So we're going to go through some heating curve practice problems. Now all right we should have hopefully understood what heating curve is this beautiful situation, right going from a solid melting that solid to a liquid heating, the liquid up, then vaporizing that liquid to a gas and eating that gas up right? And we know are two main equations to use during a heating curve if we understand that we should be able to solve. And he had a question that deals with heating curves.
Okay. So this one's, real basic. All right so a nice cube that has 20 milliliters is in the freezer at negative, 12 degrees Celsius. And it is taken out of the freezer, and it's put on the counter. And it melts.
Okay, we would all know that if you took an ice cube out of the freezer and left it on the counter that thing would melt. Now you have a pleasant puddle on your counter. Congrats. Okay. So Melton gets up to room temperature.
Okay, which would be in this case, 25 degrees, Celsius. And your job is to find Q find how much heat it, actually. Took to heat up that ice cube to melting point melt that ice cube and then heat up that lovely puddle of water on your counter up to room temperature. Okay.
So the number one mistake that kids will do that students will make okay is they will say AHA. This is easy, and they'll go Q equals MCAT. And this is bad.
Don't. Do this? Okay, trying to show you the number one trap?
Okay, everyone traps is you just think it's a no-brainer. And you say, the amount of heat required is my mass 20 mils would be 20 grams of. Water, hopefully we all remember that waters density is one gram per mil. If not just trust me, okay. So I have 20 grams, and they'll use the number that they remember for water per specific heat, which is four point. One, eight, they'll say, 4.18, joules per gram.
Degree Celsius, then they'll say, the delta T was from negative 12 all the way up to 25, which would be what 37 degrees Celsius, and then they'll get an answer that's, super wrong. Bad don't do this. Okay, this is why it's actually important to.
Understand your heating curves, okay. And this is a trap that none of you are going to fall into okay. So when you get a question like this, the first thing to do is to draw a heating curve all right just cover that up. Okay. So draw a heating curve for this problem. Specifically for this issue, all right, I have my temp, always a degree Celsius over time.
Okay? And initially I'm dealing with water right? I start at right here, negative, 12 degrees Celsius. And it wants me to heat up all the way to 25, so I'm. Gonna get up eventually to 25 degrees Celsius, however, in between negative 12 and 25 degrees, Celsius, something happens to water. Okay at zero degrees.
Celsius, water, melts, it's, a very exciting. Right? So this is a multistep issue.
Okay, I'm going to go from negative 12. You might like my ice cube it's going from negative 12 up to zero degrees Celsius. And then I've hit my melting point. And my ice is going to melt. So it plateaus right at flat lines it's, a long, flat line. Sorry, okay. And then when I get to.
This point everything has melted, and I am now going to raise the temperature of my water up to room temperature. This is a three-step issue. I have part 1 part 2, part, 3 more calculating than we would sometimes like, okay.
So during part 1, everything is a solid during part 2, I'm going from a solid to a liquid during part 3. Everything is just a liquid. Okay.
And if you remember from this horrible situation, right which equations to use for which parts of the graph, anytime there's, an actual change in. Temperature I'm going to use Q equals I've cat and anytime there is a phase change. I'm going to use Q equals mole, Delta, H, ok. So multistep issue. Here we go.
Alright. So for part 1, I had Q equals M cat, right? And this is just for ice only for the solid. So the Q of just heating up the solid ice cube is the mass of my ice, 20 mils.
So 20 grams because, it's water. Okay, you should be given a table like this right? So you shouldn't have to memorize the number. If you do, if your teacher makes you memorize these.
Numbers good on you man, it's, not that bad it's, the only few numbers, but hopefully you're given a table all right. So you get 20 grams. And then you need the specific heat of ice, not of liquid water. You want ice solid water, right there?
Okay, 2.11. Okay. So specific heat of solid water, 2.11 joules per gram, degrees, Celsius. And my delta T, just a part 1 I'm going from negative 12 up to 0. So I changed my temperature, a positive, 12 degrees.
I. Multiply, these things together grams cancel out, agree, Celsius. Cancels out, and I get an answer of five hundred.
Six point, four, joules, that's part, one then I have part two, which is going to be fusion. Right? Melting. Q equals mole Delta H. We have a small problem because it asks for the moles of water. So you actually have to know how to convert between grams and moles, which is not hard all right.
So 20 grams of water and do a simple conversion. Get rid of grams I want to get this into MOL use your molar mass. One mole is 18 point. O, two grams it's like one point, one. Moles you're, just gonna check to make sure I don't lie to you. Yes. Okay.
One point one mole, all right. So now I have my moles of water and I can solve q. Equals one point one mole's times the Delta H. This Delta H is of fusion. Not vaporization right?
I'm, not vaporizing, I'm just melting. And again, that should be given to your vaporization. Nope.
Fusion. Yeah, 6.0. One kilojoule per mole given value.
Okay. So x, 6.0, one, KJ per mole. Your moles will cancel out. And you will find that q. First step two is equal to. Six point six, seven kilojoules all right last, but not least is this part of step three right heating of the liquid.
This is the easiest part because this is the part that we've all done before. Okay. So Q equals MCAT for liquid water. Q equals M is your mass should still be 20 mils. So it should still be 20 grams your specific heat of liquid water. Four point one eight jewels per gram, degrees, Celsius and your delta T. Just of step three I went from zero degrees up to 25 degrees. So 25 degrees Celsius.
Okay, multiply all those three things together grams cancel degrees, Celsius cancels, which is nice because then I get an answer in joules I'm solving for heat, and it's, 2090, joules, yay, okay. The problem is I now have joules kilojoules and joules I cannot add all three of these things yet, because they need to be in the same units. So I just need to know how to convert between jewels and kilojoules very easy. Hopefully we all know how to do that, but you just move your decimal. One, two, three spaces.
Back this is zero point, five, zero, six, four, kilojoules, it's already in kilojoules. So you're, good here's, my decimal, so I. Move it one two three spaces to the left and I would get to point zero, nine, zero, kilojoules. Okay. So to give my actual total answer, of course, I have no other color for you, I have to add up all three steps, I'll, do it right here? Okay.
So for part one, my answer was zero point. Five, zero, six, four, kilojoules, that's, how much energy it took to heat up the ice first step - I'm going to add.Then together, okay, how much energy it took how much heat it took heat energy. It took to melt the ice cube, which would be six point, six, seven kilojoules. And then you add that to step three, which would be two point zero, nine.
Zero, kilojoules, very fun to watch me, write out numbers. Okay, add all those three things together. And you get an answer of nine point.
Two, six, six kilojoules. This is the actual answer right, find cute find how much heat it would actually take to heat up that Ice Cube from the low. Freezing temperature of your freezer, the negative 12 degrees of your freezer, have it melt and have it sit in a puddle right there on your counter at 25 degrees, Celsius, okay, three-step problem, make sure you actually draw out your heating curve so that you realize it's a three-step problem and that you don't, screw up and just try and do this in a one-step problem and get the wrong answer. Okay. Good all right.