Hess's Law Example Problem

so we need to calculate this enthalpy for this reaction and we are given three subreactions to do that and to complete this we need to use Hess's law which basically states that the enthalpies of the constituent reactions add to the enthalpy of the total reaction. so let's do this first, we need to manipulate these three equations so that they add up to this and I see here in this first equation that we have a CH a C 2 H 2 on this side of the left side, but the total reaction requires 2 C 2 H 2 is in the right side, so let's reverse this whole first equation and that will give us 2 co2 plus h2o, which produces C 2 H 2 plus 5 halves of co2 and as you can see, I wrote that Delta H is on the side and when we reverse the equation we need to do the same with the Delta H or the enthalpy of the reaction, so instead of a negative change of one thousand two hundred ninety-nine point five kilojoules per mole of enthalpy we are going to have a positive enthalpy change, so this goes to be positive one thousand two hundred ninety-nine point five kilojoules per mole of reaction and one mole of reaction is just this whole equation here now, let's move on to the next one.

I see that the carbon is in the same place on the left side of the equation, but we need two moles of carbon, so we have to multiply this whole equation by two and what we do here will be the same for the enthalpies, so instead of negative three hundred ninety-three point five we're going to multiply that by two, which gives us negative 787 kilojoules per mole of reaction kilojoules per mole of reaction and now we have two C plus two o2, which gives two moles of co2, well, the last one I see we have each one: it's on the left side of the equation as we need it to be here we could just ignore them and ignore them so it looks like we could leave this third equation alone and I also said we could ignore them because they're not even in occlusion here, so that's going to tell us that they're probably going to cancel out once we add these three together, so let's see how that works.

I forgot to write down the enthalpy B for the sauce equation, so let me write that down and now let's add all of these together, so I see two co2 here. Is there any other place where we have co2? And yes, it's here, so these two cancel each other out because they're on opposite sides of the equation. Now I have water. we have another H here and since this one is on the left, this one is on the right, they cancel C - H - I don't see any more, so let's leave it on the right side of the equation and then we have five halves - now I see you Or two here and we go - this way when we add two and a half that will leave us with five halves so all these oxygens cancel out and now we are left with two C plus h2 produces C - H - just like we needed here, so it's a sure sign that we are on the right path.

Now all we have to do is add these enthalpies, so 1200 99.5 - 787 - two eighty-five point eight, which gives us two hundred twenty-six point seven kilojoules per mole and that should be the answer