Question

Which is not true in case of an ideal gas? (a) It cannot be converted into a liquid. (b) There is no interaction between the molecules. (c) All molecules of the gas move with same speed. (d) At a given temperature, \(P V\) is proportional to the amount of the gas.

Short answer

The statement which is not true in case of an ideal gas is (c) All molecules of the gas move with the same speed.

Step-by-step solution

Understanding the properties of an ideal gas

An ideal gas is a theoretical concept in which it is assumed that all gases behave ideally at all conditions of pressure and temperature. For this model, we can make the following important assumptions - The gas consists of point particles with no volume, the movement of gas particles is random, the collisions between particles are elastic, there is no interaction between particles, and there are no forces of attraction or repulsion between them. By understanding these properties, we can now examine the validities of the statements given in the exercise.

Evaluating each statement

Let's take each statement and determine its accuracy based on the properties of an ideal gas. \n (a) An ideal gas cannot be converted into a liquid - This is true, ideal gases are assumed not to condense to liquids or solids, regardless of the temperature or pressure. \n (b) There is no interaction between the molecules - This is true as well. For an ideal gas, there are no forces of attraction or repulsion between particles. \n (c) All molecules of the gas move with the same speed - This statement is false. Even though the gas particles are in constant, random motion, there are differences in the velocities of individual molecules due to the random nature of their movements.\n (d) At a given temperature, PV is proportional to the amount of the gas - This is a rendition of the ideal gas law where PV=nRT, where n is the amount of the gas. So, this statement is true.

Identifying the false statement

From the evaluation above, we can notice that answer (c) is the false statement about an ideal gas. Therefore, the correct answer to this question is (c) All molecules of the gas move with the same speed.

Key concepts

Ideal Gas Law

The Ideal Gas Law is a fundamental principle in chemistry and physics that connects the physical properties of an ideal gas. Simply put, it can be expressed by the equation \( PV = nRT \), where \( P \) stands for pressure, \( V \) signifies volume, \( n \) is the amount of gas (in moles), \( R \) is the ideal gas constant, and \( T \) represents temperature in Kelvin. This equation shows us that for a given amount of gas at a constant temperature, any increase in volume leads to a proportional decrease in pressure, and vice versa.

Therefore, an ideal gas follows this law exactly without deviation. However, in the real world, no gas is truly ideal; real gases can diverge from this behavior under high pressure or low temperature when the gas particles are closer together and interact more strongly. Understanding this law is crucial for many applications in science and engineering, such as predicting the behavior of gases in different conditions and designing systems where gas behavior is a key factor.

Gas Particles Behavior

Gas particles are known for their high-energy, chaotic movement. They are in a constant state of random, straight-line motion and only change direction when they collide with another particle or with the walls of their container. These collisions among ideal gas particles are perfectly elastic, meaning that there is no net loss of kinetic energy from the collisions.

The speed of gas particles is not uniform; instead, the particles follow a distribution of speeds known as the Maxwell-Boltzmann distribution. This concept refutes the statement that all gas particles move at the same speed. The distribution of speeds arises due to the random nature of particle collisions. At any given temperature, there is a wide range of particle speeds, with some particles moving faster or slower than others. Although the average kinetic energy of the particles determines the temperature of the gas, individual particle speeds can vary significantly.

States of Matter

Matter can exist in different states, primarily known as solid, liquid, and gas. These states of matter are distinguished by the arrangement and movement of particles. In solids, particles are closely packed together in a fixed arrangement and only vibrate in place. In liquids, the particles are still close together but can move freely around each other, allowing the liquid to flow. Gases have particles that are far apart and move independently of each other with high kinetic energy.

This independence of movement in gases leads to the property that gases will fill the entire volume of their container, taking its shape, which differs from the behavior of solids and liquids. The idea that an ideal gas cannot be converted into a liquid is based on the assumption that cooling or compressing a gas would not lead to a phase change as ideal gases do not experience the forces necessary for condensation. Real gases, on the other hand, can change states under suitable conditions of temperature and pressure.