Hess's Law

Enthalpy, you may recall, is a state function. This means that the enthalpy change for a chemical reaction is independent of the path by which the products are obtained. In 1840, the Russian chemist Germain Henri Hess, a professor at the University of St. Petersburg, discovered this result by experiment. Hess's law Hess's law states that the total energy (or enthalpy) change for a chemical reaction is the same, whatever route is taken.

The enthalpy changes for some reactions canno be measured directly. To find these you use an indirect approach. Chemistrs use enthalphy changes that they can measure to work out enthalpy changes that they cannot. In particular, it is ofter easy to measure enthalpies of combustion.

To understand Hess’s law fully and to see how you can use it, consider a simple example. Suppose you would like to find the enthalpy change for the combustion of graphite (carbon) to carbon monoxide.

The direct determination of this enthalpy change is very difficult, because once carbon monoxide forms it reacts further with oxygen to yield carbon dioxide. If you do the experiment in an excess of oxygen, you obtain only carbon dioxide, and the enthalpy change is the heat of complete combustion of graphite. On the other hand, if you do the experiment in a limited quantity of oxygen, you obtain a mixture of carbon monoxide and carbon dioxide, and the heat of reaction is a value appropriate for a mixture of these products. How can you obtain the enthalpy change for the preparation of pure carbon monoxide from graphite and oxygen? The answer is to apply Hess’s law. To do this, imagine that the combustion of graphite to carbon monoxide takes place in two separate steps:

In the first step, you burn 2 mol of graphite in 2 mol of oxygen to produce 2 mol of carbon dioxide. In the second step, you decompose this carbon dioxide to give 2 mol of carbon monoxide and 1 mol of oxygen. The net result is the combustion of 2 mol of graphite in 1 mol of oxygen to give 2 mol of carbon monoxide. You can obtain this result by adding the two steps, canceling out 2 mol CO₂ and 1 mol O₂ on both sides of the equation.

According to Hess’s law, the enthalpy change for the overall equation (which is the equation you want) equals the sum of the enthalpy changes for the two steps. Now you need to determine the enthalpy changes for the separate steps. You can determine the enthalpy change for the first step by simply burning graphite in an excess of oxygen, as described in the bomb calorimeter experiment. The result is ΔH = −393.5 kJ per mole of CO₂ formed. For 2 mol CO₂, you multiply by 2

The second step, the decomposition of carbon dioxide, is not an easy experiment. However, the reverse of this decomposition is simply the combustion of carbon monoxide. You could determine the ΔH for that combustion by burning carbon monoxide in an excess of oxygen. The experiment is similar to the one for the combustion of graphite to carbon dioxide.

From the properties of thermochemical equations (Section 6.4), you know that the enthalpy change for the reverse reaction is simply (−1) times the original reaction.

If you now add these two steps and add their enthalpy changes, you obtain the chemical equation and the enthalpy change for the combustion of carbon monoxide, which is what you wanted.

You see that the combustion of 2 mol of graphite to give 2 mol of carbon monoxide has an enthalpy change of −221.0 kJ.

«Measurement of Heat of Reaction: Bomb calorimeter Index The Joule-Thomson effect »