A gas, X diffuses 4 times as fast as another gas, Y, which in turn diffuses twice as fast as another gas, Z. If the molecular weight of Z is 128, the molecular weight of the X is _________.
Question
A gas, X diffuses 4 times as fast as another gas, Y, which in turn diffuses twice as fast as another gas, Z. If the molecular weight of Z is 128, the molecular weight of the X is _________.
Solution
The rate of diffusion of a gas is inversely proportional to the square root of its molar mass. This is known as Graham's law of diffusion.
Given that gas X diffuses 4 times as fast as gas Y, and gas Y diffuses twice as fast as gas Z, we can say that gas X diffuses 8 times as fast as gas Z (4 times 2).
Let's denote the molar mass of gas Z as Mz and the molar mass of gas X as Mx. According to Graham's law:
Mz/Mx = (rate of diffusion of X / rate of diffusion of Z)^2
We know that the rate of diffusion of X is 8 times that of Z, and the molar mass of Z is 128. Substituting these values into the equation gives:
128/Mx = (8)^2
128/Mx = 64
Solving for Mx gives:
Mx = 128/64 = 2
So, the molar mass of gas X is 2.
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