ALEKS - Using Heat of Fusion or Vaporization to Find the Heat Needed to Melt or Boil A Substance (2023)

Introduction

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Video

All right class.

So this is an Alex topic that's called using heat of fusion or vaporization to find the heat needed to do a.

You know process.

Essentially.

So this question says, calculate the amount of heat needed to melt 150 grams of solid benzene, and then bring it up to a temperature of forty seven point, seven degrees, Celsius.

So right away, I know that I'm going to need to look up some information if I click on this data button, right here then I can find all of this phase change properties for pure substances, data so we're, looking at benzene.

So all of this information here, that's, what I'm going to sort of probably need as I do this problem.

The other thing I want to talk about is sort of drawing out a map of this problem.

So what I might do is draw a graph of temperature versus time.

Time would also be considered energy added.

So as I move left to right, I'm, adding energy to this, you know system.

And we've seen where we have our different lines that look like this to go up in a sort of stepwise fashion.

This right here would be our Delta H of vaporization.

So that's gonna be going from a liquid phase to a gaseous phase.

This right here would be my Delta H of fusion going from a solid phase to a liquid phase.

And this would be heating up the liquid.

This would be heating up the solid and all of these sort of different sections I'm gonna have different ways to calculate the amount of energy associated with each one of those.

So in this question, what we really need to do is we need to figure out where is my starting point and where's, my ending point and we're gonna use all of this information to determine that.

So the first thing I would do is I would label where these phase changes happen.

So according to my chart here, the melting point of benzene is five point, four, nine degrees Celsius.

That means that temperature right? Here is five point, four, nine degrees, Celsius, that's, where that phase change between solid and liquid is going to happen that's.

The melting point right? And then the boiling point I can read is 80 point, oh, nine degrees, Celsius.

So this temperature here where it goes from liquid phase to gaseous phase that's going to be at 80 point, oh, nine degrees Celsius.

So the next thing I want to do sort of say, well, where is my starting point? This says, calculate the amount of heat needed to melt so right away? I know that I'm gonna be in the solid phase.

So somewhere along here, 150 grams of solid benzene and bring it up to the temperature of forty seven point, seven.

So I know, my end point right? My end points gonna be somewhere right here.

We'll say that this right here is forty seven point, seven degrees Celsius.

So this is my ending point.

And then the starting point this actually is not super clear of a question.

It actually should tell us that we're starting at, you know, solid benzene at the melting point of benzene, but I figured out that our starting point is going to be right here where we have our just completely solid.

So as I on this line, this is solid that is at the melting point, but has not changed phase yet.

So really this is going to be a two-step process.

Step one I'm gonna change the phase I'm gonna go from solid benzene here to liquid benzene.

All at the same temperature.

It's just a phase change, I'm gonna use the Delta H of fusion for that.

And then in step two I'm going to heat that benzene from five point, four, ninety degrees, Celsius up to a final temperature of forty seven point, seven, nine degrees, Celsius so that's, my two-step process.

So for step one, the way that I'm going to do that is I'm going to use the Delta H of fusion and I can look up on my data table.

The Delta H of fusion for benzene is 9 point.

8 7, kilojoules per mole.

So heat of fusion that's.

My Delta H of fusion that's, how much energy it takes right? Nine point, seven kilojoules per mole that's, how much energy it takes to change the phase of benzene from solid benzene to liquid benzene.

So this is going to be nine point, eight, seven, kilojoules and we're gonna have to pay attention to those units that are kilojoules per mole.

So if I want to figure out the amount of energy it takes to go from the start point to this point here, that's going to be, you know, I need to figure out the number of moles of benzene that I have so I have 152 grams times 1 mol over 70 just double-check.

78 0.12 grams a molar mass of benzene, just calculate in that c6h6 equals 1.94 moles of benzene.

So c6h6, 1.94 moles.

So if I just multiply these two numbers together, that's going to tell me the amount of energy that it takes 1.9 for moles to change the phase of that 152 grams of benzene from solid into liquid kilojoules per mole.

We can see that my units of moles are gonna cancel out and I get a value of nineteen point, two kilojoules.

So that's, the amount of energy takes to go from this starting point over to here.

And then we can do step two.

So in step two I'll, just do step two right here.

We're going to use Q equals s times M times delta, T we're, changing the temperature of the benzene from the melting point.

Five point four, nine degrees up to the end point of forty seven point, seven.

So I know that I need to use a delta T sort of type of equation.

This S value that we're gonna be using here, that's going to be the specific heat or heat capacity at 25 degrees Celsius, given for benzene.

One point, six three joules per gram times degrees, Celsius or degree Kelvin.

So this is going to equal one point, six three times my mass.

So to keep in mind I need to use my mass here of 152 grams.

Now times my delta T so delta T is going to equal T final, minus T initial.

So that equals in this problem, forty two point two one so I'm, taking forty seven point, seven and I'm, subtracting that from five point, four, nine, right and I looked at this five point, four nine up again on my data table.

So this is going to be the amount of energy.

It takes to go from this point here up to my end point, that's, my delta T.

This is how much I have like the mass of benzene.

And this is my specific heat capacity for benzene.

So this is going to equal ten thousand, four hundred and fifty eight, joules of energy.

So now the question is, well, what's the total amount of energy.

The total matter needed to go from the star point to the end point I'm gonna need to add these together, obviously I need to change these to both kilojoules, or both jewels I'm going to convert this one to kilojoules.

So ten point, four, five, eight, kilojoules and I'm just going to combine these two numbers.

Right? If I just combine these two numbers 19.2.

And ten point, four eight that gives me a value of twenty nine point, six kilojoules that is the total amount of energy that's going to be required to go again from the starting point all the way to the ending point.

So all of these types of problems, the things that we're going to sort of have in common is a graph that looks like this right? So this is going to be my solid.

This is going to be going from solid to liquid.

This is going to be completely liquid.

This is going to be completely gas.

This is going from liquid to gas it's, always gonna look like that where these horizontal lines are right, that's gonna be where at the melting point or boiling point are so on.

This axis I've got temperature, and then where my ending points and starting points are that's, really the key to figuring out these problems is saying, well, where's my starting point where's.

My ending point how do I go in between right? Each step of the way will be a different calculation.

And you know, we're gonna be using things that look like this, you know, Delta H of fusion.

Delta, H of vaporization up here, Q equals s times M times delta, T I need to know, my heat capacities for the different substances and the different phases.

And then it's just going to be adding all that together at the end to get my total energy that I see there all right I hope that that helps if you have more questions about this, definitely let me know.