Question

Explain the difference between diffusion and effusion. How is the effu- sion rate of a gas related to its molar mass?

Short answer

Diffusion is the spreading of particles from high to low concentration, applicable to solids, liquids, and gases. Effusion is the escape of gas through a small hole from a region of high pressure to low pressure. Effusion rate is inversely proportional to the square root of the gas's molar mass.

Step-by-step solution

Define Diffusion

Diffusion is the process by which molecules spread from areas of high concentration to areas of low concentration. It occurs in various contexts, such as the dispersion of substances throughout a liquid or gas, and does not necessarily involve a change in the phase of matter.

Define Effusion

Effusion is the process by which a gas escapes through a tiny hole into a vacuum or an area of lower pressure. Unlike diffusion, effusion involves movement through a small opening and typically considers gases only.

Compare Diffusion and Effusion

The main difference between diffusion and effusion is that diffusion involves molecules spreading out to evenly fill a space, while effusion involves gas molecules passing through a small hole from an area of higher pressure to lower pressure. Additionally, while diffusion can involve solids, liquids, or gases, effusion mostly concerns gases.

Relate Effusion Rate to Molar Mass

The effusion rate of a gas is inversely proportional to the square root of its molar mass, as stated by Graham's law of effusion. Mathematically, Graham's law can be expressed as follows: \(\text{Rate of effusion} \alpha \frac{1}{\sqrt{\text{Molar mass}}}\). This means that lighter gases effuse more quickly than heavier gases.

Key concepts

Diffusion in Chemistry

Diffusion is a fundamental concept in chemistry and a key process in the movement of particles. It occurs when particles spread out from an area where they are in high concentration to an area with lower concentration, driven by their kinetic energy. Imagine a drop of food coloring spreading in a glass of water without stirring; that is diffusion at work.

Diffusion is not just limited to liquids; it occurs in gases and sometimes even in solids, albeit at a much slower rate due to the close packing of particles in a solid. This process is critical in various natural and industrial processes. For example, the exchange of oxygen and carbon dioxide in our lungs occurs through the diffusion of gases across the alveolar membrane.

In a broader sense, diffusion helps to maintain equilibrium as substances move towards a uniform concentration throughout the medium they are in. This passive transport mechanism does not require energy, and its rate can be affected by factors such as temperature, the size of molecules, and the medium in which diffusion occurs.

Effusion of Gases

Effusion is a bit like the exclusive cousin of diffusion, specific to gases, and it involves a much more restricted pathway. When a gas is confined in a container, it exerts pressure on the container walls. If there's a tiny opening, the gas molecules will start escaping out from this hole into a lower pressure area or even a vacuum. This escape act through a small opening is what we call effusion.

Unlike diffusion, effusion examines the movement of gases through narrow openings. This process is governed by principles that were studied by scientists like Thomas Graham, who formulated the eponymous Graham's Law of Effusion. An everyday example of effusion could be the slow leaking of helium from a balloon's small pores, causing the balloon to eventually deflate.

Molar Mass and Effusion Rate

Diving deeper into the effusion process, it's fascinating to see how it relates to the molar mass of a gas. Graham's law provides a remarkable insight here, stating that the effusion rate of a gas is inversely proportional to the square root of its molar mass (\text{Rate of effusion} \( \alpha \frac{1}{\sqrt{\text{Molar mass}}}\)).

This relationship implies that lighter gases (with lower molar mass) will effuse more rapidly than heavier gases. For instance, hydrogen gas effuses much quicker than oxygen because it has a much lower molar mass. This is why a balloon filled with hydrogen will deflate faster than one filled with oxygen.

Understanding this concept is crucial in various scientific fields, such as studying atmospheric gases, manufacturing processes, and even anesthesiology, where the administration of gases based on their effusion rates can be crucial to patient care.