Describing Behavior of Real Gases with Molecular Kinetic Theory

Assumption of an ideal gas by kinetic molecular theory. Kinetic molecular theory's major utility is to understand gases and predict their behaviors. It helps in linking ideal gases' microscopic behaviors to the macroscopic properties of other gases. When using kinetic molecular theory for ideal gas five assumptions were made.Gases have many molecules in constant, random, and linear motion. This means that molecules of gases move freely in linear motion and their motion is constant and does not change.

The volume of all molecules is almost negligible compared to the total volume of gas. Because gas molecules are very far away from each other so all the volume is the volume of space they take. As individuals their volume is negligible.Because molecules are very far away from each other so intermolecular forces in the gas are negligible. Molecules move randomly and freely due to no attraction between them.

The collision between the gas molecules is elastic. This means that molecules of gas have the same kinetic energy at a constant temperature. But this does not apply when the temperature changes.At any temperature, all gas molecules have the same kinetic energy in equilibrium. This means that the average kinetic energy of gas molecules is proportional to temperature or absolute temperature.

Molecular kinetic equation. Kinetic molecular theory tells about matter's state and depends on the concept that matter is made of tiny particles. These particles move freely. Kinetic molecular gas equation and theory were developed by Bernoulli in 1738. Because molecules of gases move very freely and force of attraction is not available to bind them together.

Further, in the nineteenth century Joule, Kronig, Clausius, Boltzman, and Maxwell worked on it and gives a kinetic gas equation on the root-mean-square speed basis. This equation is used to derive the root mean square speed and density of gas molecules. Mean square root speed. Gas contains a large no of molecules and every molecule has a particular speed. Mean square root speed is the average of the square of all gas's speed. It is also known as root-mean-square speed/velocity. We can derive it from the kinetic gas equation and ideal gas laws.

Let's see an example of the root-mean-square speed of gases. From the root-mean-square formula it is clear it depends upon temperature and molecular mass, directly and inversely proportional respectively. By increasing molecular mass speed decreases and by increasing temperature speed increases. If the temperature of the gas is 300K and the gas is carbon dioxide then its root-mean-square speed is as follows.

Diffusion. It is molecular movement from high concentration to low concentration. It happens when molecules collide freely with each other. It helps in the movement of molecules from in and out of cells. The movement of molecules happens from the region of higher concentration to the region of lower concentration. It happens downward of the the concentration gradient.

Solid, liquid, and Gas DiffusionDiffusion happens in liquids and gases because molecules move freely. Diffusion is very high in gases because molecules are very far away from each other. In liquids molecules, movement is not that random so diffusion is lower than in gases but higher than in solids. In solids, molecules are tightly packed together so molecules do not exhibit diffusion.

Let’s discuss an example. When we add a tea bag to a hot cup of water it diffuses into the water and changes its color. This happens because liquid molecules move freely. When we spray deodorant it gets diffuses into the room air. Because of that, we can sense the odor. This happens because gas molecules move randomly and have a high diffusion rate.

Diffusion RateAs defined by Graham's law of diffusion rate at which gas molecules diffuse is inversely proportional to the square root of its molar mass. Its formula is as follows. It is also known as the amount of gas passing through an area unit of time. Several factors affect diffusion rate as temperature, molecular mass, and concentration gradient.

Maxwell Boltzmann Curve. Molecules in a gas move freely but not all move at the same speed. Some molecules move very fast, some move at moderate speed, and some hardly move. That’s why we cannot simply consider the speed of only one molecule. So we get to know about the distribution of the speed of gas at a specific temperature.

James Clerk Maxwell and Ludwig Boltzmann answered this query in the late eighty’s. this shows the speed of molecules distribution of ideal gas. This is called Maxwell Boltzmann distribution/curve. We can predict by this curve that if the curve is higher at a particular region, more gas molecules are moving with that speed. The area under the curve gives the number of molecules per unit speed.