Graham's Law of Diffusion, Dalton's Law of Partial Pressure

Summary

This lecture delves into Graham's Law of Diffusion and Effusion, exploring how gas molecules move from high to low concentration due to random motion, and how the diffusion and effusion rates of gases are related to their molecular masses. It covers the mathematical equations derived from kinetic theory, with examples on how to calculate molecular masses using diffusion rates. Additionally, the lecture introduces Dalton's Law of Partial Pressures, explaining how the total pressure in a gas mixture equals the sum of individual partial pressures. Several examples help solidify these concepts, including solving problems related to diffusion, effusion, and partial pressures.

Takeaways

• 😀 Graham's Law of Diffusion explains how gas molecules mix due to random motion, moving from high to low concentration until equilibrium is reached.
• 😀 Effusion refers to the escape of gas through a small pinhole without molecular interaction, compared to diffusion which happens through an open space.
• 😀 Graham's Law of Diffusion states that the rate of diffusion of two gases is inversely proportional to the square root of their molar masses.
• 😀 The average kinetic energy of gases is directly proportional to temperature, and this relationship helps derive the equation for diffusion rates.
• 😀 Lighter gas molecules diffuse faster than heavier molecules, as the rate of diffusion is inversely proportional to the square root of the molecular mass.
• 😀 The solubility coefficient of a gas also influences its diffusion rate – more soluble gases diffuse slower as they are more likely to dissolve in liquid.
• 😀 The rate of diffusion can be related to density, where the rate is inversely proportional to the square root of the gas's molar mass.
• 😀 In a given example, the molecular weight of a gas can be determined by comparing its diffusion rate to a reference gas like oxygen.
• 😀 Graham's Law can be applied in effusion problems, where you calculate the time taken for a gas to diffuse through a pinhole using the ratio of diffusion times.
• 😀 Dalton's Law of Partial Pressures explains how the total pressure in a gas mixture is the sum of the partial pressures exerted by each gas in the mixture.
• 😀 Mole fraction and partial pressure can be used to quantify the contribution of each gas to the total pressure in a mixture, and mole calculations are important in deriving these values.

Q & A

What is Graham's Law of Diffusion?

Graham's Law of Diffusion states that the rate of diffusion or effusion of two gases is inversely proportional to the square root of their molar masses.

How does diffusion differ from effusion?

Diffusion is the mixing of gas molecules by random motion under conditions where molecular collisions occur, and gases mix freely until equilibrium is reached. Effusion, on the other hand, is the escape of gas molecules through a pinhole without molecular collisions.

What is the mathematical expression for the rate of diffusion or effusion of a gas?

The rate of diffusion or effusion of gas A compared to gas B is given by the equation: (rate A / rate B) = √(Molecular mass B / Molecular mass A), where the rates are inversely proportional to the square root of the molecular masses.

What does Graham's Law imply about the rate of diffusion of lighter gases?

According to Graham's Law, lighter gas molecules will diffuse faster than heavier gas molecules, as the rate of diffusion is inversely proportional to the square root of the gas's molecular mass.

What role does the solubility coefficient of a gas play in its diffusion rate?

The solubility coefficient indicates how easily a gas dissolves in a liquid. A gas that is more soluble will diffuse slower because the gas molecules are more likely to dissolve in the liquid rather than move through a membrane.

What is the relationship between temperature and the kinetic energy of gas molecules?

According to the kinetic theory of gases, the temperature in Kelvin is directly proportional to the average kinetic energy of gas molecules, meaning that higher temperature results in higher kinetic energy and faster molecular motion.

What is the formula for the average kinetic energy of a gas?

The average kinetic energy of a gas is given by the formula KE = 1/2 mv², where m is the mass of the gas molecule and v is its velocity.

How does the density of a gas relate to its rate of diffusion or effusion?

The density of a gas, defined as mass/volume, is inversely related to the rate of diffusion or effusion. A higher density gas will diffuse slower than a gas with lower density.

What does Dalton's Law of Partial Pressures state?

Dalton's Law of Partial Pressures states that the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures exerted by each individual gas in the mixture.

How is the partial pressure of a gas in a mixture calculated?

The partial pressure of a gas in a mixture is calculated by multiplying the mole fraction of the gas by the total pressure of the gas mixture. Alternatively, it can be expressed as Pi = Yi * PT, where Yi is the mole fraction and PT is the total pressure.