The volume of a fixed mass of gas is 10cm3 when its pressure is 400cmHg. Determine the volume of the gas when its pressure is 200cmHg.

1. Analyze the question

We are given the initial volume ($V_1$) and initial pressure ($P_1$) of a fixed mass of gas. We need to find the new volume ($V_2$) when the pressure changes to a new value ($P_2$), assuming the temperature remains constant.

2. Explain the concept

This problem is governed by Boyle’s Law. Boyle’s Law states that for a fixed mass of gas at a constant temperature, the pressure ($P$) is inversely proportional to the volume ($V$).

The formula is:

Where:

• $P_1$ = Initial pressure
• $V_1$ = Initial volume
• $P_2$ = Final pressure
• $V_2$ = Final volume

3. Show the solution

Given data:

• $V_1 = 10\text{ cm}^3$
• $P_1 = 400\text{ cmHg}$
• $P_2 = 200\text{ cmHg}$
• $V_2 = ?$

Step-by-step calculation: Using the formula $P_1V_1 = P_2V_2$:

To find $V_2$, divide both sides by 200:

4. Identify the answer

Comparing our result to the given options, the correct answer is D.

5. Tip

When using Boyle's Law, remember the relationship: If pressure is halved, volume must double. In this question, the pressure dropped from 400 to 200 (it was halved), so the volume must increase from 10 to 20 (it doubled). This is a quick way to verify your answer without even needing a calculator!