Question

STATEMENT-1 : An ideal gas is enclosed within a container fitted with a piston. When volume of this enclosed gas is increased at constant temperature, the pressure exerted by the gas on the piston decreases. STATEMENT-2 : In the above situation the rate of molecules striking the piston decreases. If the rate at which molecules of a gas having same average speed striking a given area of the wall decreases, the pressure exerted by gas on the wall decreases. (1) Statement- 1 is True, Statement- 2 is True; Statement-2 is a correct explanation for Statement- 1 (2) Statement- 1 is True, Statement- 2 is True; Statement-2 is NOT a correct explanation for Statement- 1 (3) Statement- 1 is True, Statement- 2 is False (4) Statement- 1 is False, Statement-2 is True

Short answer

(1) Statement- 1 is True, Statement- 2 is True; Statement-2 is a correct explanation for Statement- 1

Step-by-step solution

- Analyze Statement 1

Evaluate the condition described. According to Boyle's Law, for an ideal gas at constant temperature, the pressure (P) and volume (V) are inversely proportional. That is, when volume increases, pressure decreases. Hence, Statement 1 is true.

- Analyze Statement 2

Consider the relationship between the rate of molecules striking the piston and the pressure. When volume increases, molecules have more space to move, so the rate of collision with the walls and piston decreases. The pressure exerted on the walls or piston is directly related to these collisions. Therefore, as the rate of molecules striking decreases, the pressure decreases. Statement 2 is true.

- Evaluate Explanation

Determine if Statement 2 explains Statement 1. Statement 2 describes why the pressure decreases when the volume increases: fewer molecules strike the piston or wall per unit time. Thus, Statement 2 is a correct explanation for Statement 1.

Conclusion

Both statements are true, and Statement 2 correctly explains Statement 1.

Key concepts

Boyle's Law

Boyle's Law is a fundamental principle in chemistry, describing the behavior of an ideal gas under constant temperature. The law states that the pressure (P) of a gas is inversely proportional to its volume (V).
This can be expressed mathematically as: \( P \propto \frac{1}{V} \). When the temperature is held constant, increasing the volume of the gas will result in a decrease in pressure, and vice versa. This is because spreading the gas molecules over a larger volume reduces the number of collisions they have with the walls of the container per unit time.
For instance:

• If you have a balloon, and you stretch it to make it larger without changing the amount of air inside, the pressure inside the balloon decreases.

By understanding Boyle's Law, one can predict how changes in volume affect gas pressure in various practical situations.

Gas Pressure

Gas pressure results from collisions of gas molecules with the walls of their container. The force exerted by these collisions distributed over the surface area creates pressure. This is why gas pressure is directly related to the number of collisions that occur.
The more frequent and forceful the collisions, the higher the pressure. Pressure can be increased by:

• Increasing the number of gas molecules in a given volume (more collisions occur).
• Raising the temperature (molecules move faster, colliding more forcefully).

Gas pressure is crucial in many applications, from inflating tires to understanding the behavior of gases in the atmosphere.
For example:

• When you pump air into a tire, you increase the number of air molecules inside the tire, which increases the pressure.
• Heating a closed container with a fixed amount of gas will raise the pressure as the gas molecules move faster due to increased kinetic energy.

Molecular Collision

Molecular collisions among gas particles and with container walls are fundamental to understanding gas behavior. These collisions are responsible for gas pressure and temperature.
As volume increases, such as when gas is allowed more space in a container, molecules have more room to move and collide less frequently. This results in a drop in pressure. Conversely, reducing the volume compresses the gas, leading to more frequent collisions and higher pressure.
If we keep temperature constant, the average speed of gas molecules does not change:

• Fewer collisions with the walls occur, which decreases pressure.

Understanding molecular collisions helps explain phenomena like diffusion, where gas molecules spread out to fill available space and create uniform distribution.
In real-world terms:

• Perfume spreading through a room is due to molecular collisions causing the scent to travel from an area of high concentration to lower concentration areas.