Given the following data, what is the enthalpy associated with the given equation? ##

#2H_2(g) + O_2(g) rarr 2H_2O(g)# #;DeltaH_1^@=-484*kJ*mol^-1# #(i)#

#2CO(g) + O_2(g) rarr 2CO_2(g)# #;DeltaH_2^@=-566*kJ*mol^-1# #(ii)#

We want #DeltaH_"rxn"^@# for..........

#CO_2(g) + H_2(g) rarr CO(g) +H_2O(g)# #;DeltaH^@=??# #(iii)#

If I add #(i)-(ii)#, I get...........

#2H_2(g) + cancel(O_2(g)) +2CO_2(g) rarr 2CO(g) + cancel(O_2(g)) +2H_2O(g)#

#=2H_2(g) +2CO_2(g) rarr 2CO(g) +2H_2O(g)#

But this is EQUAL to #2xx(iii)#

And thus #DeltaH_"rxn"^@=1/2(DeltaH_1^@-DeltaH_2^@)#

#1/2(-484-(-566))*kJ*mol^-1=+41*kJ*mol^-1#....if I have done my 'rithmetic rite!

This is the Hess's law

In the Hess's law you should add both the reactions like this

For example

Hess's law states that the addition of total heat absorbed and and released of some reactions is equal to#DeltaH#of the combined equation in one or many steps.This applies to the first law of thermodynamics,principle of conservation of energy
And you should know that the energy absorbed or released is expressed as #DeltaH#(enthalpy)

For an equation like

A + B=AB
C+B= CB

A + B = AB
C+ B= CB

Cancel the same reactants on both sides and add the reaction

A + C = CB + AB

Even though its not possible

So if we add the the #DeltaH# of the reactions we can get the #DeltaH# of this reaction

Even you can get the #DeltaH# of sensible reaction by reversing the #DeltaH# of a more sensible reaction

For example if the #DetaH# of this reaction is

C + B = CB #DeltaH# = x
CB = C +B #DeltaH = -x#
And consider
A + B#DeltaH = d#

Now again do what we did before

A + B = AB
CB = C + B

CB + A = C + AB

And now add the #DeltaH# of this reaction is #-x + d#

Do the same for this reaction

#2H_2 + O_2 rarr 2H_2O#
#2CO + O_2 rarr 2CO_2#

If we cancel the same terms on both side that is #O_2# and add the reactions we get

#2H_2 + 2CO = 2H_2O + 2CO_2#

And that's not a sensible reaction and what we wanted
so we do what we did in the above example

#2H_2 + O_2 rarr 2H_2Ocolor(white)(XXX)DeltaH = "-484kJ/mol"#
# 2CO(g) + O_2(g) -> 2CO_2(g) ∆H = -566 kj/mol#
#2CO_2(g) rarr 2CO(g) + O_2(g)color(white)(XXX)DeltaH = "-("-566 kj/mol") = "566kJ/mol"#

Add both the reactions

#2CO_2(g) + 2H_2(g) + O_2(g) -> 2CO(g) + 2H_2O(g) + O_2(g)#

Cancel the same terms

#2CO_2(g) + 2H_2(g) + cancel(O_2(g)) -> 2CO(g) + 2H_2O(g) + cancel(O_2(g))#

Now add the #DeltaH#

#-484kJ/mol + 566kJ/mol = 82kJ/mol#

But this is the #DeltaH# of

#2CO_2(g) + 2H_2(g) -> 2CO(g) + 2H_2O(g) #

not

#CO_2(g) + H_2(g) -> CO(g) + H_2O(g) #

To caculate the #DeltaH#of this reaction divide the #DeltaH# by two

= 41kJ/mol