Final answer:
The final pressure of the gas after heating the closed tank to 373 K, with the original pressure of 406 kPa at 303 K, is calculated using Gay-Lussac's law, resulting in a pressure of 499.80 kPa. The answer is D. 499.80 kPa.
Step-by-step explanation:
The student is asking about the change in pressure of a gas inside a closed tank when the temperature is increased, having the initial pressure and temperature and the final temperature available, under the assumption that the volume of the tank remains constant. According to Gay-Lussac's law, which states that the pressure of a gas is directly proportional to its temperature in kelvins when the volume is constant, we can calculate the final pressure. We use the formula P1/T1 = P2/T2 where P1 is the initial pressure (406 kPa), T1 is the initial temperature (303 K), P2 is the final pressure, and T2 is the final temperature (373 K).
The initial pressure and temperature were 406 kPa and 303 K, respectively. After heating, the temperature rose to 373 K. Applying the formula:
- P1/T1 = P2/T2
- (406 kPa) / (303 K) = P2 / (373 K)
- P2 = (406 kPa * 373 K) / 303 K
- P2 = 499.80 kPa
Therefore, the correct answer is D. 499.80 kPa.