Certainly! Let's solve this problem step-by-step using Boyle's Law.
Boyle's Law states that for a given mass of gas at a constant temperature, the product of the pressure and volume is constant. Mathematically, this can be expressed as:
[tex]\[ P_1 V_1 = P_2 V_2 \][/tex]
Where:
- [tex]\( P_1 \)[/tex] is the initial pressure.
- [tex]\( V_1 \)[/tex] is the initial volume.
- [tex]\( P_2 \)[/tex] is the final pressure (standard pressure in this context).
- [tex]\( V_2 \)[/tex] is the final volume we need to find.
Given:
- Initial volume ([tex]\( V_1 \)[/tex]) = 500.0 mL
- Initial pressure ([tex]\( P_1 \)[/tex]) = 745.0 mmHg
- Standard pressure ([tex]\( P_2 \)[/tex]) = 760.0 mmHg
We need to solve for the final volume ([tex]\( V_2 \)[/tex]) at standard pressure.
Rearranging the formula to solve for [tex]\( V_2 \)[/tex]:
[tex]\[ V_2 = \frac{P_1 \times V_1}{P_2} \][/tex]
Now, plug in the given values:
[tex]\[ V_2 = \frac{745.0 \text{ mmHg} \times 500.0 \text{ mL}}{760.0 \text{ mmHg}} \][/tex]
Perform the multiplication and division:
[tex]\[ V_2 = \frac{372500.0 \text{ mmHg} \times \text{mL}}{760.0 \text{ mmHg}} \][/tex]
[tex]\[ V_2 \approx 490.13157894736844 \text{ mL} \][/tex]
So, the volume of the gas at standard pressure (760.0 mmHg) will be approximately 490.13 mL.
