To determine the final volume of the gas when pressure and temperature change, we can use the combined gas law. The combined gas law formula relates the pressure, volume, and temperature of a gas:
[tex]\[
\frac{P1 \cdot V1}{T1} = \frac{P2 \cdot V2}{T2}
\][/tex]
where:
- [tex]\(P1\)[/tex], [tex]\(V1\)[/tex], and [tex]\(T1\)[/tex] are the initial pressure, volume, and temperature, respectively.
- [tex]\(P2\)[/tex], [tex]\(V2\)[/tex], and [tex]\(T2\)[/tex] are the final pressure, volume, and temperature, respectively.
Given:
- Initial volume, [tex]\(V1 = 735 \, \text{mL}\)[/tex]
- Initial pressure, [tex]\(P1 = 1.20 \, \text{atm}\)[/tex]
- Initial temperature, [tex]\(T1 = 112^\circ \text{C}\)[/tex]
- Final pressure, [tex]\(P2 = 0.85 \, \text{atm}\)[/tex]
- Final temperature, [tex]\(T2 = 25^\circ \text{C}\)[/tex]
Firstly, we need to convert the temperatures from degrees Celsius to Kelvin:
[tex]\[
T1 = 112 + 273.15 = 385.15 \, \text{K}
\][/tex]
[tex]\[
T2 = 25 + 273.15 = 298.15 \, \text{K}
\][/tex]
Now, using the combined gas law formula, we need to isolate [tex]\(V2\)[/tex]:
[tex]\[
\frac{P1 \cdot V1}{T1} = \frac{P2 \cdot V2}{T2}
\][/tex]
Rearranging for [tex]\(V2\)[/tex]:
[tex]\[
V2 = \frac{P1 \cdot V1 \cdot T2}{P2 \cdot T1}
\][/tex]
Substitute the given values into the equation:
[tex]\[
V2 = \frac{1.20 \, \text{atm} \times 735 \, \text{mL} \times 298.15 \, \text{K}}{0.85 \, \text{atm} \times 385.15 \, \text{K}}
\][/tex]
Calculate the values step-by-step:
[tex]\[
V2 = \frac{(1.20 \times 735 \times 298.15)}{(0.85 \times 385.15)}
\][/tex]
[tex]\[
V2 = \frac{262,887}{327.37775}
\][/tex]
[tex]\[
V2 \approx 803.2570961657414 \, \text{mL}
\][/tex]
Thus, the final volume of the gas is approximately [tex]\( 803.26 \)[/tex] mL when the pressure and temperature are changed as specified.
