Sure, let's solve this problem step-by-step.
1. Identify the known quantities:
- Initial volume, [tex]\(V_1 = 0.450 \text{ L}\)[/tex]
- Initial pressure, [tex]\(P_1 = 1.00 \text{ atm}\)[/tex]
- New volume, [tex]\(V_2 = 2.00 \text{ L}\)[/tex]
2. Identify what we need to find:
- The new pressure, [tex]\(P_2\)[/tex]
3. Use the relationship [tex]\(P_1 V_1 = P_2 V_2\)[/tex]:
This equation states that the product of the initial pressure and volume is equal to the product of the new pressure and volume, provided the temperature remains constant.
4. Rearrange the formula to solve for [tex]\(P_2\)[/tex]:
[tex]\[
P_2 = \frac{P_1 V_1}{V_2}
\][/tex]
5. Substitute the known values into the equation:
[tex]\[
P_2 = \frac{(1.00 \text{ atm}) \times (0.450 \text{ L})}{2.00 \text{ L}}
\][/tex]
6. Perform the calculation:
[tex]\[
P_2 = \frac{0.450 \text{ atm} \cdot \text{L}}{2.00 \text{ L}}
\][/tex]
[tex]\[
P_2 = 0.225 \text{ atm}
\][/tex]
Therefore, when the volume of the gas changes to 2.00 L, the pressure is [tex]\(0.225 \text{ atm}\)[/tex]. Thus, the correct answer is:
[tex]\[
\boxed{0.225 \text{ atm}}
\][/tex]
