Heats of combustion of alkanes

alkanes are very unreactive but they do undergo combustion reactions so if you take methane and react it with oxygen you'll get carbon dioxide and water as the products and for all hydrocarbons you're going to get co2 and h2o as the products of a combustion reaction Delta H zero for this reaction is negative 890 kilojoules per one mole of methane which means one mole of methane if you combust one mole of methane you're going to get 890 kilojoules of heat and so this is an exothermic reaction heat is given off so the heat of combustion is the heat that's released on the complete combustion of one mole of a substance in this case we're talking about methane let's talk about hexane next let me draw out the structure for hexane so we have six carbons and notice we have two ch3 groups so here's a ch3 and here's a ch3 so ch3 and ch3 and then we have four ch2 groups so here's one two three and four so that's why you have a four right here so there are four ch2 groups in hexane and here we have the heat of combustion and now we're going to talk about the heat of combustion as the negative change in the enthalpy so negative Delta H zero in terms of kilojoules per mole that gives us a positive value here so for hexane it's four thousand one hundred and sixty-three kilojoules for every one mole of hexane that we combust notice what happens as we move on to heptane here we're increasing in one ch2 group we're going from four ch2 groups to five ch2 groups so now I have five ch2 groups we get an increase in the heat of combustion so more heat is released and that makes sense if you increase the number of carbons you're going to increase in the heat of combustion so if you increased by one ch2 group how much how much do we increase in terms of the heat of combustion well if you take four thousand one hundred sixty-three and subtract that from 4817 that's a difference of 654 kilojoules the pattern continues move on to octane so octane now we have six ch2 groups so we've added one more we've increased our heat of combustion to five thousand four hundred and seventy-one kilojoules per one mole and that is also an increase of 654 kilojoules so for nonane with one more ch2 right we could predict we could estimate the heat of combustion and we could just add six hundred and fifty four to five thousand four hundred and seventy one so we can go ahead and set that up over here so we have five thousand four hundred and seventy one we're adding 654 to that that would give us a five here and then seven and five is 12 so we carry the one that gives us 11 so we get six thousand one hundred and twenty-five so if I write that in here 6125 kilojoules per mole is a pretty good estimation for the heat of combustion of nonane heats of combustion are really useful when you're trying to compare the stability of isomers for example here we have three isomers octane two methyl heptane and two to dimethyl hexane so all these molecules have the molecular formula c8h18 so if we write out the combustion reaction so we have + o2 we know the products are co2 and h2o so we have co2 plus h2o let's go ahead and balance this we have eight carbons on the left side so we need an eight over here on the right we'll put that in front of the co2 and now let's look at hydrogen's there's 18 on the left and so we need 18 on the right and we can do that by putting a nine here because nine and two give us 18 hydrogen's now let's see how many oxygens are on the right side well we have eight and to give us sixteen oxygens here and then nine it gives us nine for the water so that's a total of 25 oxygens on the right side so we need 25 oxygens on the left side if we pretend like this two isn't here for a second we could write a 25 right here but there is a two so we need to divide by two and we're talking about one mole of c88 H teen we're going to leave this as a fraction so 25 over 2 is the amount of oxygen that's necessary to completely react with one mole of c8h18 so now we have our balance equation for our combustion reaction and if we compare these three isomers octane to methyl heptane and two to dimethyl hexane in terms of their heats of combustion we can figure out which one is the most stable isomer here we have an energy diagram for our three isomers on the left here we'll put increasing energy this way all three of our isomers would produce the same products if you combust one mole of them each one would give us eight co2 and nine h2o so there's an energy level associated with our products and we'll say this is the energy level associated with our products it's the same for all three of our isomers next we look up the heat of combustion data for the isomers and this is determined experimentally for example octane has a heat of combustion of about five thousand four hundred and seventy-one kilojoules per mole so that's how much heat is released five thousand four hundred and seventy-one kilojoules per mole and if we know the energy level of the products and we know how much energy was released we can find the energy level of our reactants so there is the energy level for octane next let's think about two methyl heptane so again the energy level the products is here and if we look up the heat of combustion for two methyl heptane we'll find a value somewhere around five thousand four hundred and sixty six so that's how much energy is released when you combust one mole of two methyl heptane five thousand four hundred and sixty-six kilojoules per mole since the energy level the products is the same as the one before but we have a smaller heat of combustion this time that must mean the energy level for two methyl heptane is lower than the energy level for octane and finally we move on to to to dimethyl hexane the energy level the products is the same as before the heat of combustion is five thousand four hundred and fifty eight so somewhere around five thousand four hundred and fifty eight kilojoules per mole is released right that's how much energy or heat is released when you combust one mole of two to dimethyl hexane and since we have a smaller value for you the combustion that must mean the energy is lower for to to dimethyl hexane now we can finally compare the stabilities of our isomers the higher the energy the less stable the compound so octane has the highest energy level has the highest heat of combustion so this is the least stable out of these three this is the least stable the lower the lower the energy for our starting compound the more stable it is so that must mean that two to dimethyl hexane is the most stable isomer out of these three so now we can think about trends as we go from as we go from octane to to methyl heptane to to to dimethyl hexane we're increasing in branching so we're increasing in the amount of branching that we have what happened to the heats of combustion right if we define heat of combustion as the negative of the change in the enthalpy the heats of combustion decrease we went from five thousand four hundred seventy one to five thousand four hundred sixty six to five thousand four hundred and fifty-eight so there was a decrease in the heat of combustion and what about stability we got more stable as we branched more so increased branching in general means increased stability so it's important to be able to analyze heat of combustion data just remember the lower the energy the more stable the compound so the compound that had the highest heat of combustion was the least stable and the compound with the lowest heat of combustion was the most stable so branched alkanes are lower in energy or more stable than straight chain alkanes