Question

State Graham's law of diffusion.

Short answer

Answer: According to Graham's law of diffusion, hydrogen gas will diffuse 4 times faster than oxygen gas.

Step-by-step solution

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. Mathematically, this can be expressed as: \[\frac{Rate_1}{Rate_2} = \sqrt{\frac{Molar\,Mass_2}{Molar\, Mass_1}}\] Here, 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 their respective molar masses.

Explain the relationship between rate of diffusion and molar mass

According to Graham's law of diffusion, the lighter gas will diffuse faster than the heavier gas. This is because gas particles with lower molar mass have higher average velocities, allowing them to cover larger distances in a given time compared to gas particles with higher molar mass. In other words, if the molar mass of gas 1 is lower than the molar mass of gas 2, the rate of diffusion of gas 1 will be higher than that of gas 2.

Give an example

Let's consider two gases, hydrogen (H2) with a molar mass of 2 g/mol, and oxygen (O2) with a molar mass of 32 g/mol. We want to determine the ratio of their rates of diffusion. Using Graham's law of diffusion, we have: \[\frac{Rate_{H2}}{Rate_{O2}} = \sqrt{\frac{Molar\,Mass_{O2}}{Molar\, Mass_{H2}}} = \sqrt{\frac{32}{2}}\] Calculating the square root of the ratio: \[\frac{Rate_{H2}}{Rate_{O2}} = \sqrt{16} = 4\] This result means that hydrogen gas will diffuse 4 times faster than oxygen gas.