Answer :

To solve the problem, we need to determine the final volume of the gas using the combined gas law, which relates the initial and final states (pressure, volume, and temperature) of a gas. Here's a step-by-step solution:

1. Initial Conditions:
- Initial volume ([tex]\(V_1\)[/tex]) = 115 mL
- Initial pressure ([tex]\(P_1\)[/tex]) = 45.8 kPa
- Initial temperature ([tex]\(T_1\)[/tex]) = [tex]\(57.2^{\circ}C\)[/tex]

2. Final Conditions:
- Final pressure ([tex]\(P_2\)[/tex]) = 99.3 kPa
- Final temperature ([tex]\(T_2\)[/tex]) = [tex]\(112.3^{\circ}C\)[/tex]

3. Convert Temperatures to Kelvin:
- The Kelvin temperature scale is required for gas law calculations. Convert Celsius to Kelvin using the formula:
[tex]\[
T (K) = T (^{\circ}C) + 273.15
\][/tex]
- [tex]\(T_1\)[/tex] in Kelvin = [tex]\(57.2 + 273.15 = 330.35 \, K\)[/tex]
- [tex]\(T_2\)[/tex] in Kelvin = [tex]\(112.3 + 273.15 = 385.45 \, K\)[/tex]

4. Use the Combined Gas Law:
The combined gas law is given by:
[tex]\[
\frac{P_1 \times V_1}{T_1} = \frac{P_2 \times V_2}{T_2}
\][/tex]
Rearranging to solve for the final volume ([tex]\(V_2\)[/tex]):
[tex]\[
V_2 = \frac{P_1 \times V_1 \times T_2}{P_2 \times T_1}
\][/tex]

5. Calculate the Final Volume ([tex]\(V_2\)[/tex]):
Substitute the known values into the equation:
[tex]\[
V_2 = \frac{45.8 \times 115 \times 385.45}{99.3 \times 330.35}
\][/tex]

6. Result:
- The final volume of the gas, [tex]\(V_2\)[/tex], is approximately 61.89 mL.

This step-by-step explanation shows how to find the final volume of the gas using its initial and final conditions with the combined gas law.

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Rewritten by : Barada