Heating and Cooling Curves - Video Tutorials & Practice Problems

The Heating Curve

in this new video, we're gonna take a look at heating and cooling curves. So we're gonna say here in heating and cooling curves we have the representation of the amount of heat, absorb or release during phase changes. Now, let's pretend that this heating curve represents that of water and we call it a heating curve because you can see that over time, as our time increases going this way, our temperature is increasing. And we're gonna say here that we know that water either freezes or melts at zero degrees Celsius, and then we should know that water either start to condense or starts to boil at 100 degrees Celsius. Okay, so these are key temperatures. You need to know for water. If it were some other type of compound, um, like, let's say methanol or heck, saying you wouldn't know what they're melting or boiling points were, so they would have to tell you those numbers. Okay, so just remember, for water is expected that you do know the values of zero degrees Celsius and 100 degrees Celsius, but for other compounds, they would give it to you whether you're taking out of the quiz homework or an exam. Now we're gonna notice that at these temperatures of zero degrees Celsius and degrees Celsius are Linus flat, meaning there is no change in our temperature. Okay, so here and here there's no change in our temperature. But then, at temperatures that are not so degrees Celsius 400 degrees Celsius, our temperature does change. Now we're gonna need room, guys. So let's talk about these different phases. We know that below zero degrees Celsius, it's so cold that water will exist as a solid. So we're gonna say here that water exists as a solid up to zero degrees Celsius once it hits zero degrees Celsius, Then we're going undergoing a phase change. And what's happening here is that our solid water, which is ice, starts to melt. So on this plateau on this line here, that's not increasing. We're gonna be a solid liquid mix the solid ist slowly melting into a liquid. At this point here, all of it is melted, and now it's completely a liquid. So this part here that's increasing is all liquid. Then when we get to 100 degrees Celsius, which is right here, our water starts to boil. And again, we're undergoing another phase. Change. So on this line here we have liquid as well as gas, sometimes called vapor. Okay, so you could say a liquid gas mix or liquid vapor mix. And once we get to this end part here, all of the liquid has evaporated, and now it's all gas. So as we start to climb up again, it's all gas. Now, Now, let's talk about what's happening at each one of these spots. So here, we're gonna say, this is one, three and five. This is too. And four. All right, so we're gonna say here a few key things that we need to recognize in terms off this heating curve. So we're gonna say during face changes. So during face changes them. And we're talking about segments two and four. We're gonna say we can tell that temperature remains constant. That's pretty obvious. It's not increasing, it's flat. But here's some other things that are not as obvious because your temperature is staying constant. That means your average kinetic energy is remaining constant as well. So just remember, your average kinetic energy energy is connected to the temperature off your substance And if the temperature of the substance is not changing, so your average kinetic energy for that substance won't change either. Now, we're gonna say here that during these face changes, because this is a heating curve are particles are going to start to spread themselves out. Because if you think about it in a solid, all the particles are tightly packed together. Then as we become a liquid, they're moving around more freely. But they're still in pretty close, um, vicinity to each other. They're just sliding on top of each other. And then as we become a gas, that's when they really spread themselves out. Now, during our face changes again, which are these blue parts where the temperatures remaining constant, We're gonna say here the particles are spreading out, and that's because the kinetic energy again is not changing the average kinetic energy staying the same, and heat is being transferred into potential energy. So during phase changes, heat is transferred into potential energy. Remember, potential energy is just the energy of your position, or, in this case, the energy of your state. So solid have the lowest potential energy liquids have the next highest, and then gasses have the highest potential energy. And remember, during these face changes were going from one phase to another phase. Now, during temperature changes, what can we say? So here, during temperature changes, we're gonna say that heat energy is converted into kinetic energy. And because this is a heating curve in the temperature is increasing. We're gonna say increasing temperature would mean that we're gonna have an increase in our average kinetic energy. Finally, the last thing we talk about in terms of this heating curve is what type of equations do we use at each one of these positions were gonna say, Here are temperature is changing for segment one here, and so that's gonna be Q equals M cat. So an equals mass C represents the specific heat of the substance. Delta T is the change in temperature, so that's final minus initial temperature. Now here, water exists as a solid until it gets to zero degrees Celsius, where it starts to melt. So here the specific heat will be for the solid. Now we're all accustomed to remembering the specific heat of water when it's a liquid. But there's also specific heat of water when it's a solid, so it's ice. And when it is a gas or steam, we'll talk about the Delta H values in a moment. Remember for a line segment one. Because the temperatures change against Q equals M cat during phase changes, there is no change in temperature, so that portion of the equation drops out. It then becomes Q equals. M times Delta H I am here. Could be either in grams or moles. How do we know which one it is? We look at the units for Delta H, and here in these examples that I give to you, Delta H is have grams in them. So m in this case would represent grams. If it was Jules per mole or killing joules per mole, then M would represent moles. Now, here on this first phase change, we're going from a solid to a liquid, so that means we're melting or fusion. So another name for melting is fusion. Then in line segment three, temperature starts to change again. So it's going back to Q equals M cat on on this part of the line world liquid completely. So here this will be the specific heat for the liquid then online Segment four. Again, We're undergoing a face change, so there's no change in temperature, so Q equals. M Times Delta H On this face change. We're going from a liquid to a gas, so that represents vaporization. So we use Delta H. Vape, then finally, for the last segment, it has been completely transformed into gas, and the temperature is changing again. So Q equals M cat one more time. And here because it's a gas, we're going to use the specific heat for the gas. So that's how we look in terms of this heating curve below. We have the cooling curve. Um, check out the very next video where I go into looking at the cooling curve. But remember, if you know what the parts of the heating curve are, the cooling curve is just everything in the opposite direction.

