Question

The pressure in the vessel that contained pure oxygen dropped from 2000mm to 1500 mm in 47 minutes as the oxygen leaked through a small hole into the vacuum. When the same vessel was filled with another gas, the pressure dropped from 2000 mm to 1500 mm in 74 minutes. What is the molecular weight of the gas?
A. 73
B. 75
C. 79
D. 80

Answer 1

For this problem, we have to find the relationship between the rate of diffusion and molecular mass as given by Graham's law of diffusion. After which we can put all the given values and calculate the molecular weight of the gas.

Complete answer:
- In the given question, we have to calculate the molecular mass of the gas whose pressure decreases from the 2000 mm to 1500 mm in 74 minutes.
- Now, we know that according to Graham's law of diffusion, the rate of effusion of the gases of the two gases has the inverse effect on the square root of the molecular mass of the gas.
- The expression for Graham's law of diffusion is given by:
$\dfrac{\text{Rate of effusion A}}{\text{Rate of effusion B}}\text{ = }\sqrt{\dfrac{{{\text{M}}_{\text{B}}}}{{{\text{M}}_{\text{A}}}}}$
- Also, the time that is required for the gas to leak is directly proportional to the molecular mass of the gas.
- So, the expression for the above statement will be:
$\dfrac{{{\text{T}}_{\text{B}}}}{{{\text{T}}_{\text{A}}}}\text{ = }\sqrt{\dfrac{{{\text{M}}_{\text{B}}}}{{{\text{M}}_{\text{A}}}}}$ …. (1)
- Now, it is given that the time required for the gas B to leak is 74 minutes and the time required for the gas A to leak is 47 minutes.
- Also, we know that the molecular weight of the oxygen will be ${{\text{O}}_{2}}\text{ = 2 }\times \text{ 16 = 32g}$.
- So, by putting all the values in equation (1) we will get:
$\Rightarrow \dfrac{74}{47}\text{ = }\sqrt{\dfrac{{{\text{M}}_{\text{B}}}}{32}}$
$\Rightarrow {{\text{M}}_{\text{B}}}\text{ = }\dfrac{{{74}^{2}}}{{{47}^{2}}}\text{ }\times \text{ 32 = 79}\text{.3g }\sim \text{ 79g}$

Therefore, option C is the correct answer.

Note:
Diffusion is the transfer of the gas molecules from the higher region to the lower region whereas the effluent is the leakage of the gas from the small hole whose size is smaller than the mean free path of the molecules.