The standard enthalpies of formation of gaseous propyne (C₃H₄), propylene (C₃H₆), and propane (C₃H₈) are +185.4, +20.4, and -103.8 kJ/mol, respectively. (c) Which is the most efficient fuel in terms of heat evolved per unit mass?

Video transcript

Hello everyone. So in this problem we're given this set of data right here. We're trying to see or determine the compound that produces the most heat per unit mass in this part is going to be referring to all of the combustion reactions are going on. And of course the formula for our delta age of reaction is going to equal to the delta H. Of the products minus the delta age of the reactivates. Alright. And so most of these values for men delta H. S are either going to be given to me are found online. But for you guys, you can Probably ask your professor if they have provided you with one of maybe a shed that has all the data ages or maybe it's given to you by your textbook. I'm just going to use the ones that I have. So first we'll start for our beauty. Put it in this blue indigo color. So keep in mind we're doing a combustion reaction. So we'll have C4 age 10 plus 13 halves Of our 0. 2. And that's going to combust and produce four moles of c. 0. 2 And five moles of H 20. So we're going to go ahead and use this formula here for all three of these delta ages of the reaction. Alright, continuing on. So my delta H of the reaction is going to equal to Well first we want to go ahead and find the sum of the delta asia for my of my products. So we'll do the four C. 02 and then five H. 20. So let's see We have four moles of R. C. 02 and each delta H. Of C. 02 is going to equal to negative 300 .5 Killer Jewels Per Mole. And then we're adding five times the delta age of H. 20. And that's going to equal to - 0.82 Killer jules Permal. And then we're going to go ahead and subtract this by the some of the delta H. For my reactive. And so I'll do the delta age of my c. four h. 10. So my butane first And that's going to equal to negative 125 0.6 killer jewels per mole. And the delta H. Of my 02 is just zero. So putting all of this into my calculator, I'll get a value of negative 2657 0. killer jewels per mole as my unit. All right now moving on to my beauty, I'll do this in this green color. So same exact process. We're going to go ahead and use this formula. We're gonna write out our combustion reaction and plug in values. All right scrolling down. So my reaction, it's going to be We have C4 C four H eight Adding 602 to go ahead and make four C. 02 and four H. Two Os scrolling down a little bit more. We'll have that. The delta H. Another reaction is equaling two four times Negative. 0.5 kila jules Perma. We're going to add more times -2 41.82. Kill it jules promote. And just to specify that this value is talking about our C. 02 and this value here, it's going to be referring to H 20. And then we're going to go ahead and subtract the delta age of all of our reactant. So we're going to have delta age of our beauty Being negative 0.63 kila jules Permal and our delta H. Of our 0. 2 again is just zero. Putting all this into my calculator. I'll get a total of negative 2540 0. killer jewels per more. All right, next I have my butin just growing up in this purple color. So first we need to go ahead and write out our combustion reaction for this. So we have our C. Four age six Plus a love and half of r. 0. 2 To go ahead and make our formals of c. 0. 2 And three moles of H. 20. So again, using the formula we have that the delta H. Of the reaction equaling two four times -393.5 kila jules Permal plus three times The -241.82 killer jewels per mall. I'm gonna go ahead and subtract this by a delta age of all our reactant. So we have, let's see here, we have The 165 to kill a jewels per mole. And of course our 02 delta H. Is just equal to zero. I'm putting all this into my calculator. I get a total of negative 2464. killer jewels. Her mom. No going back to the problem. It's saying which one produces the most heat per unit mass. So let's go ahead and do some dimensional analysis. So off to the side, I'll go ahead and do this in the pink color. Will do my dimensional analysis. So continuing on here then for the first one we have given this value. So maybe I'll just put another start. We'll just use that as our conversion factor. I apologize. We will not be using this as the conversion factor but rather we'll be using the molar mass because instead of our mold, that's not our per unit mass, we need grams in our case. So the only way to do that is of course using our molar mass. So we have most on the bottom here because it's Permal to moses on the bottom and kill jewels on top. So we want to go ahead and cancel moles and go to grams. And so we'll have the one more being on top. So you cancel the units on the bottom. And of course the Mueller mass for my C four H Is going to equal to 58 0.12 g. As you can see the moles will cancel beautifully leaving us with a total of 45 0. and the units of course it's just killed jules per gram. All right. Moving on to the 2nd 1 here again, using the moller mess. So Course one moles on top and the molar mass of my C four H 8. That's going to be equal to 56.11 g. Again, the moles will cancel out nicely leaving us with the value of 45 .2. Again, units is killer jewels. Program the last one. So of course we have our one mole on top and the molar mass of my C four H six is equal to 54.91 g. Again, the unit's pockets up beautifully and we get the total or the conversion factor or affected conversion product as 0.5 units being killed jules programs. And now we're simply comparing These three values here. So if you look closely only the decimal place is the one that's different. So if you compare the 7.2 and the .5 of course this is going to be our biggest value which is going to be beauty. And so again the question is asking which compound will produce the most heat. And from our calculations here that's in highlight, we know that it's going to be this one. This one has the highest value, and that means that the butane is going to go ahead and produce the most heat per unit mass. So our final answer is going to be a.