the temperature.
We can write the ratio of densities as:
d1/d2 = (M1/M2) × (P1/P2) × (T2/T1) --(1)
where P1 and P2 are the pressures of the two gases at the same temperature T1 = T2.
Since the two gases are diffusing at the same temperature and pressure, their diffusion rates can be expressed as:
r1 ∝ 1/√d1 and r2 ∝ 1/√d2
Taking the ratio of these two rates, we get:
r1/r2 = √(d2/d1)
Substituting the given ratio of densities from equation (1), we get:
r1/r2 = √(16) = 4
Therefore, the ratio of the rates of diffusion of the two gases is 4:1. Hence, option (b) is the correct answer.
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