The Cooling Curve

So in our discussion of the heating curve, we learned a few things. Now let's apply what we learn to the cooling curve. So from the name, we know that it is going the opposite way. But actually, before we begin talking about the cooling curve, let's go back to the heating curve. Um, let's talk about We talked about all the different portions of the heating curve, but I neglected to tell you why the links of things were different. So notice that the basic phase change from a solid to a liquid is smaller, then from a liquid to a gas. That's because when you're going from a solid to a liquid, you're basically freeing the molecules from being completely stuck together. But even in the liquid, they're still pretty close to one another, so you didn't separate them by that much of a distance. Therefore, the basic melting time is not gonna be that big. But if we're going from a liquid to a gas, you actually have to separate the molecules very far apart because in gas is, the molecules are great distances away from each other and to go from being sliding on top of each other being close together to being very separated. That requires a good amount of time, a good amount of energy. So that's why the size of this line here is much larger hoops, and it just disappeared. Okay, so that's why that line there is much larger because it takes way more energy to be absorbed in order. Go from a liquid to a gas because you're trying to spread the molecules even farther apart on. Remember, in all this process, we're taking in heat, so that means our Q will be positive. So this is an Indo thermic process where heat is being absorbed by the water so that we can break bonds in a cooling curve were releasing heat because, remember, if you're releasing heat molecules are very energetic. They're bouncing everywhere, and you're trying to cool them off. How do you that give them time to release their excess energy and they move slower, move slow enough and we'll start to stick together. So in a cooling curve, were releasing heat, so cue was negative, which would mean that we're exo thermic, and the whole point of an exile thermic process is to form bonds now if we take a look here, we could still think of this in terms of water. So at 100 degrees Celsius, water can either become vaporize where it's going from a liquid to a gas or it could start to condense. So here, remember, we have an equilibrium between liquid and gas, So liquid gas mixture. So here, that would mean that are delta h of vaporization would equal the delta H off condensation. And remember, condensation means you're going from a gas to a liquid. So you're forming bonds. So it's an exile thermic process. So it's negative. Okay, so this would be negative. Okay, so they're related to each other. I'm gonna say they're equal going to stay there directly related to each other. Then here at zero degrees Celsius, water can either start to melt, work and start to freeze. So here we can say, when we're talking about Delta H effusion, which deals with melting, we could connect that to Delta H. You're freezing. Okay. Why am I telling you this? Because I want you to realize here that I gave you Delta H of fusion here and delta h of vaporization. We could change this toe freezing. All we have to do is make the sign negative, because freezing means we're making bombs for your exile. Thermic so the sun would become negative. Here, Vaporization is related is connected to condensation. And here that would mean the sign is negative. Okay, We still have at these parts. Q equals M times Delta H. But now this would doubIe delta h of condensation. And then here this will be Q m times Delta H of freezing and then here would have these temperatures changing. So those will be cubicles and cat here. Remember, where a gas completely, which would mean that this C is for gas is for the gas form. Here we are all liquid. So this see would be for the liquid version of water. And here we're solid. So see here would be for the solid form of water. As we start to look at examples and questions in the calculations that involved keep in mind some of the key features we've talked about in terms of heating curves and cooling curves, heating curves. We have to absorb energy in order to go from one phase to another. Absorbing energy means that we're endo thermic, so our values would be positive. If you're in a cooling curve, you're releasing heat in order to form bonds. So your ex a thermic So you're you're variables. Your values will be negative. Okay, you get accused that air negative at the end. So keep in mind these fundamentals, And as we look at questions apply, we learned here to answer those questions.

