How much heat in kilojoules is required to warm 10.0 g of ice, initially at -10.0^∘ C, to steam

How much heat in kilojoules is required to warm 10.0 g of...

Key Concepts

Unit Conversion

Unit conversion is the process of converting quantities from one unit to another to maintain consistency across calculations. In thermodynamics, converting energy units (e.g., from joules to kilojoules) ensures accurate representation and comprehension of the energy scales involved.

Energy Calculation in Multi-step Processes

This involves breaking down a thermodynamic process into various steps, such as heating a substance, changing its phase, and further heating the new phase. The total energy required is obtained by summing the energy components for each individual step.

Phase Changes

Phase changes involve transitions between different states of matter, such as solid to liquid (melting) and liquid to gas (vaporization). Understanding these transitions is crucial because they require specific amounts of energy (latent heats) that do not change the temperature.

Latent Heat

Latent heat is the amount of heat absorbed or released by a substance during a phase change at a constant temperature. It includes latent heat of fusion (melting) and latent heat of vaporization (boiling), both of which are essential when a substance changes its state without a temperature change.

Specific Heat Capacity

This concept refers to the amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius. It is a crucial factor when calculating the energy required to change the temperature of a material without a phase change.

Transcript

00:02 Hi there.

00:04 In this problem, we are starting out with some ice and warming it up until it becomes steam.

00:09 So that sounds like a heating curve problem.

00:15 So i want to start off by sketching out a heating curve for water.

00:21 Because we're working with water here.

00:23 So any heating curve, our x -axis represents heat being added.

00:31 And our y -axis represents the temperature in degrees celsius.

00:37 So if we start out with i, and we start adding heat at a constant rate, that ice is going to warm up until it reaches its melting point.

00:47 And then it will flat line at its melting point, which for water is of course 0 degrees celsius.

00:53 So it will flatline until it is all melt and becomes liquid water.

00:57 Once it is all liquid water, it will heat up again until it reaches its boiling point and then it will again flatline until it all changes to vapor.

01:11 And then that vapor can be heated up again.

01:14 And of course, the boiling point of water is 100 degrees celsius.

01:20 All right.

01:20 So in each of these regions, heat needs to be added.

01:25 In the regions where we have a positive slope, heat is being used to warm it up.

01:30 In the regions of the melting point and the boiling point where it's flatlined, the heat is being used for the change in state.

01:39 So the change of state, when it is boiling, is the heat of vaporization.

01:49 For water, that is 40 .7 kilojoules per mole.

02:03 And the flat line where it's melting is the heat of fusion.

02:13 And both of these values are coming from the table in the unit.

02:17 Heat of fusion and heat of vaporization is unique to each different substance.

02:21 The heat of fusion for water at its melting point is 6 .02 kilojoules per mole.

02:27 All right, so we have a way to calculate the amount of energy required to melt and to boil this.

02:39 We also need to be able to calculate the amount of energy where it is heating up.

02:44 For each of those regions, i'm going to use the equation, q equals the heat capacity times the mass, times the change in temperature.

02:55 For each of these, the heat capacity is going to be slightly different.

02:59 The heat capacity for steam is different than liquid water, which is different than ice.

03:05 All right, but what i've just come up with here is pretty much a plan.

03:08 What i see is i am going to need to, sorry, let me reverse that, i am going to need to calculate the energy for each of these separate regions.

03:18 So i'm going to have to calculate the energy to warm the ice up to its melting point.

03:22 I'm going to have to calculate the energy to melt that ice, then the amount of energy to warm the liquid water up, the amount of energy to boil the liquid water to make it all change to gas, and then the amount of energy required to heat that gas back up again.

03:46 And what we're doing is we are going from negative 10 degrees celsius.

03:54 Oops, wait a minute, i think it was 10 .0.

03:56 Let me get my significant figures there.

03:59 Negative 10 .0 degrees celsius to 110.

04:06 And 10.

04:10 All right.

04:11 So that's where we're starting, where we're going.

04:12 We're going to have to do this in five parts.

04:15 We need a little bit of other information, like how much water we have.

04:19 The amount of water is going to determine how much energy we have to put in.

04:24 So we have 10 grams of water.

04:33 And as i look at my heat of fusion and my heat of vaporization, i see that that's kilojoules per mole.

04:38 So i know i am going to need moles of water for two of these calculations.

04:43 So i'm going to go ahead right now and calculate and change that to moles.

04:49 The molar mass of water is 18 grams of water in every mole.

04:56 That means that these 10 grams of water would be 0 .556 moles.

05:03 All right.

05:09 Some other information, my heat capacities.

05:12 Given to us in the problem is the heat capacity for steam.

05:18 It is 1 .84 joules per gram degree celsius.

05:27 For liquid water, heat capacity we have used in the past, it is 4 .184, joules per gram degrees celsius.

05:43 For ice, the heat capacity is 2 .09 joules per gram degree celsius.

05:56 The delta heat of vaporization, which i tried to put in that table, or in my little drawing up there, but it's a little hard to read, so let me rewrite that.

06:03 Heat of vaporization for water at its boiling point is 40 .7 kilojoules per mole and the heat of fusion.

06:16 For water at its freezing point is 6 .02.

06:24 Okay.

06:26 We have all of the information we need...

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