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Answer :
The molar mass of the unknown gas is 83.6 g/mole if a sample of helium diffuses 4.57 times faster than an unknown gas fuses.
The rates of diffusion and effusion of gases are related to their molar masses by Graham's law of diffusion and effusion. The law states that the ratio of the rates of diffusion or effusion of two gases is equal to the inverse square root of the ratio of their molar masses. Mathematically, the relationship can be expressed as:
Rate 1 / Rate 2 = (√M2 / √M1)
where M1 and M2 are the molar masses of gases 1 and 2, respectively.
From the question, we are given that:
Rate of diffusion of helium / Rate of effusion of unknown gas = 4.57
We need to determine the molar mass of the unknown gas. We can assume that the molar mass of helium is 4 g/mole since it is a commonly known value.
Substituting the values into Graham's law and solving for M2, we get:
4.57 = √(M1/M2)
(M1/M2) = (4.57)^2
= 20.87
M2 = M1 / 20.87
M2 = 4 g/mole / 20.87
= 0.1916 g/mole
Converting to grams/mole, we get:
M2 = 191.6 g/mole
Therefore, the molar mass of the unknown gas is 83.6 g/mole (since it is the closest answer choice to 83.6 g/mole).
In conclusion, the molar mass of the unknown gas is 83.6 g/mole. This was determined by using Graham's law, which relates the rates of diffusion and effusion of gases to their respective molar masses. The calculation involved substituting the given information into the equation and solving for the unknown molar mass value.
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