Will the ratio of the rates of effusion for two gases be the same as the ratio of the rates of diffusion for the two gases be the same? As I understand it, Graham's law applies to both effusion and diffusion, so the two ratios would be the same, right?
correct.
Yes, you are correct. According to Graham's law of effusion and diffusion, the ratio of the rates of effusion for two gases is equal to the square root of the ratio of their molar masses. This law applies to both effusion - the process of gas escaping through a small hole into a vacuum, and diffusion - the process of gas particles spreading out to fill a volume.
To calculate the ratio of the rates of effusion or diffusion, you would need to follow these steps:
1. Determine the molar masses of the two gases. The molar mass represents the mass of one mole of a substance and is usually expressed in grams per mole (g/mol).
2. Take the square root of the ratio of the molar masses. This will give you the ratio of the rates of effusion or diffusion.
For example, if you have two gases with molar masses of 16 g/mol and 32 g/mol, the ratio of their rates of effusion or diffusion would be:
√(32 g/mol ÷ 16 g/mol) = √2:1
This means that the rate of effusion or diffusion for the gas with the molar mass of 32 g/mol is approximately 1.414 times faster than the gas with the molar mass of 16 g/mol.
So, to answer your question directly, yes, the ratio of the rates of effusion for two gases will be the same as the ratio of the rates of diffusion for the two gases. Both processes are governed by Graham's law, which relates the molar masses of the gases to their rates of effusion and diffusion.