Final answer:
The final pressure of an ideal gas heated from 200 degrees Celsius to 400 degrees Celsius with an initial pressure of 45 torr is approximately 64 torr, calculated using Gay-Lussac's Law.
Step-by-step explanation:
To find the final pressure of a sample of an ideal gas that is heated from 200 degrees Celsius to 400 degrees Celsius, we can use the Gay-Lussac's Law, which states that the pressure of a gas is directly proportional to its temperature in kelvins, provided that the volume and the amount of gas are kept constant.
First, we convert the temperatures from Celsius to Kelvin by adding 273.15 to each temperature. This gives us:
- Tinitial = 200 °C + 273.15 = 473.15 K
- Tfinal = 400 °C + 273.15 = 673.15 K
Next, we use the formula Pfinal / Tfinal = Pinitial / Tinitial, where P is the pressure and T is the temperature in Kelvins. Inserting the values we are aware of, we obtain:
Pfinal / 673.15 K = 45 torr / 473.15 K
By solving for Pfinal, we find that Pfinal = (45 torr * 673.15 K) / 473.15 K
Pfinal ≈ 64 torr
Therefore, the final pressure of the gas after being heated is approximately 64 torr.