Problem

The heat of atomization is the heat required to c…

03:31

Problem 118 Hard Difficulty

Calculate Hrxn for the combustion of octane (C8H18), a component of gasoline, by using average bond energies, and then calculate it using enthalpies of formation from Appendix IIB. What is the percent difference between your results? Which result would you expect to be more accurate?

Answer

$0.88 \%$

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Chemistry 102

Chemistry 101

Chemistry: Structure and Properties

Chapter 9

Thermochemistry

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Video Transcript

So this problem wants us to take the combustion of octane, which is to see eight h eighteen plus twenty five o two, form sixteen co, two plus eighteen h two o and all of these Aaron the Gashes state and wants us to find the Delta h of this reaction using bond energies and using Delta H of formation and then finally, percent difference between them and explain which one is more accurate. And so the first thing we'LL do is with bond energies or an trapeze on DH. So the way we do this is that Delta h of reaction is equal to the sum of the H is off Bond's broken minus the sum of the ages of bonds formed and so referencing the previous page from our octane. Since we have two of them on eighteen ch bonds, we have thirty six total ch bonds plus ah, fourteen total cc bonds and then we have twenty five oxygen. So we have twenty five o double bonds. So these are our bonds broken, and then we subtract our bonds formed. We have thirty two c o double bonds formed because we have two of these per carbon dioxide and we have sixteen. So thirty two and then similarly with the water, we have thirty six. Um oh h Bones. And that's because we have two per water and eighteen waters, so we have thirty six of those. So now we can plug in all of the values. For those we have thirty six times for fourteen. That is the ah Bond energy of CH than fourteen times three forty seven for CC and then twenty five times for ninety eight for oh, double bond. And then we subtract thirty two times seven ninety nine, which is the C e o double bond and then thirty six times for sixty four thee o h bond. And when we do this, that gives us three, two, two, one two minus for two, two, seven, two. Which gives us negative ten thousand sixty killa jewels. So this is our answer for using ah bond energies a rental piece. Now we can use Delta h of formation for these. And so the way we do this is that our Delta h of reaction is going to equal the Delta H information of the products minus the Delta H information of the reactant ce and so we'LL start with the products We have eighteen Delta H formation of H two o gas plus sixteen times the Delta H L Formation of co two gas And then we subtract the reactant CE We have twenty five times the Delta H of formation off O two gas which is zero Ah, and then we we subtract the whole thing so we'll add the two times the delta h of formation of our octane And so when we do this, we end up with negative i'll plug in the values first actually, So we have eighteen times the h two o one is negative two forty one point eight The co two is negative three ninety three point five The O two is zero and the thie octane is negative to forty nine point seven three. And so when we combined these and add them together and subtract, we get that the Delta h of reaction using this method is negative one o one for nine Killa Jules. And so now we have our two answers with our two different methods. And so, in order to find the percent difference, we take the absolute value off one of our answers and subtract the other one and then divide by the original. And we do absolute value here just so that we get a positive percent and then we multiplied by one hundred. But that gives us a zero point eight eight percent difference. So there isn't that large of a difference here at all. It's less than one percent. However, the using the Delta H of formations is going to be more accurate as the bond energies are based on the average bond energy off that bond. And so the Delta H of formation is specific. Her molecule Ah, whereas when it's specific per bond, it is not quite as accurate. So those are the final answers, and the Delta H of formation method is more accurate.

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