A sample of nitrogen gas has a pressure of 986 torr at 186°C. Assuming the volume and amount of gas remain constant, at what temperature in °C will the sample of gas have a pressure of 685 torr?

• A. 75°C
• B. 150°C
• C. 100°C
• D. 200°C

Answer: (A)

Verified step by step guidance

1. Identify the initial and final conditions of the gas. The initial pressure \( P_1 \) is 986 torr, and the initial temperature \( T_1 \) is 186°C. The final pressure \( P_2 \) is 685 torr, and we need to find the final temperature \( T_2 \) in °C.
2. Convert the initial temperature from Celsius to Kelvin, since gas law calculations require temperatures in Kelvin. Use the formula: \( T(K) = T(°C) + 273.15 \).
3. Apply Gay-Lussac's Law, which states that for a given amount of gas at constant volume, the pressure of the gas is directly proportional to its temperature in Kelvin. The formula is: \( \frac{P_1}{T_1} = \frac{P_2}{T_2} \).
4. Rearrange the formula to solve for the final temperature \( T_2 \): \( T_2 = \frac{P_2 \times T_1}{P_1} \).
5. Substitute the known values into the equation: \( T_2 = \frac{685 \text{ torr} \times (186 + 273.15) \text{ K}}{986 \text{ torr}} \). Calculate \( T_2 \) in Kelvin, then convert it back to Celsius by subtracting 273.15.