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Chapter 5: Problem 3

State Graham's law of diffusion.

Short Answer

Expert verified
Answer: Hydrogen gas diffuses 4 times faster than oxygen gas.

Step by step solution

01

1. State Graham's law of diffusion

Graham's law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of its molar mass. In other words, lighter gases diffuse faster than heavier gases.
02

2. Express the law in mathematical form

We can represent Graham's law of diffusion mathematically as follows: $$\frac{Rate_{1}}{Rate_{2}} = \sqrt{\frac{Molar\_Mass_{2}}{Molar\_Mass_{1}}}$$ where \(Rate_{1}\) and \(Rate_{2}\) are the rates of diffusion of Gas 1 and Gas 2, respectively, and \(Molar\_Mass_{1}\) and \(Molar\_Mass_{2}\) are the molar masses of Gas 1 and Gas 2, respectively.
03

3. Provide an example to illustrate the application of Graham's law

For example, let's compare the diffusion rates of hydrogen (H\(_2\)) and oxygen (O\(_2\)) gases. The molar masses of hydrogen and oxygen are roughly 2 g/mol and 32 g/mol, respectively. Using Graham's law of diffusion, we can calculate the ratio of their diffusion rates: $$\frac{Rate_{H_2}}{Rate_{O_2}} = \sqrt{\frac{32}{2}} = \sqrt{16} = 4$$ This means that hydrogen gas diffuses 4 times faster than oxygen gas.

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