A sample of gas has a volume of 32 L at 75°C. At what temperature (in °C) will the volume be equal to 16 L, assuming pressure and amount of gas remain constant?

• A. −99°C
• B. −148°C
• C. 37.5°C
• D. 0°C

Answer: (A)

Verified step by step guidance

1. Identify the gas law that relates volume and temperature at constant pressure and amount of gas. This is Charles's Law, which states that \(\frac{V_1}{T_1} = \frac{V_2}{T_2}\), where \(V\) is volume and \(T\) is temperature in Kelvin.
2. Convert the initial temperature from Celsius to Kelvin using the formula \(T(K) = T(^\circ C) + 273.15\). So, \(T_1 = 75 + 273.15\) K.
3. Assign the known values: \(V_1 = 32\) L, \(V_2 = 16\) L, and \(T_1\) as calculated in Kelvin. The unknown is \(T_2\) in Kelvin.
4. Rearrange Charles's Law to solve for \(T_2\): \(T_2 = \frac{V_2 \times T_1}{V_1}\).
5. Calculate \(T_2\) in Kelvin using the values, then convert back to Celsius by subtracting 273.15: \(T_2(^\circ C) = T_2(K) - 273.15\).