Question

A sample of nitrogen gas has a temperature of 22.7oC when the volume of the container is 12.2L and it is under 150.4kPa of pressure. What temperature, in Kelvin, would the gas need to be in order to occupy a 9.7L container at 101.3kPa? Show all your work and round your answer to the hundredths place.

Answer 1

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;

$\dfrac{P_1 \times V_1}{T_1} = \dfrac{P_2 \times V_2}{T_2}$

$\therefore \ T_2 = \dfrac{P_2 \times V_2 \times T_1 }{P_1 \times V_1}$

Plugging in the values gives;

$\therefore \ T_2 = \dfrac{101.3 \, kPa \times 9.7 \ L \times 295.85 K}{150.4 \ kPa \times 12.2 \ L} \approx 158.4327959 \ K$

The final temperature of the gas, T₂ ≈ 158.4 K