00:02
Hey there.
00:03
In this problem, before i start, i want to collect some information.
00:07
What we are trying to do, of course, is to take some steam and cool it all the way down to ice and not only ice, but ice at negative 50 degrees celsius.
00:21
So i want to start off by sketching a heating curve.
00:28
And you might say, well, wait a second, we are not heating this water.
00:30
We are cooling it.
00:31
And that is correct.
00:32
But that means it's going to be the opposite.
00:35
Of my heating curve.
00:37
So on a heating curve, the x -axis represents heat added, and the y -axis is the temperature in degrees celsius.
00:51
So if we take water, the heating curve for water is going to show that we start with solid ice at a temperature colder than its melting point.
00:59
So we have to warm it up to its melting point, at which point it flatlines while it's melting, the temperature doesn't change.
01:07
So that's going to be water's melting point, which is zero.
01:12
Then it's going to warm up again until it gets to its boiling point, which is 100, at which point it's going to flatline again, and then once it is all steam, it can warm up again.
01:29
All right, so this is the basic heating curve.
01:31
And what we are doing is we are starting with steam.
01:35
That is at 145 degrees celsius.
01:40
And we are trying to cool it all the way down to negative 50.
01:50
Right? so that means energy is going to be given off.
01:53
First, there's going to be some energy given off while it cools, then while it condenses, then while it cools again, then while it freezes, then when it cools yet again down to the negative 50.
02:06
So what we really have to do here is we're going to have to calculate five different regions and add them together.
02:14
So i'm going to label these as a, b, c, d, and e.
02:21
For parts a, c, and e, we are going to be cooling it down.
02:28
So to calculate the amount of energy, we're going to have to take the equation, cube, that's heat, equals the heat capacity times mass, times the change in temperature.
02:48
So i'm going to use this equation for parts a, c and e.
02:52
However, each one's going to vary slightly because the heat capacity of water is different, whether it's a solid liquid or a gas.
03:02
We'll get those values here in a moment.
03:05
But that's the equation that i'm going to use for parts a, c, and e.
03:15
Part b represents the heat of vaporization.
03:24
So i'm going to have to calculate the amount of energy needed there to condense the water from steam to liquid water by using the heat of vaporization.
03:34
For part d, i'm going to have to use the heat of fusion for water.
03:42
And again, i'm going to calculate each of these five regions and add those values all together to get my final answer.
03:49
So let's look at some information, some things we know, some constants and things that we're going to need to use for this problem.
03:59
First of all, we are told that we're starting out with one mole, of water.
04:08
And it's steam, so it's actually in the gaseous phase to start with, but we have one mole of it.
04:13
And we are trying to, as i mentioned before, we're trying to go from 145 degrees celsius to negative 50.
04:27
And we have some constants here, some heat capacities.
04:31
Heat capacity for steam is 1 .84 joules per grams degrees celsius.
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Heat capacity for liquid water is 4 .184 joules per grams degrees celsius.
04:59
Heat capacity for solid water, i'm just gonna put ice here, is 2 .09 joules per grams degrees celsius.
05:13
These are all constants.
05:15
The steam and the ice were given to us, the water we know from earlier chapters.
05:20
We also need the heat of vaporization.
05:25
So looking at the tables in the chapter, the heat of vaporization for water, and we have to look it up by substance because the heat of vaporization and the heat of fusion are going to vary depending upon the substance, but for water at its boiling point, it's 40 .7 kilojoules per mole, and the delta heat of fusion for water at its freezing point is 6 .02.
06:00
This energy is given off when something is condensing.
06:04
Or freezing.
06:07
So when i actually use these values, i'm going to use them as negatives to show that the energy is being given off.
06:14
All right, i think that is all the information we need.
06:17
So remember, we are going to be calculating, i'm going to be calculating each of these different regions, region a, using the q equal c times m times delta d, the region b using heat vaporization, region c, region d, and region e.
06:34
So let's go ahead and get started.
06:36
And then i'm going to have to add those all together all right so first of all region a where we are cooling down that steam that we're starting with we're going to take the heat capacity for steam which is 1 8 .84 jules per gram degrees celsius we're going to multiply by the mass of the water we have we have one mole of water we are given one mole well if we think about the molar mass of water and look at that by the values together on the periodic table, and it's going to be equal to 18 grams of water because that is the definition of molar mass.
07:20
So i have 18 grams of water.
07:26
And then delta t, change in temperature, means t final, which is 100 degrees.
07:33
We're going to cool it down to its condensation point or its boiling point.
07:39
So that's going to be 100 degrees celsius minus 145, which was our initial.
07:47
I'm going to go ahead and calculate this, and i get negative 1490.
07:58
Now, let's think about the units here...