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It is divided in to multiple steps because delta H Fusion only calculates the phase change value. But the solid first needs to heat up to 0.0 Celsius which is one Delta H value and then you must add the n*DeltaHFusion to calculate the Delta H of the overall rxn.
You need to separate the processes of the energy required to melt the ice, and the energy required to raise the temperature of the ice that has melted (or you could think of it as the energy coming out of the surrounding in order to change the temperature of the water that came from the melted ice at 0 degrees C). Multiplying the enthalpy of fusion for water by the mass of ice present will give you the former, and using the q=mCdeltaT equation will give you the energy being input to raise the temperature of the water from the ice.
the temperature doesn't change during a phase change. you can keep adding heat but the temperature doesn't change. you would need to calculate the energy needed to raise the temperature to the melting point, then find the amount of energy needed to actually melt the substance
I remember it best by thinking of the phase change diagram. There are sloped/diagonal parts and there are horizontal parts. You have to calculate each part separately. Delta Hfus and Delta Hvap are used during those horizontal parts. During the sloped parts, you can used the normal mCdeltaT equation.
You have to account for phase change. Melting ice goes from solid to liquid, so you have to add the equation for solid: q=mCdeltaT, to the phase change equation from solid to liquid: q=mdeltaH. mass(m) can also be in moles(n).
You've got to remember that temperature does not increase when the heat is added during a phase change. Therefore, we cannot include it in the regular equation, which is why we multiply the heat inputted by the moles and use that to calculate the delta H Fusion.
There are multiple steps because there are different phases occurring. For example when ice goes from solid to liquid, the bonds are breaking as heat is rising. And then at deltaH fusion the temperature is at 0 because heat is being added to the system.
when dealing with phase changes, you have to account for the energy spent during the actual phase change itself. Say you have 1 mol of water that just got to 100C. It doesn't all evaporate at one instant, it takes x amount of time. In this situation you would apply Hvap
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