A sample of gas occupies 25.0 L at 100°C and constant pressure. What volume will the gas occupy at 200°C, assuming ideal gas behavior?

• A. 50.0 L
• B. 12.5 L
• C. 31.6 L
• D. 25.0 L

Answer: (C)

Verified step by step guidance

1. Identify the type of gas law applicable. Since the pressure is constant and the temperature and volume change, Charles's Law is appropriate. Charles's Law states that volume is directly proportional to temperature (in Kelvin) at constant pressure.
2. Write down Charles's Law formula: \(\frac{V_1}{T_1} = \frac{V_2}{T_2}\), where \(V_1\) and \(T_1\) are the initial volume and temperature, and \(V_2\) and \(T_2\) are the final volume and temperature.
3. Convert the given temperatures from Celsius to Kelvin by adding 273.15: \(T_1 = 100 + 273.15\) K and \(T_2 = 200 + 273.15\) K.
4. Substitute the known values into the equation: \(\frac{25.0\, \text{L}}{T_1} = \frac{V_2}{T_2}\), then solve for \(V_2\) by rearranging the equation to \(V_2 = 25.0 \times \frac{T_2}{T_1}\).
5. Calculate \(V_2\) using the temperatures in Kelvin to find the new volume the gas will occupy at 200°C under constant pressure.