Question

Certain volume of a gas exerts on its walls some pressure at temperature \(T\). If the volume of the gas is reduced to half, the pressure becomes double at the same temperature \(T\) because (1) Weight of the gas increases with pressure (2) Speed of the gas molecule decreases (3) More number of gas molecules strike the surface per second (4) Gas molecules attract each other

Short answer

More number of gas molecules strike the surface per second.

Step-by-step solution

- Understand the Relationship Between Volume and Pressure

In this problem, we need to identify why the pressure exerted by a gas doubles when its volume is halved while maintaining the same temperature. The key concept here is Boyle's Law, which states that for a given amount of gas at constant temperature, the pressure and volume of the gas are inversely proportional. This can be written as: \[ P_1 V_1 = P_2 V_2 \]where \( P_1 \) and \( P_2 \) are the initial and final pressures, and \( V_1 \) and \( V_2 \) are the initial and final volumes.

- Apply Boyle's Law

Given that the volume of the gas is reduced to half (\( V_2 = \frac{V_1}{2} \)), apply Boyle's Law:\[ P_1 V_1 = P_2 \left( \frac{V_1}{2} \right) \]Solving for the final pressure \( P_2 \) gives:\[ P_2 = 2P_1 \]This shows that the pressure doubles when the volume is halved.

- Analyze the Options

To understand why the pressure doubles, examine the options given:1. Weight of the gas increases with pressure2. Speed of the gas molecule decreases3. More number of gas molecules strike the surface per second4. Gas molecules attract each otherSince the exercise specifies the same gas and temperature, we can eliminate options 1 and 2. The gas molecules are expected to behave ideally, their speed does not decrease, and their weight does not increase. Option 4 can also be eliminated as we assume ideal gas behavior, meaning no significant intermolecular forces. Therefore, the correct explanation is that more gas molecules strike the surface per second.

Key concepts

Gas Pressure and Volume Relationship

Boyle's Law is at the heart of understanding the relationship between gas pressure and volume. Named after Robert Boyle, this fundamental law in chemistry states that for a fixed amount of gas at a constant temperature, the pressure of the gas is inversely proportional to its volume. In simpler terms, if you decrease the volume of a gas, its pressure increases, provided the temperature remains unchanged. This relationship can be mathematically represented as \( P_1 V_1 = P_2 V_2 \), where \( P_1 \) and \( P_2 \) are the initial and final pressures, and \( V_1 \) and \( V_2 \) are the initial and final volumes, respectively.
For instance, if you were to halve the volume of a gas, its pressure would double. This is because the gas molecules are now confined to a smaller space, causing them to collide more frequently with the walls of the container.

Ideal Gas Behavior

When exploring Boyle's Law, it's essential to consider the concept of ideal gas behavior. In an ideal gas, the molecules are assumed to have negligible volume and no intermolecular forces acting between them. This assumption simplifies the calculations and allows us to use Boyle's Law directly.
The behavior of real gases can deviate from the ideal model, especially under high pressure or low temperature. However, for most practical purposes and under standard conditions, gases behave approximately ideally. This is why Boyle's Law plays such a vital role in understanding gas behavior in chemistry.

• No intermolecular attraction
• Negligible molecular volume
• Elastic collisions among molecules and container walls

These assumptions make the math simpler and applicable to many real-life scenarios.

Boyle's Law Applications

Boyle's Law isn't just a theoretical concept; it has practical applications across various fields. In medicine, for example, it is crucial for understanding how breathing works. When you inhale, your lung volume increases, causing the internal pressure to drop and drawing air in. When you exhale, the lung volume decreases, increasing the pressure and pushing air out.
This law is also important in everyday devices like syringes and hydraulic systems. In scuba diving, divers use Boyle's Law to plan their dives, ensuring they ascend slowly to avoid decompression sickness, which can occur due to rapid changes in pressure.
Understanding Boyle's Law helps explain how and why gases behave the way they do, making it indispensable in both academic and practical contexts.

• Respiratory function in humans
• Operation of syringes and pumps
• Scuba diving safety