A sample of gas occupies a volume of 1.0 L at 25°C and constant pressure. What volume will the gas occupy at 100°C, assuming ideal gas behavior?

• A. 4.00 L
• B. 0.80 L
• C. 1.25 L
• D. 2.00 L

Answer: (C)

Verified step by step guidance

1. Identify the gas law applicable to this problem. Since the pressure is constant and the temperature and volume change, Charles's Law is appropriate. Charles's Law states that the volume of a gas is directly proportional to its absolute temperature when pressure is constant.
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 to each temperature: \(T(K) = T(^\circ C) + 273.15\). So, calculate \(T_1 = 25 + 273.15\) and \(T_2 = 100 + 273.15\).
4. Substitute the known values into the equation: \(V_1 = 1.0\,L\), \(T_1\) and \(T_2\) as calculated, and solve for \(V_2\) by rearranging the formula to \(V_2 = V_1 \times \frac{T_2}{T_1}\).
5. Calculate the ratio \(\frac{T_2}{T_1}\) and multiply by the initial volume \(V_1\) to find the final volume \(V_2\). This will give the volume the gas occupies at 100°C under constant pressure.