How do you convert from #"kJ/g"# to #"kJ/mol"# ?

Your goal here is to convert kilojoules per gram, #"kJ g"^(-1)#, to kilojoules per mole, #"kJ mol"^(-1)#, which is equivalent to saying that you need to convert the amount of energy per unit of mass to the amount of energy per unit of mole.

In order to do that, you essentially need to use a conversion factor that will take you from grams to moles. As you know, this conversion factor is the molar mass of the given compound.

In order to convert kilojoules per gram to kilojoules per mole, you need to multiply by grams per mole.

#"kilojoule"/color(red)(cancel(color(black)("gram"))) * color(red)(cancel(color(black)("gram")))/"mole" = "kilojoule"/"mole"#

Now, let's say that you're dealing with a compound that has a molar mass of #x# #"g mol"^(-1)#. This tells you that #1# mole of this compound has a mass of #x# #"g"#.

Let's assume that when #"1 g"# of this compound undergoes combustion, #y# #"kJ"# of heat are being given off. You can use the molar mass of the compound as a conversion factor to say that

#y quad overbrace("kJ"/(1 color(red)(cancel(color(black)("g")))))^(color(blue)("= kJ g"^(-1))) * overbrace((x quad color(red)(cancel(color(black)("g"))))/("1 mole"))^(color(blue)("the molar mass of the compound")) = overbrace(((xy) quad "kJ")/"1 mole")^(color(blue)("= kJ mol"^(-1)))#