# What is Hess's law of heat summation?

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.

EXAMPLE

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

Solution

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.