Molecular Motion: Definition, Types, and Kinetic Theory | PDF

MOLECULAR MOTION ---------------- **Introduction** Matter can exist in three states- solid, liquid and gas. These [states of matter](https://byjus.com/chemistry/three-states-of-matter/) can be differentiated on the basis of the position or motion of their constituent particles. In solid-state, par...

MOLECULAR MOTION ---------------- **Introduction** Matter can exist in three states- solid, liquid and gas. These [states of matter](https://byjus.com/chemistry/three-states-of-matter/) can be differentiated on the basis of the position or motion of their constituent particles. In solid-state, particles cannot move from their position. They can only vibrate at their mean position. On the contrary, in gaseous state particles can move randomly due to their high kinetic energy. They do not have a fixed position but show random movement. The liquid state can be considered as an intermediate state of matter in which particles can be moved and do not have a fixed position but their kinetic energy is less than gaseous particles and more than solid particles. They acquire the shape of the container in which they are. So we can say that all particles show motion more or less. They are in constant motion and also different from molecules such as liquid molecules have more freedom of movement compared to solid molecules. At the same time, they show less movement compared to gaseous molecules. In other words, we can say that gaseous molecules have the greatest degree of motion. Molecular Motion Definition --------------------------- ***Molecular motion is defined as the movement of constituent particles or molecules in a certain direction.*** The molecular motions are affected by heat and temperature. This is because temperature is the measurement of the average kinetic energy of the molecules and represents the motion of molecules. Similarly, heat transfers energy among constituent molecules that increase the kinetic energy of molecules. The mathematical relation between kinetic energy and temperature can be shown below; **E = kT** where, E=Energy, k = boltzmann constant, T=temperature Types of Molecular Motion ------------------------- The different types of molecular motions are ***Translational motion:*** In such kind of motion, molecules can move from one place to another in the same or different direction but always remains on the same axis. ***Rotational motion:*** In this type of motion, the molecule can rotate in and around the axis. ***Vibrational motion:*** In this type of motion, molecules can vibrate at their mean position. These motions are very common in [solid state](https://byjus.com/jee/solid-state/). ***Electronic motion:*** In this type of motion, electrons can move from place to place and orbital to orbital. Electronic motions cause a change in the colour of substances. Different Types of Motion ------------------------- Unlike the solid and liquid states, molecules in the gaseous state show random motion. That is the reason; gases take the shape of the container and spread quickly in space. The random motion of molecules in the gaseous state is due to high kinetic energy in molecules. They have weak intermolecular interactions between them. Three States of Matter Three States of Matter The intermolecular space between gaseous molecules is very large. They can show all the three types of molecular motion, vibrational, rotational and translational motion. In ***vibrational motion***, molecules move back and forth whereas in ***rotational motion*** the molecule rotates in space. In ***translational motion,*** molecules move in certain directions. Molecules of solid-state are capable of vibrational motion due to strong [intermolecular forces](https://byjus.com/chemistry/different-types-of-intermolecular-forces/). Therefore, they show the least random molecular motions. Like solids, liquids are capable of vibrational motion but at the same time, they can also show rotational and translational motions due to weak intermolecular forces between molecules. Hence, liquids can show random molecular motions but are less random compared to gas molecules. So we can say that random motion is related to temperatures, intermolecular forces of attractions, the kinetic energy of molecules and heat transfer. **Random Molecular Motion** Unlike solid and liquid states, molecules in a gaseous state show random motion. That is the reason, gases take the shape of container and spread quickly in space. The random motion of molecules in the gaseous state is due to high kinetic energy in molecules. They have weak intermolecular interactions between them. The intermolecular space between gaseous molecules is very large. They can show all three types of molecular motion: vibrational, rotational and translational motion. In vibrational motion, molecules move back and forth whereas in rotational motion the molecule rotates in space. In translational motion, molecules move in certain directions. Molecules of solid-state are capable of vibrational motion due to strong intermolecular forces. Therefore, they show the least random molecular motions. Like solids, liquids are capable of vibrational motion but at the same time they can also show rotational and translational motions due to weak intermolecular forces between molecules. Hence, liquids can show random molecular motions but less random compared to gas molecules. So we can say that random motion is related to temperatures, intermolecular forces of attractions, the kinetic energy of molecules and heat transfer. **Measure of Molecular Motion** All atoms or molecules require different amounts of energy for different types of molecular motion. The light absorbed during motion can be used to measure molecular motion. We can measure the frequencies of absorbed light and correlate them with some bonding arrangements which are present in the molecules. Various types of spectroscopy methods like [NMR spectroscopy](https://byjus.com/chemistry/nmr-spectroscopy/), UV-spectroscopy, Mass spectroscopy, and Infrared spectrums can be