Consider three gases: chlorine, freon-12, and radon. According to Grahams law of diffusion which gas would you expect to diffuse the fastest through a room? Which would diffuse slowest?
According to Graham's law of diffusion, the rate of diffusion of a gas is inversely proportional to the square root of its molar mass. In other words, lighter gases tend to diffuse more rapidly than heavier gases.
To determine which gas would diffuse the fastest through a room, we need to compare their molar masses. The molar mass of chlorine is approximately 35.45 g/mol, the molar mass of freon-12 (also known as dichlorodifluoromethane) is about 120.91 g/mol, and the molar mass of radon is about 222 g/mol.
Now, let's calculate the square roots of their molar masses:
Square root of chlorine's molar mass ≈ √35.45 ≈ 5.95 g/mol
Square root of freon-12's molar mass ≈ √120.91 ≈ 10.99 g/mol
Square root of radon's molar mass ≈ √222 ≈ 14.90 g/mol
Since the rate of diffusion is inversely proportional to the square root of the molar mass, we can see that chlorine has the smallest square root value, followed by freon-12 and radon.
Therefore, according to Graham's law of diffusion, chlorine would diffuse the fastest through a room, while radon would diffuse the slowest.
Remember, this relationship is based solely on molar mass and does not take into account other factors that may affect diffusion, such as temperature or pressure.