How much heat (in kJ) is evolved in converting 1.00 mol of...

How much heat (in kJ) is evolved in converting 1.00 mol of steam at $145^{\circ} \mathrm{C}$ to ice at $-50^{\circ} \mathrm{C} ?$ The heat capacity of steam is $2.01 \mathrm{J} / \mathrm{g} \cdot^{\circ} \mathrm{C},$ and that of ice is 2.09 $\mathrm{J} / \mathrm{g} \cdot^{\circ} \mathrm{C}$ .

How much heat (in kJ) is evolved in converting 1.00 mol of steam at
$145^{\circ} \mathrm{C}$ to ice at $-50^{\circ} \mathrm{C} ?$ The heat capacity of steam is $2.01 \mathrm{J} / \mathrm{g} \cdot^{\circ} \mathrm{C},$ and
that of ice is 2.09 $\mathrm{J} / \mathrm{g} \cdot^{\circ} \mathrm{C}$ .

Key Concepts

Thermodynamic Energy Balance

This concept involves summing up all individual energy changes—including those due to temperature changes (using specific heat capacity) and those due to phase changes (using latent heat)—to determine the total energy evolved or absorbed in a process.

Specific Heat Capacity

This is the amount of energy required to raise the temperature of a unit mass of a substance by one degree. It is used when calculating the energy change associated with temperature changes in a single phase, without any change in state.

Latent Heat

Latent heat refers to the energy absorbed or released during a phase change at a constant temperature. It is crucial for calculating the energy changes during transitions such as condensation or freezing.

Phase Changes

Phase changes involve transitions between different states of matter, such as from gas to liquid or liquid to solid. During these transitions, energy changes occur that do not involve a temperature change and are accounted for by latent heat.

Transcript

00:02 Heat is a form of energy that flows from a hotter body to a colder body.

00:06 Consider here one mole of ice or rather one mole of steam that's water in the form of gas.

00:16 Initially at temperature of 145 degrees celsius, we want to find the total heat that is needed in order to solidify it.

00:26 That means to turn it into ice at negative 50 degrees celsius.

00:32 So we note that the following process that this sample of ice or sample of steam would undergo.

00:38 First it should cool down by losing q1 heat to its boiling temperature of 100 degrees celsius.

00:48 Now after reaching the boiling temperature, it will condense by giving off q2 so that from vapor turns into let's say h2o vapor.

01:03 Let's label the states of matter h2o gas.

01:08 Initially it turns into still h2o gas but at a lower temperature.

01:14 Now after losing q2, it will turn into liquid and after it has turned into liquid, it will cool down some more until it reaches the freezing temperature by releasing q3.

01:30 Once it is at freezing temperature, it will freeze at constant temperature still at zero, turning liquid into solid by releasing q4.

01:41 And finally once it is in ice form, it will cool down further by releasing q5 amount of heat so that it turns its temperature lowers down to negative 50 degrees centigrade.

01:56 So we have two of five heat terms here and after that we will add them all together.

02:04 So for the states or for the process that involves heat at our temperature change, we will use the formula m times c times delta t such as for q1, we will multiply the mass, the specific heat and the change in the temperature delta t.

02:24 We have one mole of water.

02:28 One mole of water has mass equivalent to its molar which is 18 .02 grams.

02:36 So we have the mass being equal to 18 .02 then multiplied by the specific heat since it is steam, we use the specific heat of steam which is 2 .01.

02:49 The change in temperature is 100.

02:52 That's the final temperature minus the initial temperature which is 145.

02:56 So we solve for and we get negative 1629 .909 joules.

03:06 So let's do the same for 3 and 5 because those are the ones involving temperature change.

03:15 So we have still 18 .02, the specific heat since it is a liquid state, we have that as 4 .18...

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