used to measure the molecular motion. These methods also provide sufficient information about the structure of molecules. Each type of absorption indicates a certain type of bond-like absorption frequency of the C-H bond is different from H-H or O-H bond. **kinetic theory of gases** The **kinetic theory of gases** explains the three macroscopic properties of a gas in terms of the microscopic nature of atoms and molecules making up the gas. Usually, the physical properties of solids and liquids can be described by their size, shape, mass, volume, etc. However, when we talk about gases, they have no definite shape or size, while mass and volume are not directly measurable. The kinetic theory of gases is useful and can be applied in this case. With the help of the kinetic theory of gases, the physical properties of any gas can be generally defined in terms of three measurable macroscopic properties: the pressure, volume and temperature of the container where the gas is stored or present. We will learn about this concept in detail below. What Is the Kinetic Theory of Gases? ------------------------------------ The kinetic theory of gases is a theoretical model that describes the molecular composition of the gas in terms of a large number of submicroscopic particles, which include atoms and molecules. Further, the theory explains that gas pressure arises due to particles colliding with each other and the walls of the container. The kinetic theory of gases also defines properties such as temperature, volume and pressure, as well as transport properties such as viscosity and thermal conductivity and mass diffusivity. It basically explains all the properties that are related to the microscopic phenomenon. The significance of the theory is that it helps in developing a correlation between the macroscopic properties and the microscopic phenomenon. In simple terms, the kinetic theory of gases also helps us study the action of the molecules. Generally, the molecules of gases are always in motion, and they tend to collide with each other and the walls of the containers. In addition, the model also helps in understanding related phenomena, such as the Brownian motion. Kinetic Theory of Gases Assumptions ----------------------------------- The kinetic theory of gases considers the atoms or molecules of a gas as constantly moving point masses with huge inter-particle distances and may undergo perfectly [elastic collisions](https://byjus.com/physics/elastic-collision/). Implications of these assumptions are as follows: **i) Particles** Gas is a collection of a large number of atoms or molecules. **ii) Point Masses** Atoms or molecules making up the gas are very small particles like a point (dot) on a paper with a small mass. **iii) Negligible Volume Particles** Particles are generally far apart such that their inter-particle distance is much larger than the particle size, and there is large free unoccupied space in the container. Compared to the volume of the container, the volume of the particle is negligible (zero volume). **iv) Nil Force of Interaction** Particles are independent. They do not have any (attractive or repulsive) interactions among themselves. **v) Particles in Motion** The particles are always in constant motion. Because of the lack of interactions and the free space available, the particles randomly move in all directions but in a straight line. **vi) Volume of Gas** Because of motion, gas particles occupy the total volume of the container, whether it is small or big, and hence the volume of the container is to be treated as the volume of the gases. **vi) Mean Free Path** This is the average distance a particle travels to meet another particle. **vii) Kinetic Energy of the Particle** Since the particles are always in motion, they have average [kinetic energy](https://byjus.com/physics/kinetic-energy/) proportional to the temperature of the gas. **viii) Constancy of Energy/Momentum** Moving particles may collide with other particles or containers. But the collisions are perfectly elastic. Collisions do not change the energy or momentum of the particle. **ix)** **Pressure of Gas** The collision of the particles on the walls of the container exerts a force on the walls of the container. Force per unit area is the pressure. The pressure of the gas is thus proportional to the number of particles colliding (frequency of collisions) in unit time per unit area on the wall of the container. Kinetic Theory of Gases Postulates ---------------------------------- The kinetic theory of gas postulates is useful in understanding the macroscopic properties from the microscopic properties. - Gases consist of a large number of tiny particles (atoms and molecules). These particles are extremely small compared to the distance between the particles. The size of the individual particle is considered negligible, and most of the volume occupied by the gas is empty space. - These molecules are in constant random motion, which results in colliding with each other and with the walls of the container. As the gas molecules collide with the walls of a container, the molecules impart some momentum to the walls. Basically, this results in the production of a force that can be measured. So, if we divide this force by the area, it is defined to be the pressure. - The collisions between the molecules and the walls are perfectly elastic, which means when the molecules collide, they do not lose kinetic energy. Molecules never slow down and will stay at the same speed. - The average kinetic energy of the gas particles changes with temperature; i.e., the higher the temperature, the higher the average kinetic energy of the gas. - The molecules do not exert any force of attraction or repulsion on one another except during collisions. ### A) Understanding Gas Laws of Ideal Gases **i) Pressure α Amount or Number of Particles at Constant Volume** The collision of the particles on the walls of the container creates pressure. Larger the number of the particle (amount) of the gas, the more the number of particles colliding with the walls of the