Heating and Cooling Curves Example 2

by Jules Bruno
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how much total energy in joules is required to convert 55.8 g of ice at negative five degrees Celsius to a gas at 100 degrees Celsius. All right, So step one 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 five degrees negative five degrees Celsius is here And we're gonna climb until we hit 100°C 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°C. At this point our liquid starts to become vaporized into a gas. Now we don't go beyond 100°C because we're start 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 are a solid here we're transitioning from a solid to a liquid. Here were liquid and here we're transitioning from a liquid to a gas. Remember what 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 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 em cat. So here Q equals M. Cat and here Q equals M. Cap. We need to add up all the cues together. So we calculate all the heat Q. Involved using appropriate specific heats and M. Papi's of a substance involved. Now here since this is a heating curve, it's endo thermic. So all the signs would be positive for specific heats and for entry piece if we're undergoing a cooling curve we'll be releasing heat. So they would have a negative sign. They would have a negative sign in terms of our entropy of fusion and our entropy 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. Two, Q three and Q four. We're gonna do the math here. And once we do that we go to step four, we add them all together to get our total energy or total heat involved. So she won has to do with us going from negative five degrees Celsius 200. Re Celsius, Q two has to do what I do with us being at 0°C or phase change occurs. Q three has to do with us going along and increasing temperature as a liquid. So Q equals M. Cat again. Well actually it's uh more specifically we're gonna say it's from 0°C to 100°C and then Q four is at 100°C. So remember as the temperature is changing those become cuticles. And castle Q equals M. Cat here, Q. Equals and cat here top at zero degrees Celsius. And at 100 degrees Celsius, these are phase changes. So Q. Equals M. Times delta H. Ad zero degrees Celsius. It's delta H. Infusion. Because we're melting and at 100 were 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. 558g of water. Here it is solid ice. Right? So the specifically devices this so 2.09 jules over g times degrees C. And Delta T. is final temperature minus initial temperature. So that's 0 -1 -5. Which is a positive five. So this comes out to 583.11 jewels. For here we're dealing with 55.8 g. Again, Delta HF fusion is 3 30 for jules over grants. So g cancel out. And we have 18637.2 jewels Here we're dealing with 0-100°C, which means we're dealing with liquid water. So we're gonna use the specific heat of liquid water which is 4.184. So cue here equals 55.8 g times 4.184 jewels over grams times degree Celsius. And then it's final temperature minus initial temperature. So this comes out to 23 346. jewels. And then finally At 100°C, we have to convert all of the liquid water into gas. So mass is 55 8 g. Entropy of vaporization is 2 to 60 jewels over grams. So here this comes out 1-6108 jewels. So all we have to do here is we have to add up each one of these cues that we got. So this plus this, plus this, plus this. So we'd say here talk, you total is us adding all of them together. When we add them all up together, we get 168, 03 jewels Here, let's do this in terms of 366. So this comes out to 1.69 times 10 to the five jewels. So this is the amount of heat energy that had to be absorbed for us to transition from ice and negative five degrees Celsius to gas at 100 degrees Celsius. So just keep in mind when we're undergoing a temperature change, we use Q equals end cap at phase changes, temperatures staying constantly becomes Q equals and times delta H.