 The problem reads, calculate delta H for the reaction C-H4 gas plus NH3 gas goes to H-C-N gas plus 3H2 gas from the reactions, and these are three reactions to which we are given the change in enthalpy. And we're to calculate the final change in enthalpy. Now the idea here is to use Hess's Law. Hess's Law states that energy changes are state functions so it doesn't depend on the path, doesn't depend on the intermediate steps here. The amount of energy depends only on the states of the reaction and the states of the product but not on the intermediate steps, provided everything is at the same temperature and pressure. So we are assuming that these four reactions satisfy Hess's Law. Okay, so what does that mean? That means that what we're going to do is find factors for each of these so that we get this reaction and we're going to multiply delta H times each of the respective factors and add it up. So what's key here? NH3. NH3, this is on the wrong side and there's two of them. So we need to multiply by minus one-half. So we're going to multiply this by minus one-half. Next, what's key here? CH4. Right number, wrong side, so minus one. And the last one is we see HCN, it's on the correct side but there's too many of them. So it's just one-half times that. So what do we have? We have, let's write these down, minus one-half and two, minus one-half times three, minus three-halves H2. And on this side, let's draw a line. We have minus one-half times two, so minus NH3. So delta H of this reaction here is minus one-half times minus 91.8. Next one down. We have minus C, minus 2H2 on this side, and on this side we have minus CH4. And so of this reaction, the change in enthalpy is minus, minus 74.9. And this one is one-half, so one-half H2, plus one-half times two, that would be one C, plus one-half N2, and on this side we have HCN. And delta H now is one-half of 270.3. First let's make sure everything's the same unit. We've written down the numbers correctly. We've written down the same factors, yes. And we're going to check this part by making sure we get the original reaction. So first of all, the odd things out should cancel. Here it goes. One minus one-half N2 goes with one-half N2. And minus C goes with plus C. We should be only left with reactants that are here. So we have minus three-halves, that's minus 1.5, minus two, that's minus 3.5, and then plus one, so minus 3H2 on this side. And on this side, let's bend this so we don't waste our space here. We have minus NH3, minus CH4, and plus HCN. Put the minuses on the other side. What do we get? We get NH3 plus CH4 goes to HCN plus 3H2. Is that the same? It is indeed. We're good to go. So now we just need to add these up. So delta H of the main reaction is, let's get a calculator, minus 0.5 times minus 91.8 minus, and then that's going to be times minus again. So let's raise that minus and put in a plus 74.9. And then we have plus 0.5 times 270.3. So minus 5 times minus, and then those two minuses together are plus, and then this is plus. So we're good. Enter 255.95. So 255.95, and that is kilojoules per mole is our answer. So the change in enthalpy for this reaction here is 255.95 kilojoules per mole.