Question

The Kinetic Molecular Theory of Gases Learning Goal To understand some aspects of molecular motion in the gas phase The kinetic molecular theory of gases explains how gas molecules behave in terms of motion, speed, and energy One important aspect of this theory deals with the relationship between temperature and the average speed of the gas molecules. Increasing the temperature of a gas sample increases the average kinetic energy of the molecules. The kinetic energy of a molecule determines its speed It is important to realize that not all molecules in a sample will have the same kinetic energy, which is why we refer to the average kinetic energy and the average speed. The speed of a particle with average kinetic energy is called the root mean square (rms) speed, vrms The rms speed may be expressed by the following equation: vrms=√3RT/MWhere R is the ideal gas constant, T is the absolute temperature, and M is the molar mass of the substance in kilograms per mole The constant motion of gas molecules causes diffusion and effusion. Diffusion is the gradual mixing of two substances resulting from the movement of their particles. Effusion is the gradual escape of gas molecules through microscopic holes in their container. Part A Which of the following state ments are true? Check all that apply The average kinetic energy of gas molecules increases with increasing temperature There are gas molecules that move faster than the average The temperature of a gas sample is independent of the average kinetic energy The average speed of gas molecules decreases with decreasing temperature All the gas molecules in a sample cannot have the same kinetic energy

Answer 1

Answer:

The average kinetic energy of gas molecules increases with increasing temperature

There are gas molecules that move faster than the average

The average speed of gas molecules decreases with decreasing temperature

All the gas molecules in a sample cannot have the same kinetic energy

Explanation:

The average kinetic energy of the particles in an ideal monoatomic gas is given by:

$E_k = \frac{3}{2}kT$ (1)

where

k is the Boltzmann constant

T is the absolute temperature of the gas

While the rms speed of the particles in a gas is given by

$v_{rms}= \sqrt{\frac{3RT}{M}}$ (2)

where

R is the gas constant

T is the absolute temperature

M is the molar mass

Let's now analyze each statement:

- The average kinetic energy of gas molecules increases with increasing temperature  --> TRUE. If we look at eq.(1), we see that the average kinetic energy is directly proportional to the temperature.

- There are gas molecules that move faster than the average --> TRUE. The distribution of the speed of the particles in a gas is spread around the rms speed, but of course not all the particles are moving at that speed: some particles are moving faster, while some are moving slower.

- The temperature of a gas sample is independent of the average kinetic energy --> FALSE. As we see from eq.(1), the two quantities are related to each other.

- The average speed of gas molecules decreases with decreasing temperature --> TRUE. As we see from eq.(2), the average speed is proportional to the square root of the temperature: so, when the temperature decreases, the average speed decreases as well.

- All the gas molecules in a sample cannot have the same kinetic energy --> TRUE. In fact, each particle will have a different kinetic energy, depending on its speed (different speed means also different kinetic energy).