Use the following data to sketch a heating curve for one...

Use the following data to sketch a heating curve for one mole of methanol. Start the curve at $-100^{\circ} \mathrm{C}$ and end it at $100^{\circ} \mathrm{C}$. $$\begin{array}{ll}\hline \text { Boiling point } & 65^{\circ} \mathrm{C} \\\hline \text { Melting point } & -94^{\circ} \mathrm{C} \\\hline \text { Heat of vaporization } & 35.3 \mathrm{kJ} / \mathrm{mol} \\\hline \text { Heat of fusion }\left(\Delta \mathrm{H}_{\text {fus }}\right) & 3.18 \mathrm{kJ} / \mathrm{mol} \\\hline \text { Molar heat capacity }(\ell) & 81.1 \mathrm{J} /\left(\mathrm{mol} \cdot^{\circ} \mathrm{C}\right) \\\hline \text { Molar heat capacity }(g) & 43.9 \mathrm{J} /\left(\mathrm{mol} \cdot^{\circ} \mathrm{C}\right) \\\hline \text { Molar heat capacity }(\mathrm{s}) & 48.7 \mathrm{J} /\left(\mathrm{mol} \cdot^{\circ} \mathrm{C}\right) \\\hline\end{array}$$

Use the following data to sketch a heating curve for one mole of methanol. Start the curve at $-100^{\circ} \mathrm{C}$ and end it at $100^{\circ} \mathrm{C}$.
$$\begin{array}{ll}\hline \text { Boiling point } & 65^{\circ} \mathrm{C} \\\hline \text { Melting point } & -94^{\circ} \mathrm{C} \\\hline \text { Heat of vaporization } & 35.3 \mathrm{kJ} / \mathrm{mol} \\\hline \text { Heat of fusion }\left(\Delta \mathrm{H}_{\text {fus }}\right) & 3.18 \mathrm{kJ} / \mathrm{mol} \\\hline \text { Molar heat capacity }(\ell) & 81.1 \mathrm{J} /\left(\mathrm{mol} \cdot^{\circ} \mathrm{C}\right) \\\hline \text { Molar heat capacity }(g) & 43.9 \mathrm{J} /\left(\mathrm{mol} \cdot^{\circ} \mathrm{C}\right) \\\hline \text { Molar heat capacity }(\mathrm{s}) & 48.7 \mathrm{J} /\left(\mathrm{mol} \cdot^{\circ} \mathrm{C}\right) \\\hline\end{array}$$

Key Concepts

Heating Curve

A heating curve is a graph that represents the change in temperature of a substance as heat is added over time. It typically shows segments where the temperature increases as heat is added (sensible heat) and flat regions where the heat goes into changing the state rather than raising the temperature (phase transitions).

Specific Heat Capacity

Specific heat capacity is a property that defines how much heat energy is required to raise the temperature of a given amount of a substance by one degree Celsius. It plays a crucial role in the parts of the heating curve where the substance is being heated without undergoing a phase change, allowing for the calculation of energy addition during temperature changes.

Phase Transitions

Phase transitions refer to the changes between the states of matter—solid, liquid, and gas—that occur when heat is added or removed. On a heating curve, phase transitions appear as flat regions because the temperature remains constant while the substance absorbs or releases latent heat to overcome intermolecular forces during melting or boiling.

States of Matter

The states of matter (solid, liquid, and gas) are physical forms in which a substance can exist depending on temperature and pressure. Understanding these states is crucial for interpreting heating curves, as different heat capacities and latent heat values apply to each state, influencing the shape of the curve during both sensible heating and phase transitions.

Latent Heat

Latent heat is the amount of heat energy required for a substance to undergo a phase change at constant temperature. This energy does not cause a temperature change but instead facilitates the change in molecular structure, characteristic of transitions between solid, liquid, and gas states.

Transcript

00:01 Okay, now we do problem 51.

00:04 So we have to write everything down first.

00:08 Okay, now i have 51.

00:13 So the first time we have to write boiling boiling point, 65 degrees, right? and we have mountain boy about 94 celsius degrees.

00:26 And heat of vaporization.

00:36 We have delta -h fusion about, about 53 .3 kilojou over more, right? and next heat of fusion, let's add up fusion.

00:55 Oh sorry, so this would be the vaporization here.

01:03 Let's hit off vaporization.

01:08 So hit up fusion.

01:12 So for this delta -edge fusion equal 3 .18 kilojou over more unless we have more like heat capacity more like heat capacity if this is in a liquid phase so we have this equal you see this equal 81 .1 jow over more.

01:56 So this equal 81 .1 joll over more.

02:05 But because we see this kilojou, so we continue convert it to kilojou, right? so later we can add together.

02:17 Okay and next more like heat capacity if they are in gas phase.

02:29 So this equal 43 .9 jow over more.

02:35 And then this must be equal 0 .0439 kiosho over more.

02:44 So the last one, heat up, motor heat capacity in a solid phase.

02:51 Okay, now this equals 48.

02:54 48 .7 jow over more.

02:58 So this equal 0.

03:01 For 87 kilojou over more.

03:05 Okay? and then we now we can start to draw the curve of the methanol.

03:24 So we have to draw the good line here.

03:38 Okay.

03:44 And now we start from negative 100, right? so this from here to this negative.

03:55 Let's see.

03:58 So what temperature here? okay.

04:03 And for this we say from this one to this one, this should be the, it's still melting, right? and then it continues to higher temperature, that boiling point.

04:19 This should be 65, right? 65.

04:29 And then boiling boil.

04:31 During this time, the liquid phase and the boiling phase, the other gas phase, stay together.

04:42 And we need to draw the horizontal light.

04:48 This one, because it needs more temperature to all of them vaporize, so we have to get the line stronger, longer.

04:56 And then it continues to, after they finish, vaporate, the temperature will increase.

05:06 And this is not only the gas in this side...