Another complex (multi-step) problem

Here's one more multi-step heat problem.

35.00 g of an organic compound are melted and then heated to 85.5^oC. The compound is then cooled slowly. At 79.6^oC it begins to freeze. If it loses 5420 calories of heat while it cools and freezes, what is the heat of fusion? (the specific heat of the compound is 0.67 cal/g ^oC).

Once more, this is a two step process: cooling and freezing. We can again use the formula

What do we know?

There are several VERY important issues associated with "sign" in this problem.

• ΔT is -5.9oC. Remember that ΔT is always final T - initial T
• heat (in the problem itself) is also negative because any time heat is leaving (exothermic) the value is recorded as a negative value.
• Our answer will also be negative, since we will be finding the amount of heat that must be removed in order to freeze the compound. (Normally, heat of fusion (ΔH_fus)is recorded as the heat that must be added to melt a compound)

Since we are looking for the heat of fusion, we'll need to rearrange the equation. First we'll move the temperature change factor to the left side

then, we'll isolate the heat of fusion

After that, we can substitute in our values and solve the equation