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 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. $$ \begin{array}{ll} \hline \text { Melting point } & 176 \mathrm{~K} \\ \text { Boiling point } & 338 \mathrm{~K} \\ \Delta \mathrm{H}_{\text {fus }} & 2.2 \mathrm{~kJ} / \mathrm{mol} \\ \Delta \mathrm{H}_{\text {vap }} & 35.2 \mathrm{~kJ} / \mathrm{mol} \\ \mathrm{C}_{\mathrm{s}, \text { solid }} & 105 \mathrm{~J} / \mathrm{K} \\ \mathrm{C}_{\mathrm{s}} \text { , liquid } & 81.3 \mathrm{~J} / \mathrm{mol} \cdot \mathrm{K} \\ \mathrm{C}_{\mathrm{s}, \text { gas }} & 48 \mathrm{~J} / \mathrm{mol} \cdot \mathrm{K} \\ \hline \end{array} $$

Draw a heating curve (such as the one in Figure 12.36 ) 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.
$$
\begin{array}{ll}
\hline \text { Melting point } & 176 \mathrm{~K} \\
\text { Boiling point } & 338 \mathrm{~K} \\
\Delta \mathrm{H}_{\text {fus }} & 2.2 \mathrm{~kJ} / \mathrm{mol} \\
\Delta \mathrm{H}_{\text {vap }} & 35.2 \mathrm{~kJ} / \mathrm{mol} \\
\mathrm{C}_{\mathrm{s}, \text { solid }} & 105 \mathrm{~J} / \mathrm{K} \\
\mathrm{C}_{\mathrm{s}} \text { , liquid } & 81.3 \mathrm{~J} / \mathrm{mol} \cdot \mathrm{K} \\
\mathrm{C}_{\mathrm{s}, \text { gas }} & 48 \mathrm{~J} / \mathrm{mol} \cdot \mathrm{K} \\
\hline
\end{array}
$$

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.

Transcript

00:01 Draw heating curves such as the one in figure 12 .36 for one mole of methanol beginning at 170 kelvin and ending at 350 kelvin.

00:08 Assume that the values given here are constant over the relevant temperature ranges.

00:13 So in order to be able to draw the heating curve, we need to figure out the important temperatures and the important amounts of energy.

00:23 So the important temperatures of course are the 170 kelvin, which is our starting point.

00:28 The 176 kelvin, which is our melting point, the 300 ,000.

00:31 138 kelvin, which is our boiling point, and the 350 kelvin.

00:36 So those are the important points for our y -axis.

00:40 Now for the x -axis, for energy, we're going to have to do some calculations.

00:45 The substance methanol is a solid from 170 to 176 kelvin.

00:50 So that means for 6 kelvin and for one mole, it's going to be a solid.

01:01 So we're going to use the 105 joules per mole kelvin.

01:09 And we're going to multiply because the kelvin and the kelvin.

01:11 Moles cancel and we get 630 joules or if we convert that 0 .63 kilojoules.

01:26 Now so that's for when it's a solid.

01:28 Our next section is for when it's melting which we also call fusion so we want to use the heat of fusion for this part and since that's kilojoules per mole and we have one mole we can just use that number as it's 2 .2 kilojoules which is nice and simple.

01:46 Then our next section is liquid we're going to you need to use the 81 .3 joules per mole kelvin there.

01:54 And it is a liquid from 176 to 338 kelvin.

01:58 So if you subtract those two numbers, you get 162 kelvin and the one mole.

02:06 And we'll use the 81 .3 joules per mole kelvin.

02:11 So that moles and the kelvin cancel...

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