More exam questions....

A number of people are still struggling with some of these ΔH manipulations, so let's look at a a bare-bones example. For the reaction A -> B, you have determined that ΔH = +10kJ/mol. If this is true, what's ΔH for the reaction B -> A? The difference in enthalpy between substance "A" and substance "B" is 10kJ/mol, the sign just tells you which is higher (or lower), therefore, ΔH for the reaction B -> A is the same magnitude but in the opposite direction. Similarly, what about the reaction 2A -> 2B? This reaction represents twice as much "action" as the original A -> B, so the energy required (it's endothermic) must be twice as much as the original. Summarizing:
A -> B ΔH=+10kJ/mol
B -> A ΔH=-10kJ/mol
2A -> 2B ΔH=+20kJ/mol
5B -> 5A ΔH=-50kJ/mol

Another question from a previous exam, I've copied the answer key below:

13. The specific heat capacity of gold is 0.128J/g•ºC and the specific heat capacity of iron is 0.449
J/g•ºC. You have heated a 51.294g block of iron to 49.318ºC and placed it on a gold block at
21.516ºC. When the system reaches thermal equilibrium, the temperature of the gold and
iron blocks are 34.468ºC. If the system is perfectly insulated, what was the mass of the gold
block in grams? (20pts each)
The assumption that the system is perfectly insulated implies that all of the energy lost by the iron block is
transferred to the gold block. Finding the energy lost by the iron block:
Eiron = (0.449 J/g•ºC)(51.294g Fe)(14.850ºC)
And the energy gained by the gold block:
Egold = (0.128 J/g•ºC)(x g Au)(12.952ºC)
Setting these energies equal:
(0.449 J/g•ºC)(51.294g Fe)(14.850ºC) = (0.128 J/g•ºC)(x g Au)(12.952ºC)
x = 206g Au

The question came up because this problem might appear to be missing a couple negative signs. Well, it's sort of missing a couple negative signs, so let me clarify (hopefully). The block of iron starts out hot and transfers heat to the gold block. That means that the temperature change for iron should be negative (34.468-49.318 = -14.850), which will give a negative value of E_iron. But look at how the answer is worded. By stating that the energy is lost by the iron block, the answer is implying a negative sign. In this case, the way I worded the answer takes care of the positive and negative signs because I was looking at the quantity of energy independent of the direction that energy was being transferred. If you leave the negatives in when you calculate E_iron, then you will need to include an additional negative sign when you set E_iron equal to E_gold.