An increase in the pressure exerted on gas at a constant temperature results in

Analysis

The question asks for the effect of increasing pressure on a gas when the temperature is kept constant. This is a classic application of the Gas Laws, specifically Boyle's Law.

Concept: Boyle's Law

Boyle's Law states that for a fixed mass of an ideal gas at a constant temperature, the pressure ($P$) of the gas is inversely proportional to its volume ($V$).

Mathematically, this is expressed as:

Where:

• $P$ = Pressure
• $V$ = Volume
• $k$ = Constant

This means that if you increase the pressure on a gas, the particles are forced closer together, which causes the volume to decrease. Conversely, if you decrease the pressure, the volume increases.

Step-by-Step Solution

1. Identify the variables: We are dealing with Pressure ($P$) and Volume ($V$) at a constant Temperature ($T$).
2. Apply the relationship: According to Boyle's Law, $P$ and $V$ have an inverse relationship.
3. Analyze the change: The question states that pressure is increased.
4. Determine the result: Because the relationship is inverse, an increase in pressure must lead to a decrease in volume.
5. Evaluate the options: • A: Incorrect. Increasing pressure actually increases the frequency of collisions because particles are closer together. • B: Correct. This aligns with Boyle's Law. • C: Incorrect. Increasing pressure forces particles closer together, so the intermolecular distance decreases, not increases. • D: Incorrect. This describes a decrease in pressure, not an increase.

Conclusion

When you compress a gas (increase pressure) at a constant temperature, the gas molecules occupy a smaller space, resulting in a decrease in volume.

Exam Tip

Whenever you see a gas law question, remember the "P-V-T" rule:

• Boyle's Law: Temperature is constant ($P \propto 1/V$).
• Charles's Law: Pressure is constant ($V \propto T$).
• Pressure Law: Volume is constant ($P \propto T$).
• Memory Trick: Think of a balloon. If you squeeze it (increase pressure), it gets smaller (decrease volume).