container. At constant temperature and volume, the larger the amount (or the number of particles) of the gas, the higher will be the pressure. **ii) Avogadro's Law -- N α V at Constant Pressure** When there is a greater number of particles, it increases the collisions and the pressure. If the pressure is to remain constant, the number of collisions can be reduced only by increasing the volume. At constant pressure, the volume is proportional to the amount of gas. **ii) Boyle's Law -- Pressure**  **at Constant Temperature** At a constant temperature, the kinetic energy of particles remains the same. If the volume is reduced at a constant temperature, then the number of particles in unit volume or area increases. If there is an increased number of particles in the unit area, then it increases the frequency of collisions per unit area. At constant temperature, the smaller the volume of the container, the larger the pressure. **ii) Amonton's Law: P α T at Constant Volume** The kinetic energy of the particle increases with temperature. When the volume is constant, with increased energy, particles move fast and increase the frequency of collisions per unit time on the walls of the container and hence the pressure. At constant volume, the higher the temperature, the higher will be the pressure of the gas. **iv) Charles's Law -- V α T at Constant Pressure** The change of temperature changes proportionately to the pressure. If the pressure also has to remain constant, then the number of collisions has to be changed proportionately. At constant pressure and a constant amount of substance, collisions can be changed only by changing the area or volume. At constant pressure, volume changes proportionally to temperature. ### B) Understanding Non-Ideal Gas Behaviour All the gas molecules obey the ideal gas laws only under special conditions of low pressures and high temperatures. The deviations of the real gases from the [ideal gas](https://byjus.com/chemistry/derivation-of-ideal-gas-equation/) behaviour are traced mainly to making wrong or incorrect assumptions in the postulates, and they are given below: - The particles are point charges and have no volume: Then, it should be possible to compress the gases to zero volume. But, gases cannot be compressed to zero volume, which indicates that particles do have volume though small and cannot be neglected. - Particles are independent and do not interact:  Particles do interact depending upon their nature. The interactions affect the pressure of the gas. Volume and interactions differ from gas to gas. Many gas laws have been developed for real gases incorporating correction factors in the pressure and volume of the gases. - Particle collisions are not elastic: Particle collisions are elastic, and they exchange energy. The particles hence do not have the same energy and have a distribution of energy. ### C) Maxwell -- Boltzmann Molecular Distribution of Energy and Velocity The kinetic theory of gas postulates predicted the particles as always in motion and that they have kinetic energy proportional to the temperature of the gas. This concept was used by Maxwell -- [Boltzmann](https://byjus.com/jee/stefan-boltzmann-law/) to find the distribution of gaseous particles between energy zero to infinity and calculate the most probable, average and root mean square velocity of the particles. Frequently Asked Questions on Kinetic Theory of Gases ----------------------------------------------------- Q1 What is the main basis of the kinetic theory? Kinetic theory explains the behaviour of gases based on the idea that gas consists of rapidly moving atoms or molecules. Q2 What are real gases? The gases that show deviation from ideal gas features are called real gases. Q3 What is mean energy? The kinetic energy of one mole of gas is known as mean energy or the internal energy of the gas, and is denoted by U. Q4 What are the three main points of the kinetic model? The simplest kinetic model is based on the assumptions that:\ (1) The gas is composed of a large number of identical molecules moving in random directions, separated by distances that are large compared with their size.\ (2) The molecules undergo perfectly elastic collisions (no energy loss) with each other and with the walls of the container but otherwise do not interact.\ (3) The transfer of kinetic energy between molecules is heat. Q5 What do you mean by the degree of freedom (n)? The degree of freedom is defined as the number of possible independent ways in which the position and configuration of the system may change. Q6 What is the degree of freedom of the monoatomic gas molecule? The degree of freedom of the monoatomic gas molecule is, n = 3. Molecular Motion in Gases: Precise note and Problems Introduction to Molecular Motion in Gases The motion of gas molecules is governed by kinetic theory, which explains how microscopic molecular behavior determines macroscopic properties such as pressure, temperature, and volume. The study of molecular motion involves understanding the statistical distribution of velocities, intermolecular collisions, and the resulting transport processes in gases. **Distribution Functions and Boltzmann\'s Principle** **Maxwell-Boltzmann Distribution** The Maxwell-Boltzmann distribution describes the probability of gas molecules having a particular velocity at a given temperature. It is derived using statistical mechanics principles and assumes that the molecules in a gas are non-interacting and follow classical mechanics.  Boltzmann\'s Principle  This principle underpins the idea that a system evolves toward a state of maximum entropy, corresponding to thermodynamic equilibrium. Substituting k~B~ = 1.38 x 10^-23^ J/K, T = 300 K, m = 5.32 x 10^-26^kg  Intermolecular Collisions  Transport Processes in Gases Viscosity Viscosity is a measure of a fluid\'s resistance to flow. In gases, it arises from the transfer of momentum between layers of gas molecules. Diffusion Diffusion describes the movement of gas molecules from regions of high concentration to low concentration. The diffusion coefficient (D) is given by: