Draw a heating curve (such as the one in Figure 11.36 ) for...

Draw a heating curve (such as the one in Figure $11.36$ ) for 1 mole of methanol beginning at $170 \mathrm{~K}$ and ending at $350 \mathrm{~K}$. Assume that the values given here are constant over the relevant temperature ranges. $$ \begin{array}{ll} \hline \text { Melting point } & 176 \mathrm{~K} \\ \hline \text { Boiling point } & 338 \mathrm{~K} \\ \hline \Delta \mathrm{H}_{\text {fus }} & 2.2 \mathrm{~kJ} / \mathrm{mol} \\ \hline \Delta \mathrm{H}_{\text {vap }} & 35.2 \mathrm{~kJ} / \mathrm{mol} \\ \hline \mathrm{C}_{\text {s, solid }} & 105 \mathrm{~J} / \mathrm{mol} \cdot \mathrm{K} \\ \hline \mathrm{C}_{\text {s,liquid }} & 81.3 \mathrm{~J} / \mathrm{mol} \cdot \mathrm{K} \\ \hline \mathrm{C}_{\text {s,gas }} & 48 \mathrm{~J} / \mathrm{mol} \cdot \mathrm{K} \\ \hline \end{array} $$

Draw a heating curve (such as the one in Figure $11.36$ ) for 1 mole of methanol beginning at $170 \mathrm{~K}$ and ending at $350 \mathrm{~K}$. Assume that the values given here are constant over the relevant temperature ranges. $$
\begin{array}{ll}
\hline \text { Melting point } & 176 \mathrm{~K} \\
\hline \text { Boiling point } & 338 \mathrm{~K} \\
\hline \Delta \mathrm{H}_{\text {fus }} & 2.2 \mathrm{~kJ} / \mathrm{mol} \\
\hline \Delta \mathrm{H}_{\text {vap }} & 35.2 \mathrm{~kJ} / \mathrm{mol} \\
\hline \mathrm{C}_{\text {s, solid }} & 105 \mathrm{~J} / \mathrm{mol} \cdot \mathrm{K} \\
\hline \mathrm{C}_{\text {s,liquid }} & 81.3 \mathrm{~J} / \mathrm{mol} \cdot \mathrm{K} \\
\hline \mathrm{C}_{\text {s,gas }} & 48 \mathrm{~J} / \mathrm{mol} \cdot \mathrm{K} \\
\hline
\end{array}
$$

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Key Concepts

Heating Curve

A heating curve is a graphical representation that plots temperature against the amount of heat added to a substance. It displays regions where the temperature increases within a phase and flat regions where phase changes occur without a change in temperature.

Phase Transitions

Phase transitions refer to the changes of state, such as melting and boiling, that occur as heat is added to a substance. During these transitions, energy is used to alter the internal structure rather than increase temperature.

Latent Heat

Latent heat is the energy absorbed or released during a phase change, such as fusion (melting) or vaporization (boiling), at a constant temperature. It represents the energy needed to overcome intermolecular forces without a temperature change.

Specific Heat Capacity

Specific heat capacity is the amount of heat required to raise the temperature of a given quantity of a substance by one degree. Different phases of a substance typically have different specific heat capacities, affecting the slope of the heating curve.

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