Question

Which of the following assumptions is incorrect according to kinetic theory of gases? (a) Particles of a gas move in all possible directions in straight lines. (b) All the particles, at any particular time, have same speed and same kinetic energy. (c) There is no force of attraction between the particles of a gas at ordinary temperature and pressure. (d) The actual volume of the gas is negligible in comparison to the empty space between them.

Short answer

Option (b) is incorrect according to the kinetic theory of gases because gas particles have a distribution of speeds and kinetic energies, not a uniform speed and energy.

Step-by-step solution

Understanding Kinetic Theory Assumptions

The kinetic theory of gases is a theoretical model that describes the behavior of gases. According to this theory, gas particles are in constant, random motion and frequently collide with each other and the walls of their container. Some basic assumptions include: particles move in straight lines until they collide; particles do not exert forces upon each other except during collisions; and the volume of the particles is negligible compared to the volume of the container.

Evaluating Option (a)

Option (a) states that particles of a gas move in all possible directions in straight lines which is a correct assumption in kinetic theory. Gas particles indeed move randomly and in straight lines between collisions.

Evaluating Option (b)

Option (b) is incorrect as it asserts that all particles, at any particular time, have the same speed and kinetic energy. In reality, gas particles follow a distribution of speeds and consequently have a range of kinetic energies. This statement contradicts the kinetic theory, which predicts a distribution of speeds described by Maxwell-Boltzmann distribution.

Evaluating Option (c)

Option (c) suggests that there is no force of attraction between the particles of a gas at ordinary temperature and pressure. This is a correct assumption of the kinetic theory as it considers gas particles to only interact during elastic collisions and not by attractive forces.

Evaluating Option (d)

Option (d) claims the actual volume of the gas particles is negligible compared to the empty space between them. This is also a correct assumption of the kinetic theory, which treats gas particles as point particles with no volume.

Key concepts

Maxwell-Boltzmann Distribution

Understanding the Maxwell-Boltzmann distribution is crucial when studying the kinetic theory of gases. This statistical distribution describes the range of speeds (and consequently the kinetic energies) of particles in a gas.

Unlike the incorrect assumption mentioned in option (b), which suggested that all gas particles have the same speed and kinetic energy, the Maxwell-Boltzmann distribution shows that particles in a gas have a variety of speeds, and hence kinetic energies. Imagine a busy street: not all cars travel at the same speed; some are fast, others slow, with most falling somewhere in the middle. Similarly, gas particles whiz around at different speeds, and when plotted, this variety creates a distribution curve.

The curve is not symmetrical; it has a peak at the most probable speed, where the majority of particles are found. The likelihood of particles having very high or very low speeds is less, which is why the curve tapers off on both ends. This distribution is fundamental to understanding concepts such as temperature and pressure in gases.

Gas Particle Behavior

Gas particles are the moving characters of the kinetic theory's narrative. Their behavior sets the stage for understanding gas laws and explains how temperature, volume, and pressure interrelate.

These tiny actors are in relentless motion; they travel in straight lines at various speeds and change direction only when they collide with each other or the walls of their container, akin to a ball bouncing in a room. These collisions are, importantly, elastic, meaning that when particles 'bump' into each other, there is no overall loss of kinetic energy—much like two perfectly bouncy balls colliding.

It's these collisions that create pressure on the walls of the container, and the temperature of the gas reflects the average kinetic energy of the particles. The important thing to remember is that all of this movement and interaction happens without any long-range forces; gas particles are not 'holding hands' or pushing each other away from a distance. They only 'communicate' through direct, brief collisions.

Kinetic Theory Assumptions

The kinetic theory has several underpinning assumptions that simplify the complex reality of particle dynamics to something more manageable and predictably mathematical.

Firstly, gas particles are assumed to be point-like in size, meaning that they occupy negligible space compared to the expanse of the container they are in. It's a bit like saying that grains of sand in a large playground are so small that the space they take up can be overlooked.

Secondly, these particles are assumed not to attract or repel each other, moving independently except during collisions. This is similar to assuming individuals in a crowded room move about with no concern for one another, rather than forming groups or consciously staying apart.

Lastly, the collisions between these particles and between particles and the container walls are perfectly elastic. This means that no energy is lost to heat or sound during collisions—a simplification that doesn't quite hold in the real world but makes the math much more straightforward. These simplifying assumptions allow scientists to create models that accurately predict gas behavior under a variety of conditions.