Make a rough, qualitative plot of the standard molar entropy versus temperature for methane from 0 K to 298 K. Incorporate the following data into your plot: mp = -182 °C; bp = -164 °C; °S = 186.2 J/(K*mol) at 25 °C.

Verified step by step guidance

1. Convert the melting point (mp) and boiling point (bp) from Celsius to Kelvin. Use the formula: \( T(K) = T(°C) + 273.15 \).
2. Identify the phases of methane at different temperature ranges: solid below the melting point, liquid between the melting and boiling points, and gas above the boiling point.
3. Understand that the standard molar entropy (\( S^\circ \)) generally increases with temperature due to increased molecular motion and disorder.
4. Note that at phase transitions (melting and boiling points), there is a significant increase in entropy due to the change in state, even though the temperature remains constant during the transition.
5. Sketch the plot: start at 0 K with \( S^\circ = 0 \), increase gradually in the solid phase, show a sharp increase at the melting point, continue increasing in the liquid phase, show another sharp increase at the boiling point, and finally, increase steadily in the gas phase, reaching \( S^\circ = 186.2 \text{ J/(K*mol)} \) at 298 K.

Key Concepts

Standard Molar Entropy

Standard molar entropy is a measure of the amount of disorder or randomness in a system at a standard state, typically defined at 1 bar and a specified temperature. It reflects the number of accessible microstates for a given amount of substance. For methane, the standard molar entropy at 25 °C is 186.2 J/(K·mol), indicating its degree of disorder at that temperature.

Phase Changes and Temperature

Phase changes, such as melting and boiling, significantly affect the entropy of a substance. For methane, the melting point (-182 °C) and boiling point (-164 °C) indicate temperature ranges where the substance transitions between solid, liquid, and gas phases. These transitions are associated with changes in entropy, as the disorder increases when moving from solid to liquid to gas.

Qualitative Plotting

Qualitative plotting involves creating a visual representation of data without precise numerical values, focusing instead on trends and relationships. In this context, plotting standard molar entropy against temperature for methane requires understanding how entropy changes with temperature, particularly around phase transitions, to illustrate the general behavior of entropy from 0 K to 298 K.