What is Hess's law of heat summation?

1 Answer
Jun 23, 2014

Hess's law of heat summation states that the total enthalpy change during a reaction is the same whether the reaction takes place in one step or in several steps.


For example, in the above diagram,

#ΔH_1 = ΔH_2 + ΔH_3 = ΔH_4 + ΔH_5 + ΔH_6#.

In Hess's Law calculations, you write equations to make unwanted substances cancel out.

Sometimes you have to reverse an equation to do this, and you reverse the sign of #ΔH#.

Sometimes you have to multiply or divide a given equation, and you do the same thing to the #ΔH#.


Determine the heat of combustion, #ΔH_"c"#, of CS₂, given the following equations.

  1. C(s) + O₂(g) → CO₂(g); #ΔH_"c"# = -393.5 kJ
  2. S(s) + O₂(g) → SO₂(g); #ΔH_"c"# = -296.8 kJ
  3. C(s) + 2S(s) → CS₂(l); #ΔH_"f"# = 87.9 kJ


Write down the target equation, the one you are trying to get.

CS₂(l) + 2O₂(g) → CO₂(g) + 2SO₂(g)

Start with equation 3. It contains the first compound in the target (CS₂).

We have to reverse equation 3 and its ΔH to put the CS₂ on the left. We get equation A below.

A. CS₂(l) → C(s) + 2S(s); -#ΔH_"f"# = -87.9 kJ

Now we eliminate C(s) and S(s) one at a time. Equation 1 contains C(s), so we write it as Equation B below.

B. C(s) + O₂(g) → CO₂(g); #ΔH_"c"# = -393.5 kJ

We use Equation 2 to eliminate the S(s), but we have to double it to get 2S(s). We also double its #ΔH#. We then get equation C below.

C. 2S(s) + 2O₂(g) → 2SO₂(g); #ΔH_"c"# = -593.6 kJ

Finally, we add equations A, B, and C to get the target equation. We cancel things that appear on opposite sides of the reaction arrows.

A. CS₂(l) → C(s) + 2S(s); -#ΔH_"f"# = -87.9 kJ
B. C(s) + O₂(g) → CO₂(g); #ΔH_"c"# = -393.5 kJ
C. 2S(s) + 2O₂(g) → 2SO₂(g); #ΔH_"c"# = -593.6 kJ

CS₂(l) + 3O₂(g) → CO₂(g) + 2SO₂(g); #ΔH_"c"# = -1075.0 kJ

Hope this helps.