Which of the following water samples has the greatest average kinetic energy per molecule?

• A. A sample of ice at 0 °C
• B. A sample of H2O vapor at 120 °C
• C. A sample of liquid H2O at 0 °C
• D. A sample of liquid H2O at 25 °C

Answer: (B)

Verified step by step guidance

1. Recall that the average kinetic energy of molecules in a substance is directly proportional to its absolute temperature (in Kelvin). The relationship is given by the equation: \(\text{KE}_{\text{avg}} = \frac{3}{2} k_B T\), where \(k_B\) is the Boltzmann constant and \(T\) is the temperature in Kelvin.
2. Convert all given temperatures from Celsius to Kelvin by adding 273.15 to each Celsius temperature: \(T(K) = T(^\circ C) + 273.15\).
3. Calculate the Kelvin temperatures for each sample: ice at 0 °C, liquid water at 0 °C, liquid water at 25 °C, and water vapor at 120 °C.
4. Compare the Kelvin temperatures of all samples because the average kinetic energy per molecule depends only on temperature, not on the phase (solid, liquid, or gas). The sample with the highest Kelvin temperature will have the greatest average kinetic energy per molecule.
5. Identify the sample with the highest temperature in Kelvin, which corresponds to the greatest average kinetic energy per molecule.