In this problem, we're going to calculate the change in internal energy, which is Delta E, when 15.5 grams of acetylene reacts. It's telling me there's an external pressure of one atmosphere pushing against this, and as it expands, or reacts, it will return to 25, and we'll make our measurement for that. Now the first law of thermodynamics tells me that the change in energy is the sum of the heat term and the work term. Since we are working against an external pressure we can, rep that's constant, we can replace the Q with delta H because Q at constant pressure environment is delta H and we're going to replace the work with minus. P delta V. So we could come in here and use the Ps and the change in volumes to calculate that or use our balance equation and use PV equals NRT. We can replace the minus P delta V with instead, delta E equals delta H minus RT delta N. And we know it's P, V equals N, R, T the volume is changing, for the most changing, in a direct relationship. So no we can look at our balanced equation and plug information in what we're calculating now, is the change in eternal energy for the balanced equation. And that's not exactly what's being asked yet but let's get it for the balanced equation the delta H is a negative 1255.5 kilojoules. All our. We'll need the one that's in units of joules. 8.314 joules per mole Kelvin but I can't add these terms unless we're in kilojoules so let's go ahead and a kilojoules is 1,000 joules. So now we have it in kilojoules per mole Kelvin. Okay, that's the R the temperature is in Kelvin at 298. because that's what 25 degrees Celsius is, and delta N, now delta N is the change in moles of gas, final minus initial. We have three moles of gas, in the balanced equation at the end, and we have three and a half moles. So that's one plus two and a half, we have three and a half moles of gas at the beginning. So as you go through and you calculate this, you are going to determine that for the reaction as balanced, we have 1254.3. Kilojoules. And I have got a plus sign here when I should have a minus sign. Okay. Minus RT delta N now we see that we're going to be subtracting a negative number so we're going to be adding a little bit back. Changes it slightly and usually the work term is much smaller than the heat portion and we see that case here, it's almost the same as the delta H, but it did bring it up, ever so slightly, to a little less negative value of 1254.3, now this, this quantity is for the equation as balanced. But they didn't ask for in the amount as balanced they want to know it when you react this amount of acetylene. So, let's start with the 15.5 grams of acetylene C2 H2. Well this relationship here is for the balanced equation so if we incorporate what we know about C2 H2 it is 1254.3 kilojoules for every one mole of C2 H2 that reacts. So I know that this is the relationship from my thermochemical equation. That I'll need to use but this is not a delta H, this is a delta E. But it doesn't, it works the same way. So the first thing I'll need to do is go from grams of C2 H2, to moles of C2 H2 okay, the molar mass is 26.04 grams per mole now, I can use that relationship that I determined above. And go from moles of C2 H2. So the total delta E and we have 1254.3 kilojoules for every one mole and this will give me negative 747. Excuse me, kilojoules. So this was for the balanced equation and this is for the amounts given.
