Kendal Orenstein

**Rutger's University**

M.Ed., Columbia Teachers College

Kendal founded an academic coaching company in Washington D.C. and teaches in local area schools. In her spare time she loves to explore new places.

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**Heat of fusion** is the energy needed for one gram of a solid to melt without any change in temperature. **Heat of vaporization** is the energy needed for one gram of a liquid to vaporize (boil) without a change in pressure. These energies are needed to break apart the intermolecular forces holding the solid or liquid together as it enters a less dense state of matter.

So we're going to talk about heat of fusion and heat of vaporization. The opposite of heat of fusion is heat of solidification and the opposite of heat of vaporization is heat of condensation. But what does all these things mean? Well this is the amount of energy it takes to change or to change a phase of 1 mol of substance so it's going to change a phase so like for example if we're talking about fusing something and we're going from a solid to a liquid. That's where we're changing the phase from solid to liquid and the amount of energy it takes to change the phase of 1 mol of substance. And the opposite of that is solidification that's going from liquid to solid they'll actually take the same amount of energy so one is endothermic and one is exothermic just the same amount of energy though. So the heat of fusion is an endothermic process it requires heat so the delta h is positive. Heat solidification is exothermic going from liquid to solid, releases heat so it's a negative delta h but at they're the same numbers.

Same thing with heat vaporization so, it's the amount of energy it takes for 1 mol of substance to change from liquid to gas is the heat of vaporization and the opposite is condensation going from gas to liquid. So we denote that with delta h of vap and delta cond, delta h of vap is endothermic being a positive delta h, and delta h condensation is actually negative meaning it's exothermic but again the numbers are identical to each other. So if talk about water, water is going to be our main substance because just because it's a common substance. It takes actually 40.7 kilo joules to change 1 mol of water from a liquid to a gas or it releases 40.7 kilo joules to change 1 mol of water from gas to liquid. And delta h fuse of water is actually much, much, much less. It takes a lot less energy to change it from solid to liquid to overcome any molcular forces that change it from solid to liquid or going from, it releases a lot less energy going from liquid to solid. So it requires a lot of energy to go to a gas and not as much energy to go to a liquid.

Let's actually look at a phase change diagram and see how that plays out on a phase change diagram. So we know that slopes of a solid and liquid and gas are dependent on specific heat and we know that the solid and gas phases have a steeper slope because their specific heats are lower. But let's look at the lines when talking about changing of phases going from solid to liquid our line is actually pretty quite small it doesn't take a lot of energy to go through that phase change. But notice it takes a lot of energy to go through the phase change of liquid to gas it's 40.7 versus 6.01. We're just dealing with intermolcular forces and how they break apart and takes a lot more energy and become a gas and a bit more chaotic. So let's about how we can use this chart when talking about how much energy it takes to go through different phases. So let's look at this problem, how much energy will it take to heat 10 grams of ice from negative 15 degrees Celsius to positive 15 degrees Celsius.

I'm actually going to use blue because we've used green already. So basically we know that this right here is 0 degrees Celsius because that's when water solidifies or melts [IB] that this is 100 degrees Celsius just to label our graph a little bit better. Okay so we're going from something like here water that's down here to water that's about here. So not only are we changing phases, we're actually up the substance changing the phase and then heating the substance a little bit more. Okay so we have 3 processes going on. So when we're heating up the substance going up the slope we have to deal with specific heat q equals mc delta t. Okay so we're dealing with 10 grams of water so I'm going to put, I'm going to mark this over here q are the amount of energy it takes to heat up 10 grams of water, our specific heat in this case ice because we're going from negative 15 is 2.03 joules per gram degrees Celsius. And our change in temperature it's not the full negative 15 to positive 15 it's going to here because going from here requires something different and this also has different specific heat, so we have to do completely different calculations. So it's actually going from negative 15 to 0, so it's actually changing 15 degrees.

Okay so I multiply these all together and I get 304.5 joules okay just to increase the temperature of that ice. Now I'm going through a phase change, so this is q1 and I'm going through a phase change and that q is equal, we know that our delta h is in kilo joules per mol. So I have to change that 10 grams to mols, because I have to make sure my units are properly lined up. So 10 grams of water we know the mol mass of water is 18 grams we're looking at our periodic table, it is 1 mol. So we have our 0.556 mols of water okay so I'm going to multiply this number by our heat of fusion and our heat of fusion is 6.01 so we know it takes 6.01 for 1 mol to melt but I only have 0.556 mols so I want to figure out how much it takes for that to melt kilo joules per mol I multiply these guys together and I get 3.34 kilo joules.

I want to change this to joules because in the end I'm going to end up adding all these things together to get the total amount of energy. So I'm going to change this to joules which make it 3,340 joules. Okay and then the last one I want to go from, I want to heat up that water, now it's water I did the phase change now we're going from 0 degree Celsius up to 15 so I'm going to do q again. q equals mc delta t the mass is 10, the c in this case is 4.184 joules per gram degrees Celsius and the change in temperature we're going from 0 to 15 so again it's 15 degrees Celsius multiply these guys all together I get 622.6 joules. So these are my in steps, these are my individual amounts of energy for each step but I wanted the total amount of energy. So I'm going to add all these guys up 3.05+3,340+622.6 and I end up with 4,272.1 joules and that's how much energy is required to get from negative 15 to positive 15. So just to make sure that you understand, this is the amount of energy it takes just to change from solid to liquid, this is the amount of energy it takes to change from liquid to gas and if you're changing away from the temperature and changing this phase and raising temperature again these are actually different calculations you're going to have to add up this is actually a pretty important c concept and these are not the same. You cannot go from negative 15 straight to positive 15 in one cell swoop you'd have to break it up. So this phase change diagram is actually really helpful in problems like these.