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Chapter 12: Problem 57

An unknown gas effuses at a speed one- quarter of that of helium. What is the molar mass of the unknown gas? It is either sulfur dioxide or sulfur trioxide. Which gas is it?

Short Answer

Expert verified
The unknown gas is sulfur dioxide (SO2).

Step by step solution

01

Use Graham's Law

Graham’s law of effusion formulas: \\(\sqrt{M_1/M_2} = r_2/r_1 \\). Here \(r\) is the rate of effusion and \(M\) is the molar mass.
02

Set up the equation

We know that the rate of effusion of the unknown gas is one quarter that of helium. So, \(r_2/r_1 = 1/4\). The molar mass of helium (\(M_1\)) is 4 g/mol. Now we can assume that the molar mass of the unknown gas is \(M_2\). Let's put these values into the equation
03

Solve the equation for M2

After substituting the given values and solving for \(M_2\), we find \(M_2 = \((4/1)^2 * 4 = 64 g/mol \)
04

Determine the gas

The molar mass of sulfur dioxide (SO2) is 64 g/mol, and the molar mass of sulfur trioxide (SO3) is 80 g/mol. Given that the molar mass of the unknown gas is 64 g/mol. Therefore, the unknown gas must be sulfur dioxide (SO2).

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