Question

Gases cannot settle at the bottom of a container. This fact can be explained by (1) Charles' law (2) Amagots' law (3) Graham's law (4) Dalton's law of partial pressures

Short answer

Dalton's law of partial pressures explains that gases cannot settle at the bottom of a container.

Step-by-step solution

Understanding the Problem

Read the given options and understand what each law explains about the behavior of gases.

Analyze the Behavior Described

Identify the characteristic of gases mentioned in the problem: gases cannot settle at the bottom of a container.

Match the Law to the Behavior

Compare each law to see which one explains why gases do not settle and stay uniformly distributed: (1) Charles' law describes the relationship between temperature and volume.(2) Amagots' law is not a standard law related to gases.(3) Graham's law deals with effusion and diffusion rates of gases.(4) Dalton's law of partial pressures states that in a mixture of non-reacting gases, the total pressure exerted is equal to the sum of the partial pressures of individual gases.

Select the Correct Law

Dalton's law of partial pressures explains that gases in a mixture distribute evenly throughout the container, as each gas exerts pressure independently of others, leading to uniform distribution.

Key concepts

Charles' law

Charles' Law explains the relationship between the volume and temperature of a gas. According to this law, if the pressure is held constant, the volume of a gas is directly proportional to its temperature in Kelvin. This means if you increase the temperature, the volume increases, and if you decrease the temperature, the volume decreases. The formula representing Charles' Law is given by: \( \frac{V_1}{T_1} = \frac{V_2}{T_2} \). This means that if you know the initial volume and temperature of a gas, as well as the final temperature, you can calculate the final volume. It helps in understanding that gas expands with heat.

Dalton's law of partial pressures

Dalton's Law of Partial Pressures states that in a mixture of non-reacting gases, the total pressure exerted is equal to the sum of the partial pressures of the individual gases. Essentially, each gas in a mixture behaves independently, and its pressure contributes to the total pressure. The formula is: \[ P_{total} = P_1 + P_2 + P_3 + ... + P_n \], where \(P_1, P_2,..., P_n \) are the partial pressures of the individual gases. This explains why gases do not settle at the bottom of a container as they distribute evenly. Each gas exerts pressure independently, resulting in a uniform distribution.

Graham's law

Graham’s Law deals with the diffusion and effusion rates of gases. Diffusion is the process by which gas molecules spread out in response to concentration gradients, while effusion refers to the process by which gas particles pass through a tiny opening. Graham’s Law states that the rate of effusion (or diffusion) of a gas is inversely proportional to the square root of its molar mass: \[ \frac{Rate_1}{Rate_2} = \sqrt{\frac{M_2}{M_1}} \.\] This means that lighter gases effuse and diffuse faster than heavier ones. For example, helium will diffuse through a balloon's pores faster than oxygen because it is lighter.

Gas behavior

Understanding gas behavior is crucial to grasping the previous laws. Gases have unique properties that make them behave differently than solids and liquids. They are highly compressible, fill any container evenly, and their particles are in constant, random motion. Key points to remember about gas behavior include:

• Particles are far apart.
• They have negligible volume compared to the container.
• They move at high speeds.
• Collisions between particles are elastic.

These behaviors are governed by various gas laws, which collectively explain how gases respond to changes in pressure, volume, and temperature. Keeping these properties in mind will help your studies of gas laws and their applications.