The enthalpy of many chemical reactions can be measured through calorimetry. However, scientists and engineers often have to calculate the enthalpy of chemical reactions that can’t be measured with this method. One obvious example of this would be the rusting of iron which is extremely slow and impractical to measure with a calorimeter. As a result chemists have devised a method to measure the enthalpy of this reaction and others using a mathematic principle known as the law of additivity of enthalpies (Hess’ Law). Hess’s Law can be written as an equation as follows:
ΔrH = Δ1H + Δ2H + Δ3H + …..
or
ΔrH = ∑ ΔrH
or, in standard conditions,
ΔrH° = ∑ ΔrH°
Using Hess’ Law allows scientists and engineers to determine the enthalpy of a reaction without direct calorimetry using two rules as follows:
- If a chemical reaction is reversed then the sign of ΔrH changes.
- if the coefficients of a chemical equation are altered then the ΔrH of that equation is altered by the same factor.
A practical example that involves the use of Hess’s Law is to determine the heat of formation of carbon monoxide. It is impractical to solve for the enthalpy change for the formation of carbon monoxide.
C (s) + 1/2O2 (g) → CO (g) ΔrH° = ?
This reaction can not be measured directly as the combustion of carbon monoxide and carbon dioxide occurs simultaneously. However, the standard enthalpy of complete combustion of carbon and carbon dioxide can be calculated using calorimetry. Once these two factors are know Hess’ Law can be applied to determine the enthalpy of formation of carbon monoxide mathematically.
(1) C (s) + O2 (g) → CO2 (g) ΔcH° = -393.5KJ
(2) 2CO + O2 (g) → 2CO2 (g) ΔcH° = -566.0KJ
Reverse the 2nd equation and divide each coefficient and the enthalpy by 2.
C (s) + O2 (g) → CO2 (g) Δ1H° = -393.5KJ
CO2 (g) → CO (g)+ 1/2O2 (g) Δ2H° = +283.0KJ
Now add both equations together and determine the enthalpy of formation for carbon monoxide.
C (s) + O2 (g) → CO2 (g) Δ1H° = -393.5KJ
CO2 (g) → CO (g)+ 1/2O2 (g) Δ2H° = +283.0KJ
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C (s) + 1/2 O2 (g) → CO (g) Δ2H° = -110.5KJ
