Question #b4e08

To calculate the enthalpy change for a reaction, in your case for the combustion of ethane, you can use the standard enthalpies of formation of the species involved in the reaction.

More specifically, you can calculate the enthalpy change of a reaction by

#DeltaH_"rxn" = sum(n * DeltaH_"f prod"^@) - sum(m * DeltaH_"f react"^@)#, where

#n#, #m# - the number of moles of the compound;
#DeltaH_"f prod"^@# - the standard enthlapy of formation of a product;
#DeltaH_"f react"^@# - the standard enthalpy of formation of a reactant.

You can get the values for the standard enthalpies of formations from here:

https://en.wikipedia.org/wiki/Standard_enthalpy_change_of_formation_(data_table)

So, the balanced chemical equation looks like this

#C_2H_(6(g)) + 7/2O_(2(g)) -> 2CO_(2(g)) + 3H_2O_((l))#

Keeping in mind that the standard enthalpy of formation for an element in its natural state is zero, you will have

#DeltaH_"rxn" = (2 * DeltaH_("f "CO_2)^@ + 3 * DeltaH_("f "H_2O)^@) - (1 * DeltaH_("f "C_2H_6)^@ + 7/2 * underbrace(DeltaH_("f "O_2)^@)_(color(blue)("=0)))#

Using the values from the table will get you

#DeltaH_"rxn" = [2cancel("moles") * (-393.5"kJ"/cancel("mole")) + 3cancel("moles") * (-285.8"kJ"/cancel("mole"))] - [1cancel("mole") * (-83.7"kJ"/cancel("mole")) + 0]#

#DeltaH_"rxn" = -"787 kJ" -"857.4 kJ" + "83.7 kJ"#

#DeltaH_"rxn" = color(green)(-"1560.7 kJ")#