How much total energy in Joules is required to convert five 5.8 grams of ice at -5�C to a gas at 100�C? 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 -5�C is here and we're going to 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 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 what the phase changes, no temperature change is occurring. So for them we'd say Q=MΔH here going from a liquid to a gases vaporization, so we'd use delta H vape. Here we're going from a solid tool liquid. So here it would be Q=MΔH Going from a solid to a liquid is melting or fusion.
And then here what the temperature changes we're going to use MCAT. So here Q=MCΔT and here Q=MCΔT. We need to add up all the queues 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.
All right. So now we're going to Add all these up together. So let's say this is Q1 where we started, Q2Q3 and Q4, we're going to 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, All right. So Q1 has to do with us going from -5�C to 100�C. Q2 has to do with DO with us being at 0�C where a phase change occurs. Q3 has to do with us going along and increasing temperature as a liquid. So Q=MCΔT again. Oh, actually it's more specific. We're going to say it's from 0�C to 100�C and then Q4 is at 100�C.
So remember, as the temperature is changing, those become Q=MCΔT, so Q=MCΔT here. Q=MCΔT here at 0�C and at 100�C. These are phase changes. So Q=MΔH Add 0�C. It's delta H of fusion because we're melting and at 100 we're being vaporized. So Q=MΔH of vaporization. All right, so now we're going to plug in the numbers that we know. We're dealing with 55.8g 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, or -5 which is a +5. So this comes out to 583.11 Joules.
For here we're dealing with 55.8g. 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 zero to 100�C, which means we're dealing with liquid water. So we're going to use the specific heat of liquid water, which is 4.184. So Q here equals 55.8g * 4.184 Joules over grams times degree Celsius, and then it's final temperature minus initial temperature. So this comes out to 23346.72 Joules and then finally add 100�C. We have to convert all of the liquid water into gas. South mass is 55.8g. Enthalpy of vaporization is 2260 Joules over grams. So here this comes out to 126108 Joules.
So all we have to do here is we have to add up each one of these queues 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 the mall together we get one six 8675.03 Joules. Here let's do this in terms of three sig fix. So this comes out to 1.69 * 10 to the five joules. So this is the amount of heat energy that had to be absorbed for us to transition from ice at -5�C to gas at 100�C. So just keep in mind when we're undergoing a temperature change, we use Q=MCΔT. Hase changes temperatures, staying constant, so it becomes Q=MΔH.