Answer:
The final temperature of the gas would need to be approximately 158.4 K
Explanation:
The details of the sample of nitrogen gas are;
The initial temperature of the nitrogen gas, T₁ = 22.7°C = 295.85 K
The initial volume occupied by the gas, V₁ = 12.2 L
The initial pressure of the gas, P₁ = 150.4 kPa
The final volume of the gas, V₂ = 9.7 L
The final pressure of the gas, P₂ = 101.3 kPa
Let 'T₂', represent the final temperature of the gas, by the ideal gas equation, we have;
[tex]\dfrac{P_1 \times V_1}{T_1} = \dfrac{P_2 \times V_2}{T_2}[/tex]
[tex]\therefore \ T_2 = \dfrac{P_2 \times V_2 \times T_1 }{P_1 \times V_1}[/tex]
Plugging in the values gives;
[tex]\therefore \ T_2 = \dfrac{101.3 \, kPa \times 9.7 \ L \times 295.85 K}{150.4 \ kPa \times 12.2 \ L} \approx 158.4327959 \ K[/tex]
The final temperature of the gas, T₂ ≈ 158.4 K
