Sure, let's solve this problem step-by-step using Boyle's Law, which states that for a given mass of gas at constant temperature, the pressure and volume are inversely proportional. Mathematically, it can be expressed as:
[tex]\[ P_1 V_1 = P_2 V_2 \][/tex]
where:
- \( P_1 \) is the initial pressure,
- \( V_1 \) is the initial volume,
- \( P_2 \) is the final pressure,
- \( V_2 \) is the final volume.
Given:
- \( V_1 = 0.450 \) L
- \( P_1 = 1.00 \) atm
- \( V_2 = 2.00 \) L
We need to find the final pressure \( P_2 \).
First, rewrite the equation to solve for \( P_2 \):
[tex]\[ P_2 = \frac{P_1 V_1}{V_2} \][/tex]
Now, plug in the given values:
[tex]\[ P_2 = \frac{1.00 \text{ atm} \times 0.450 \text{ L}}{2.00 \text{ L}} \][/tex]
Perform the multiplication and division:
[tex]\[ P_2 = \frac{0.450 \text{ atm} \cdot \text{L}}{2.00 \text{ L}} \][/tex]
[tex]\[ P_2 = 0.225 \text{ atm} \][/tex]
So, the pressure when the volume is changed to \( 2.00 \) L is \( 0.225 \) atm.
Therefore, the correct answer is:
[tex]\[ 0.225 \text{ atm} \][/tex]
