Final answer:
The true statements among those given are that O₂ will effuse faster than Cl₂ and that the higher the density of a gas, the shorter its mean free path. The statements that effusion and diffusion are the same and that perfume reaches the nose by effusion are false.
Step-by-step explanation:
The question pertains to the topics of mean free path, diffusion, and effusion of gases. Now, let's look at the true or false statements provided in the question.
Statements Analysis
- O₂ will effuse faster than Cl₂: This statement is true. According to Graham's Law, rates of effusion for gases are inversely proportional to the square roots of their molar masses. Since O₂ (molecular weight 32) is lighter than Cl₂ (molecular weight 70), O₂ will effuse more rapidly.
- Effusion and diffusion are the same: This is false. While both are processes involving the movement of gas molecules, diffusion concerns the spread of gas from higher concentration to lower concentration regions, whereas effusion is the escape of gas through a small opening into a vacuum.
- The higher the density of a gas, the shorter the mean free path: This statement is true. Mean free path is the average distance a molecule travels before colliding with another molecule. Since denser gases have more molecules in a given volume, the mean free path will be shorter.
- Perfume molecules travel to your nose by the process of effusion: This is false. Perfume molecules reach your nose primarily through the process of diffusion, moving from a region of high concentration (the perfume bottle) to low concentration (the surrounding air).
Understanding the principles of gas behavior, such as diffusion and effusion, is fundamental in chemistry. These principles explain everyday phenomena, like smelling perfume, as well as provide insight into how gases behave under various conditions.