Question

What is the relationship between rate of diffusion of a gas and its molar mass?

Short answer

The rate of diffusion of a gas is inversely proportional to the square root of its molar mass. Higher molar mass leads to a slower rate of diffusion and vice versa.

Step-by-step solution

Understand Graham's Law of Effusion

According to Graham's Law of Effusion, for two different gases at the same temperature and pressure, the ratio of the rates of effusion is given by the inverse of the square root of the ratio of their molar masses.

Apply Graham's Law to the problem

Consequently, in our case, the rate of diffusion of a gas (Rate) is inversely proportional to the square root of its molar mass (MM), i.e Ratio = k / sqrt(MM), where k is a constant. This means that as molar mass increases, the rate of diffusion decreases and vice versa.

Understand the Physical Concept

The reason behind this is that heavier molecules move more slowly than lighter ones at a given temperature, which results in a slower rate of effusion.

Key concepts

Rate of Diffusion

The rate of diffusion is an essential concept when discussing the movement of gases. Diffusion refers to the process of a substance spreading out to evenly fill its container or environment. For gases, the rate of diffusion is determined by how quickly they move from an area of higher concentration to an area of lower concentration. This movement is naturally occurring and does not require additional energy input. Several factors can influence the rate of diffusion:

• Temperature: Higher temperatures generally increase the rate of diffusion as gas molecules move more quickly.
• Size and Mass of the Molecule: Smaller and lighter molecules tend to diffuse faster than larger, heavier ones.
• Medium: Diffusion occurs at different rates in gases, liquids, and solids, with gases typically diffusing the fastest.

By understanding these factors, we can better grasp why gases diffuse at various rates under different conditions. This information is particularly useful in fields like chemistry and environmental science, where gas behavior plays a crucial role.

Molar Mass

Molar mass is a term used to describe the mass of a given substance (specifically atoms and molecules) divided by the amount of substance. The unit is usually grams per mole (g/mol). In simpler terms, molar mass tells us how much one mole of a substance weighs. It's a crucial factor in the behavior of gas molecules, especially when considering their movement and interaction with the environment. For gases, knowing the molar mass helps in calculating other properties, like density and rate of diffusion. Lighter gases with lower molar masses, such as helium, diffuse much faster than heavier gases with higher molar masses, like argon. To determine the molar mass of a compound, you simply add up the atomic masses of its constituent atoms. This can be easily done using a periodic table, making it an essential tool in any chemistry study. Understanding molar mass is fundamental to comprehending why certain gases behave differently under similar conditions.

Inverse Proportionality

Inverse proportionality is a relationship between two variables where one variable increases if the other decreases, and vice versa. This concept is directly applicable when discussing the relation between the rate of diffusion of a gas and its molar mass, as explained by Graham's Law of Effusion. According to Graham's Law, the rate at which a gas diffuses is inversely proportional to the square root of its molar mass. This means that as the molar mass of a gas increases, the rate of diffusion decreases. Conversely, gases with smaller molar masses will diffuse more quickly. Mathematically, this can be expressed as:\[\text{Rate of Diffusion} \propto \frac{1}{\sqrt{\text{Molar Mass}}}\]This relationship shows why lightweight gases spread out faster compared to their heavier counterparts. An understanding of inverse proportionality is invaluable in predicting and explaining the behavior of different gases in various scenarios.