Gas K diffuses through a porous material at a rate of 12cm^3 s.t.p where as S diffuses through the same material at a rate of 7.5cm^3 s.t.p. Given that the molecular mass of K is 16, calculate the molar mass of S
Question
Gas K diffuses through a porous material at a rate of 12cm^3 s.t.p where as S diffuses through the same material at a rate of 7.5cm^3 s.t.p. Given that the molecular mass of K is 16, calculate the molar mass of S
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.
The formula for Graham's law of diffusion is:
Rate1/Rate2 = sqrt(M2/M1)
Where: Rate1 and Rate2 are the rates of diffusion of the two gases, M1 and M2 are the molar masses of the two gases.
Given in the problem: Rate1 (for gas K) = 12 cm^3 s.t.p Rate2 (for gas S) = 7.5 cm^3 s.t.p M1 (for gas K) = 16
We are asked to find M2 (for gas S).
Substituting the given values into the formula, we get:
12/7.5 = sqrt(16/M2)
Solving this equation for M2 gives:
M2 = 16 * (7.5/12)^2
M2 = 16 * (0.625)^2
M2 = 16 * 0.390625
M2 = 6.25
Therefore, the molar mass of gas S is approximately 6.25 g/mol.
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