Final answer:
To find the final temperature of a gas when its volume and pressure are changed, the combined gas law is used. After converting the initial temperature to Kelvin, the final temperature can be calculated by rearranging the formula of the combined gas law and inserting the given values.
Step-by-step explanation:
The question involves finding the final temperature of a gas when its volume and pressure are changed. This situation can be addressed through the combined gas law, which relates the pressure, volume, and temperature of a fixed amount of gas. The combined gas law formula is P1V1/T1 = P2V2/T2, where P1, V1, and T1 are the initial pressure, volume, and temperature, and P2, V2, and T2 are the final pressure, volume, and temperature respectively. Since the temperature must be in Kelvin, we first convert 500°C to Kelvin which is 500 + 273.15 = 773.15 K.
Starting with the formula, we can rearrange it to solve for T2 (the final temperature): T2 = (P2V2T1)/(P1V1). Plugging in the given values (after converting the temperatures to Kelvin), we get T2 = (3 atm * 2.4 L * 773.15 K) / (5 atm * 2.9 L). Calculating this gives us the final temperature in Kelvin, which can then be converted back to °C if needed.