Kaplan MCAT General Chemistry Review

When we examine the behavior of gases under varying conditions of temperature and pressure, we assume that the gases are ideal. An ideal gas represents a hypothetical gas whose molecules have no intermolecular forces and occupy no volume. Although real gases deviate from this ideal behavior at high pressures and low temperatures, many real gases demonstrate behavior that is close to ideal.

Kinetic Molecular Theory of Gases

This mouthful of a theory was developed in the second half of the 19th century, well after the laws describing gas behavior had been developed. In fact, the kinetic molecular theory was developed to explain the behavior of gases, which the laws merely described. The gas laws demonstrate that all gases show similar physical characteristics and behavior irrespective of their particular chemical identity. The behavior of real gases deviates from the ideal behavior predicted under the assumptions of this theory, but these deviations may be corrected for in calculations. The combined efforts of Boltzmann, Maxwell, and others led to a simple explanation of gaseous molecular behavior based on the motion of individual molecules. Like the gas laws, which we will examine shortly, the kinetic molecular theory was developed in reference to ideal gases, although it can be applied with reasonable accuracy to real gases as well.

ASSUMPTIONS OF THE KINETIC MOLECULAR THEORY

1. Gases are made up of particles whose volumes are negligible compared to the container volume.

2. Gas atoms or molecules exhibit no intermolecular attractions or repulsions.

3. Gas particles are in continuous, random motion, undergoing collisions with other particles and the container walls.

4. Collisions between any two gas particles are elastic, meaning that there is conservation of both momentum and kinetic energy.

5. The average kinetic energy of gas particles is proportional to the absolute temperature (in Kelvin) of the gas, and it is the same for all gases at a given temperature, irrespective of chemical identity or atomic mass.

APPLICATIONS OF THE KINETIC MOLECULAR THEORY OF GASES

It’s fairly straightforward to imagine, based on the assumptions just listed, gas particles as lots of little rubber balls bouncing into and off each other and off the walls of their container. Of course, rubber balls, like real gas particles, have measurable mass and volume, and not even the bounciest rubber balls will collide in a completely elastic manner.

Average Molecular Speeds

According to the kinetic molecular theory of gases, the average kinetic energy of a gas particle is proportional to the absolute temperature of the gas:

where k is the Boltzmann constant, which serves as a bridge between macroscopic and microscopic behavior (that is, as a bridge between the behavior of the gas as a whole and the individual gas molecules). This equation shows that the speed of a gas particle is related to its absolute temperature. However, because of the large number of rapidly and randomly moving gas particles, which may travel distances as short as 6 × 10^-6 cm before colliding with another particle or the container wall, the speed of an individual gas molecule is nearly impossible to define. Therefore, the speeds of gases are defined in terms of their average molecular speed. One way to define an average speed is to determine the average kinetic energy per particle and then calculate the speed to which this corresponds. The resultant quantity, known as the root-mean-square speed (u_rms), is given by the following equation:

where R is ideal gas constant and MM is the molecular mass.

MCAT Expertise

Again, understanding concepts will be much more fruitful on Test Day than memorizing all of the facts. The higher the temperature, the faster the molecules move. The larger the molecules, they slower they move.

A Maxwell-Boltzmann distribution curve shows the distribution of speeds of gas particles at a given temperature. Figure 7.1 shows a distribution curve of molecular speeds at two temperatures, T₁ and T₂, where T₂ is greater than T₁. Notice that the bell-shaped curve flattens and shifts to the right as the temperature increases, indicating that at higher temperatures, more molecules are moving at higher speeds.

Figure 7.1

Example: What is the average speed of sulfur dioxide molecules at 37°C?

Solution: The gas constant R = 8.314 J/(K • mol) should be used, and MM must be expressed in kg/mol.

Use the conversion factor 1 J = 1 kg • m²/s²:

Graham’s Law of Diffusion and Effusion