Heating and Cooling Curves - Video Tutorials & Practice Problems
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Heating and Cooling Curves represent amount of heat (q) absorbed or released by a substance during phase changes.
Heating & Cooling Curves
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Heating and Cooling Curves Concept 1
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In these next series of videos, we're gonna take a look at heating and cooling curves. Now realizing that heating and cooling curves represent the amount of heat absorbed or released by a substance during phase changes. Now remember heat uses the variable q. Here we have a heating curve versus a cooling curve. In a heating curve, our substance is absorbing heat. It's a if it's absorbing heat, that means that it is an endothermic process. So that means q would be positive. In a cooling curve, we are releasing heat. The substance is cooling off. Releasing heat makes it an exothermic process or a q and b negative. If we take a look here at our heating curve, we have a heating curve for water. Now water can exist as a solid, a liquid or gas. Remember, at 0 degrees celsius, we can have the melting of ice. So if we add enough heat to solid ice, it gets to 0 degrees Celsius, At that point is where it undergoes a phase change. And notice that during a phase change, there's no change in heat. It's plateaued. That's because the substance is using that heat that it's been absorbing in order to finally break its bonds, loosening up its molecules and transition from a solid phase to a liquid phase. Now remember, going from solid to liquid is melting or fusion. So we can say melting slash fusion can happen here. Once all of the solid ice has melted into liquid water, it then starts to climb again in terms of temperature and here is where it exists as a liquid. Now once it gets to a 100 degrees Celsius, it's finally reached its next temperature change where it can undergo a phase change. So at a 100 degrees Celsius, the liquid water has absorbed enough energy and it can use that energy to finally break itself even further apart into the gaseous phase. Remember, going from a liquid to a gas is vaporization. If additional energy keeps getting added to the substance, it can go beyond. So at this point, it's all changed into gaseous water or water vapor, and then it could keep climbing up having its temperature change, and it exists as a gas. So that's how we look at a heating curve for water. Now, conversely, if we're looking at cooling of water, we can say that water starts up here as a gas. It's at a temperature that's above a 100 degrees Celsius. It could start to slowly release that energy and start to cool off. Once it reaches 100 degrees Celsius, we can say that it finally has released enough energy that it can undergo a phase change. Again, we've reached a plateau, there's no temperature change. It's at this point that the gaseous water is condensing down into a liquid. So here we have condensation. Here it's already a liquid so it's gonna keep releasing heat. And when we get to a 100, it undergoes another phase change where temperature remains constant. It plateaus again. Here's where our liquid is becoming a solid. So here it is undergoing freezing. And if it keeps releasing heat energy, it can keep going. And now it's a solid and temperature is changing again. So think of these two things as mirror images of each other. We can see that vaporization and condensation both can occur at a 100 degrees Celsius, and melting slash fusion can occur at 0 degrees Celsius just like freezing can. Think of this when you're looking at the temperature changes involved with any substance as it's going, between these phase changes. We can see that the temperature plateaus so that it can convert fully into new new phase and before it can continue to move up or down in terms of temperature change. Right? So now that we get the basic idea of what a heating and cooling curve is, we'll we'll continue onward with additional calculations.
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Heating and Cooling Curves Concept 2
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Now realize that with heating and cooling curves, there are significant differences between temperature and phase changes. Now taking a look at some of the key differences here, with temperature changes, we have heat being converted into kinetic energy, so the energy of motion. And realize that the higher our temperature gets, the higher kinetic energy will be as well. With temperature changes, we have our specific heat capacity formula where q equals m cap. Q represents our heat, m can either be grams or moles, and it depends on the units for our specific heat capacity, which is c. Delta t is just change in temperature, which is final temperature minus initial temperature. Now with a phase change, we're gonna say that if we look at our heating and cooling curves, we saw that the temperature plateaued. It didn't change. That's because heat is being converted into potential energy. And we know that there's a connection between temperature and kinetic energy. So if your temperature is not changing, then your kinetic energy also would not change. So here, our average kinetic energy is constant and temperature is constant. It's not changing. With a phase change, we use our new enthalpy formula, which is q equals m, which again can either be in grams or moles, times our change in enthalpy, so delta h. So keep this in mind, when temperature changes we use our heat capacity formula, but with phase changes where temperature is remaining constant, we have our enthalpy formula here.
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Heating and Cooling Curves Example 1
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Identify the line segment on the diagram where specific heat of liquid water is used to calculate energy flow. So remember, here, this is a cooling curve. Above a 100 degrees Celsius, we exist in the gaseous phase. Remember, we're looking for liquid water. Once we reach a 100 degrees Celsius, that's where we undergo our first phase change. Here we're going from a transition of a gas to a liquid. Now we want only the liquid form of water and that starts to occur at point c. Going down from c to d is where we finally have only liquid water. D to e would be us going from a liquid to a solid at another phase change, and then from e to f would be our solid form. Now if we look here on line segment c d, since we're undergoing a temperature change, because we're going from a 100 to 0, we use q equals mcat here. We're here. Our specific heat capacity c would be the specific heat capacity of a liquid water. If we're dealing with a gas, we'd still use q equals mcat, would be the specific heat of gaseous water. And then here, it would be the specific heat of ice. Now, again, going back to the question we're looking for liquid water, so that would mean the answer is option c. Line segment CD would have the specific heat of liquid water.
