A sample of gas has a volume of 100.0 mL at 135 °C and 1.00 atm pressure. What will be the volume of the gas at 25 °C and 1.00 atm, assuming the amount of gas remains constant and it behaves ideally?

• A. 50.0 mL
• B. 77.6 mL
• C. 135 mL
• D. 100.0 mL

Answer: (B)

Verified step by step guidance

1. Identify the known variables: initial volume \(V_1 = 100.0\) mL, initial temperature \(T_1 = 135\,^{\circ}\mathrm{C}\), final temperature \(T_2 = 25\,^{\circ}\mathrm{C}\), and pressure remains constant at 1.00 atm.
2. Convert the temperatures from Celsius to Kelvin because gas law calculations require absolute temperature: use \(T(K) = T(^{\circ}C) + 273.15\). So, calculate \(T_1\) and \(T_2\) in Kelvin.
3. Since pressure and amount of gas are constant, apply Charles's Law, which relates volume and temperature: \(\frac{V_1}{T_1} = \frac{V_2}{T_2}\).
4. Rearrange Charles's Law to solve for the final volume \(V_2\): \(V_2 = V_1 \times \frac{T_2}{T_1}\).
5. Substitute the known values of \(V_1\), \(T_1\), and \(T_2\) (in Kelvin) into the equation to calculate \(V_2\), the final volume of the gas.