Final answer:
To find the final temperature of the CO₂ gas after a pressure change, apply Gay-Lussac's Law using the initial temperature in Kelvin and the ratio of final to initial pressures. The final temperature is calculated to be 387.4 K.
Step-by-step explanation:
The student's question involves finding the final temperature of a sample of CO₂ gas when its pressure changes under constant volume conditions. This scenario is best described by Gay-Lussac's Law, which states that the pressure of a gas is directly proportional to its temperature in kelvins when the volume and the amount of gas are held constant. Using this law, we can set up a proportion, P₁/T₁ = P₂/T₂, where P₁ and T₁ are the initial pressure and temperature, and P₂ and T₂ are the final pressure and temperature.
To calculate the final temperature (T₂), we first convert the initial temperature from Celsius to Kelvin, T₁ = 25.0°C + 273 = 298 K. We then rearrange the proportion to solve for T₂, resulting in T₂ = T₁ * (P₂/P₁). Substituting the known values gives us T₂ = 298 K * (1.3 atm/1.0 atm) = 387.4 K, which is the final temperature of the gas.