Draw a heating curve (such as the one in Figure 12.33 ) for...

Draw a heating curve (such as the one in Figure 12.33 ) 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.

Key Concepts

Heating Curve

A heating curve is a graphical representation that shows how a substance's temperature changes as heat is added. The curve typically features segments where the temperature increases steadily within a phase and flat regions where the temperature remains constant during a phase transition.

Phase Transitions

Phase transitions occur when a substance changes from one state of matter to another, such as solid to liquid or liquid to gas. On a heating curve, these transitions are represented by horizontal lines, where the added heat is used to change the phase rather than to increase temperature.

Latent Heat

Latent heat is the amount of heat required to effect a phase change in a substance at a constant temperature. This concept explains the flat segments in a heating curve, where energy input is absorbed in overcoming the intermolecular forces during melting or boiling.

Specific Heat Capacity

Specific heat capacity is the quantity of heat needed to raise the temperature of a given amount of a substance by one degree. It determines the slope of the temperature increase during heating in regions where the substance remains in the same phase.

Transcript

00:01 Our heat curve is beginning at 170 kelvin.

00:03 This makes the methanol solid since we're below its melting point 176 kelvin.

00:09 So the first step will be to raise the methanol to its melting point, which would be an increase in 6 kelvin.

00:18 To calculate the amount of energy or heat we need to add to reach this temperature, we will take the increase in temperature desired, which is 6 kelvin, and multiply it by the specific heat of methanol as a solid, since it's good.

00:31 Currently a solid, giving us an addition of 0 .63 kilojoules.

00:41 So we're solid.

00:42 We'll have 0 .63 added, it would be at 176.

00:47 Which means our point's going to be roughly here.

00:51 And this addition happens linearly from our starting point.

00:54 So we're going to draw that straight line.

00:57 And now we're in a transition phase since all the energy that's being used or being added is going to be used to convert the method.

01:06 From a solid to a liquid.

01:10 And we calculate the amount of heat needed to add to the methanol by using the heat of fusion, which is 2 .2 kilojoules per mole.

01:19 Since you only have one mole, that means we only need to add 2 .2 kilojoules.

01:24 So we're going to be 2 .2 plus 0 .63, giving us pretty close to 3.

01:30 And since all the energies we use to change phase, we don't actually change temperature.

01:35 So we have this little straight line here.

01:38 And now all of our methanol is liquid.

01:40 So the next step is then to take the methanol from the boiling or the melting point we're currently at to the boiling point.

01:48 This is a much greater temperature increase...

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