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Heating and Cooling Curves Concept 3
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So at this point, we're thinking conceptually when it comes to heating and cooling curves. Now recall there's 2 formulas used to calculate heat at different parts of the curves. If we're undergoing temperature changes, then we have to utilize a specific heat capacity formula. Here, it'd be q equals mcat, where c, our specific heat capacity, is based on the substance existing as a gas, a liquid or a solid. Now at phase changes, our temperature is constant. It plateaus. At this point, we utilize the enthalpy formula, which is q times m q equals m times delta h. M here could either be grams or moles. The units depend on what the value of delta h is. Now we're gonna use these two formulas to calculate our total energy involved in a heating and cooling curve. So basically, we'd add up each of the line segments from either the heating or cooling curve and add them all together, so q 1 plus q 2 plus q 3, and so on if necessary, and that'll help us find out the total heat or total energy involved.
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Heating and Cooling Curves Example 2
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How much total energy in joules is required to convert 55.8 grams of ice at negative 5 degrees Celsius to a gas at a 100 degrees Celsius? Alright. So step 1 is we draw the necessary curve and label all the changes. We're starting off at ice because we are starting out below freezing point. So let's say 5 degrees negative 5 degrees Celsius is here, and we're gonna climb until we hit a 100 degree Celsius and undergo a phase change. This is where our ice starts to melt into a liquid. Once it's fully melted, it becomes a liquid and it continues to climb up until we hit 100 degrees Celsius. At this point, our liquid starts to become vaporized into a gas. Now we don't go beyond a 100 degrees Celsius because we're stop stopping exactly there. So these would this would be our curve that we're dealing with in terms of this question. Now, here we have to identify all the heats involved along with the necessary formulas. So here we're a solid, here we're transitioning from a solid to a liquid, here we're a liquid, and here we're transitioning from a liquid to a gas. Remember, when the phase changes no temperature change is occurring. So for them, we'd say q equals m times delta h. Here, going from a liquid to a gas is vaporization, so we'd use delta h vape. Here we're going from a solid to a liquid, so here it would be q equals m times delta h. Going from a solid to a liquid is melting or fusion. And then here, what the temperature changes, we're gonna use mcat. So here q equals mcat, and here q equals mcat. We need to add up all the q's together, so we calculate all the heats, q, involved using appropriate specific heats and enthalpies of a substance involved. Now here, since this is a heating curve, it's endothermic, so all the signs would be positive for specific heats and for enthalpies. If we're undergoing a cooling curve, we'd be releasing heat so they all would have a negative sign. They would have a negative sign in terms of our enthalpy of fusion and our enthalpy of vaporization. Alright. So now we're going to add all these up together. So let's say this is q one where we started, q 2, q 3, and q 4. We're gonna do the math here and once we do that, we go to step 4. We add them all together to get our total energy or total heat involved. Alright. So q one has to do with us going from negative 5 degrees Celsius to a 100 degrees Celsius. Q2 has to do with do with us being at 0 degrees Celsius where a phase change occurs. Q3 has to do with us going along and increasing temperature as a liquid, so q equals mcat again. Oh, actually, it's, more specific, we're gonna say it's from 0 degrees Celsius to a 100 degrees Celsius, and then q 4 is at a 100 degrees Celsius. So remember, as the temperature is changing, those become q equals mcat. So q equals mcat here, q equals mcat here. At 0 degrees Celsius and at a 100 degrees Celsius, these are phase changes, so q equals m times delta h. At 0 degrees Celsius, it's delta h of fusion because we're melting, and at a 100 we're being vaporized, so q equals m times delta h of vaporization. Alright. So now we're gonna plug in the numbers that we know. We're dealing with 55.8 grams of water. Here it is solid ice. Right? So the specific heat of ice is this. So 2.09 joules over grams times degrees Celsius, and delta t is final temperature minus initial temperature, so that's 0 minus a minus 5, which is a positive 5. So this comes out to 583.11 joules. For here, we're dealing with 55.8 grams again. Delta h of fusion is 334 joules over grams. So grams cancel out and we have 18637.2 joules. Here we're dealing with 0 to a 100 degrees Celsius which means we're dealing with liquid water, so we're gonna use the specific heat of liquid water which is 4.184. So q here equals 55.8 grams times 4.184 joules over grams times degrees Celsius, and then its final temperature minus initial temperature. So this comes out to 23346.72 joules. And then finally, at a 100 degrees Celsius, we have to convert all of the, liquid water into gas. So mass is 55.8 grams, enthalpy of vaporization is 2 260 joules over grams. So here this comes out to 126 108 joules. So all we have to do here is we have to add up each one of these q's that we got, so this plus this, plus this, plus this. So we'd say here, q total is us adding all of them together. When we add them all up together, we get 168,675.03 joules. Here, let's do this in terms of 3 sig figs. So this comes out to 1.69 times 10 to the 5 joules. So this is the amount of heat energy that had to be absorbed for us to transition from ice at negative 5 degrees Celsius to gas at a 100 degrees Celsius. So just keep in mind when we're undergoing a temperature change, we use q equals n cap. At phase changes, temperature is staying constant so it becomes q equals m times delta h.
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Problem
Problem
How much energy (kJ) is required to convert a 76.4 g acetone (MM = 58.08 g/mol) as a liquid at -30°C to a solid at -115.0°C?
A
-11.406 kJ
B
-39.820 kJ
C
-22.811 kJ
D
-82.592 kJ
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Problem
Problem
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?