Behavior of ideal gas under temperature change

What is the new pressure of the gas inside the container?

If the temperature changes from 20 °C to 82 °C with no change in volume or amount of gas, what is the new pressure, (P2), of the gas inside the container?

A) 805 torr
B) 820 torr
C) 895 torr
D) 830 torr

Answer:

Using Gay-Lussac's Law, where pressure and temperature are directly proportional for a given mass and constant volume of gas, the new pressure of the gas would be approximately 930 torr when the temperature rises from 20 °C to 82 °C. The provided answer options appear to be incorrect in this case.

Explanation: The question concerns the behavior of an ideal gas when subjected to a change in temperature while maintaining constant volume and quantity of gas. According to Gay-Lussac's Law, for a given mass and constant volume of an ideal gas, the pressure is directly proportional to the temperature in kelvins. To find the new pressure after a temperature change, one can use the equation "1 = (P1/T1) = (P2/T2)", where P1 and T1 are the initial pressure and temperature and P2 and T2 are the final pressure and temperature.

Initially, the pressure (P1) is 805 torr and the temperature (T1) is 20 °C, which is 293.15 K (since K = °C + 273.15). The final temperature (T2) is given as 82 °C, which is 355.15 K. Applying the equation, P2 = P1 * (T2/T1) gives us the new pressure P2. Calculating this, we get P2 = 805 torr * (355.15 K / 293.15 K), which upon solving approximately equals 930 torr.

However, the provided options do not contain this result, which suggests there might be an error in the question or the options provided. If this calculation were part of a multiple-choice question, none of the options would be correct. Therefore, it's important to recheck the question prompt and the possible answers to ensure there isn't a mistake.