Draw a heating curve (such as the one in Figure 12.36 ) for 1 mol of benzene beginning at 0^∘ C

Draw a heating curve (such as the one in Figure 12.36 ) for...

Draw a heating curve (such as the one in Figure 12.36 ) for $1 \mathrm{~mol}$ of benzene beginning at $0^{\circ} \mathrm{C}$ and ending at $100^{\circ} \mathrm{C}$. Assume that the values given here are constant over the relevant tempera- ture ranges. $$ \begin{array}{ll} \hline \text { Melting point } & 5.4^{\circ} \mathrm{C} \\ \text { Boiling point } & 80.1^{\circ} \mathrm{C} \\ \Delta \mathrm{H}_{\text {fus }} & 9.9 \mathrm{~kJ} / \mathrm{mol} \\ \Delta H_{\text {vap }} & 30.7 \mathrm{~kJ} / \mathrm{mol} \\ C_{\text {s, solid }} & 118 \mathrm{~J} / \mathrm{mol} \cdot \mathrm{K} \\ \mathrm{C}_{\text {s, liquid }} & 135 \mathrm{~J} / \mathrm{mol} \cdot \mathrm{K} \\ \mathrm{C}_{\mathrm{s}, \text { gas }} & 104 \mathrm{~J} / \mathrm{mol} \cdot \mathrm{K} \\ \hline \end{array} $$

Draw a heating curve (such as the one in Figure 12.36 ) for $1 \mathrm{~mol}$ of benzene beginning at $0^{\circ} \mathrm{C}$ and ending at $100^{\circ} \mathrm{C}$. Assume that the values given here are constant over the relevant tempera-
ture ranges.
$$
\begin{array}{ll}
\hline \text { Melting point } & 5.4^{\circ} \mathrm{C} \\
\text { Boiling point } & 80.1^{\circ} \mathrm{C} \\
\Delta \mathrm{H}_{\text {fus }} & 9.9 \mathrm{~kJ} / \mathrm{mol} \\
\Delta H_{\text {vap }} & 30.7 \mathrm{~kJ} / \mathrm{mol} \\
C_{\text {s, solid }} & 118 \mathrm{~J} / \mathrm{mol} \cdot \mathrm{K} \\
\mathrm{C}_{\text {s, liquid }} & 135 \mathrm{~J} / \mathrm{mol} \cdot \mathrm{K} \\
\mathrm{C}_{\mathrm{s}, \text { gas }} & 104 \mathrm{~J} / \mathrm{mol} \cdot \mathrm{K} \\
\hline
\end{array}
$$

Key Concepts

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. This property determines the slope of the temperature change in the regions of the heating curve where the substance is not undergoing a phase change, illustrating how different phases require different amounts of energy for temperature changes.

Latent Heat

Latent heat refers to the energy absorbed or released during a phase transition at a constant temperature. This concept is crucial for understanding heating curves because it explains why the temperature does not change during melting and boiling, even though energy is being added or removed.

Heating Curves

Heating curves are graphical representations that show how the temperature of a substance changes as heat is added. They illustrate the changes in temperature during both the heating of a single phase and the phase transitions between solid, liquid, and gas, making it easier to visualize how energy input affects the state of matter.

Phase Transitions

Phase transitions are the processes where a substance changes from one state of matter to another, such as melting (solid to liquid) or boiling (liquid to gas). During these transitions, the temperature remains constant while the substance absorbs or releases energy, which is represented by the plateau regions on a heating curve.

Transcript

00:01 Okay, we need to draw a heating curve such as the one in figure 12 .36 for one mole of benzene, beginning at 0 degrees celsius and ending at 100 degrees celsius, and we're going to assume that the values given are constant over the temperature ranges.

00:13 So our first important number we need to calculate is for the temperatures that it's a solid.

00:20 So between 0 degrees celsius and 5 .4 degrees celsius.

00:24 For this, we need to use the 118 joules per mole kelvin.

00:28 So we have the 5 .4 degrees celsius and we're going to multiply that by the one mole and by the 118 joules per mole kelvin.

00:41 Don't forget that as long as you're doing a difference in temperature it doesn't matter if you're doing degrees celsius or kelvin so that cancels and you get 637 .2 joules or 0 .64 kilojoules and if you convert our next important section is during melting or fusion, and because we have one mole, we can use the 9 .9 kilojoules as is.

01:11 After it melts, it's all a liquid, and it's a liquid from 5 .4 degrees celsius to 80 .1 degrees.

01:18 So if you subtract there, it's a liquid for 74 .7 degrees, and we have the one mole, and we're going to use the liquid this time, the 135 joules per mole kelvin.

01:36 So that cancels and you wind up with a whole lot of joules.

01:44 If we convert that to kilojoules, you get 10 .1 kilojoules for when it's a liquid.

01:52 Our next section, after it's a liquid, it vaporizes.

01:55 We're going to use the heat of vaporization.

01:58 And since there's just one mole, we can use that number as is.

02:05 And then our last section when it's a gas from 80 .1 degrees celsius to 100 degrees celsius...

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