Heating and Cooling Curves

how much energy in killing jewels is required to convert a 76.4 g of acetone here, Given the molecular weight of it, um, as a liquid at negative 30 degrees Celsius toe a solid and negative 115 degrees Celsius. All right, so in this question here, we're going from negative 30 degrees Celsius to negative 115 degrees Celsius. And from the information that were provided, we should see that the melting temperature for acetone is negative 95 degrees Celsius. Now, remember that you're melting temperature and you're freezing. Point temperature happened at the same exact temperature. So basically, if we're going from solid to liquid, that represents melting. And if we're going from liquid to solid, that represents freezing. Both happened at the same temperature, so this melting temperature could also be substituted in for our freezing temperature. Now, if we think about this, we know that were negative 30 degrees Celsius, and all we're doing is getting colder. Okay, so here we have our freezing curve because the temperature is decreasing. We know at negative 95 degrees Celsius, that's one are solid. Will transition on our liquid transition into a solid Okay, so that's a face change that's happening here. Were happening at a temperature that's higher up than that. So we have to go from negative 30 degrees Celsius to negative degrees Celsius. So that's our change in temperature. That first portion will help us get our initial heat. And because the temperature is changing this Q one a equals M cat once we get to negative 95 degrees Celsius, were undergoing a face change. So now Cule equal M times Delta H off freezing. If you want to say and then we have to go all the way down to negative 1 15 which will be somewhere down here in that part right there will give us our Q three. Which again, because temperature is changing with equal M cat. So that's what we have to do. We have to calculate Q. One Q two and Q three. Add them all. It's all up together to get our Q total. Now let's calculate Q one so Q one equals M cat. Now, as we're going from negative 30 degrees Celsius to negative 95 degrees Celsius were in our liquid phase here and We're getting colder and colder until we start changing into a solid. But remember, we're in our liquid face here, so we need the specific heat off our liquid. The specific heat of our liquid is this number right here. So bring down the 76 4 g of acetone multiplied by our specific heat and then are changing temperatures Final temperature minus initial temperature. So that's negative 95 degrees Celsius minus of minus 30 degrees Celsius. Remember, a minus of a minus really means plus, so it's really negative 95 degrees Celsius plus 30 degrees Celsius. Look at how the units cancel out. At the end, my aunts will be in jewels. So when you work that out, we're gonna get negative. 10,000 726 6 jewels, which, when I change it into killer jewels well, give me negative. 10.7266 killer jewels. So that's just our Q one. Here I change it into killer jewels because when we find Q two Q tool being killer jewels, so just keep all the units consistent. So for Q two were at this portion of my face diagram now or not, my face diagram my cooling curve. So that's equal to M times Delta H. And the whole process is freezing. I remember freezing and melting happened along the same temperature. So here, when we're talking about melting another name for melting his fusion so we can use this value here. Now, notice the units a 7 to 7. Kill a Jules per mole. All right. We don't want the grams of acetone given to us. We need to change it into moles. So we have 76.4 g of acetone. It doesn't matter if you don't know what acetone looks like, because we're given the Mueller massive acetone as 58.8 g per mole. So bring those grams down, and that's equal toe. One mole of acetone grams, cancel out. And now we'll have moles, which come out to 1.31543 moles. All right, now, this is important. Fusion means that we're melting, which means we're breaking bonds. But here we're going the opposite way. We're freezing. Freezing means we're forming bonds. Forming bonds are an exa thermic process. Okay, so bond forming is excell thermic because we're freezing in exile. Thermic processes have negative Delta H values, so we're gonna use that 7.27 kg per mole. But it's gonna be negative now, because again, this is an ex a thermic process where we are freezing our acetone in order to form bonds. So don't forget the negative sign. So moles cancel out. Now we have killed jewels, which again it will be negative. So here go my killer goals for Q two. Now, finally, we have to go from Q two to Q three and Q three. Here. We're going from negative 95 degrees Celsius to negative 115 degrees Celsius. At this point, we've already undergone our face change. All the liquid has been transformed into solid, so now we need the specific heat of our solid. So the specific heat of our solid is this value right here. So that's what we're gonna bring down for our Q equals M Cat for Q three. So cute through here equals Q three equals M cat. So it's 76.4 g of acetone. The specific heat for the solid form of acetone is this value right here and its final minus initial, so that's negative 1 15 degrees Celsius minus of minus 95 degrees Celsius. Remember, minus of a minus really means that they're adding. So we'll have. Here are the jewels at this portion, which comes out to negative 25 to 1.2 jewels. And remember, one killer Jewell is equal to 1000 jewels. Okay, so that's negative to 5 to 1 to killer jewels. So we just found out what Q one waas, which was this value que two is this value and Q three is this value. So now we want cute total. So if you total comes from adding up Q one plus Q two plus Q. Three altogether. So it up each one of those values, and we're gonna get negative 22.811 killer jewels as the amount of heat that has to be released in order to form bonds. So just remember, in a cooling curve, which is what we've shown here, your Q values have to be negative because as we're cooling an object as it's freezing, it has to release the excess heat in order to form bonds. Losing that heat means it's an exile thermic process. So our Q values have to be negative in terms of their signs. And remember, fusion, which is melting, happens at the same temperature in which freezing does so if you know the entropy or Delta H A fusion giving it a negative sign represents the entropy off freezing. Knowing these things is key to finding out the final Q value that we have, so we'll continue onward with this whole idea of cooling and heating curves later on. But just keep in mind the things that we've covered up to this point when it comes to face changes and heat.

If 53.2kJ of heat are added to a 15.5g ice cube at - 5.00 ^oC, what will be the resulting state and temperature of the substance?

• A. 322.5°C, gas
• B. -3.70ºC, solid
• C. 98.82 ºC, liquid
• D. 222.5 ºC, gas