At 2.0 atm pressure, the volume of a gas is 4.0 L. If the pressure is reduced to 1.0 atm while keeping the…

1. Analyze the question

We are given the initial pressure ($P_1$) and initial volume ($V_1$) of a gas. We need to find the new volume ($V_2$) when the pressure is changed to a new value ($P_2$), while 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 volume of the gas is inversely proportional to its pressure.

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:

• $P_1 = 2.0 \text{ atm}$
• $V_1 = 4.0 \text{ L}$
• $P_2 = 1.0 \text{ atm}$
• $V_2 = ?$

Step-by-step calculation: Substitute the values into the Boyle's Law equation:

Multiply the left side:

Solve for $V_2$:

4. Identify the answer

The new volume of the gas is 8.0 L. This matches option C.

5. Tip

Exam Strategy: Always check the relationship between the variables. Since pressure was reduced (from 2.0 to 1.0), the volume must increase (from 4.0 to 8.0) because they are inversely proportional. If your calculated volume is smaller than the initial volume when pressure decreases, you know you've made a calculation error!