Draw a molar heating curve for sodium similar to that shown...

Draw a molar heating curve for sodium similar to that shown for water in Figure 10.10 . Begin with solid sodium at its melting point, and raise the temperature to $1000^{\circ} \mathrm{C}$ . The necessary data are $\mathrm{mp}=97.8^{\circ} \mathrm{C}, \quad \mathrm{bp}=883^{\circ} \mathrm{C}$ $\Delta H_{\mathrm{vap}}=89.6 \mathrm{kJ} / \mathrm{mol},$ and $\Delta H_{\mathrm{fusion}}=2.64 \mathrm{kJ} / \mathrm{mol}$ . Assume that the molar heat capacity is 20.8 $\mathrm{J} /(\mathrm{K} \cdot \mathrm{mol})$ for both liquid and vapor phases and does not change with temperature.

Key Concepts

Molar Heat Capacity

Molar heat capacity is the amount of heat required to raise the temperature of one mole of a substance by one degree Celsius (or Kelvin). In the context of a heating curve, the molar heat capacity determines the slope of the temperature increase within a single phase before a phase transition occurs.

Latent Heat

Latent heat is the amount of energy required for a phase change at constant temperature and pressure. It includes the latent heat of fusion (for melting) and the latent heat of vaporization (for boiling), and these energies are critical in determining the length of the plateau segments on a heating curve where the substance undergoes a phase transition.

Heating Curve

A heating curve is a graph that shows how the temperature of a substance changes as it absorbs heat. It typically includes sections where the temperature increases steadily, interrupted by flat segments at phase transitions where energy is used to change the state rather than raise the temperature. This curve helps illustrate the relationship between heat input, temperature change, and phase behavior of the substance.

Phase Transitions

Phase transitions are changes in the state of matter, such as from solid to liquid (melting) or liquid to gas (vaporization), that occur at specific temperatures. During these transitions, the temperature remains constant even though heat energy is being absorbed or released, reflecting the breaking or formation of intermolecular bonds.

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