T - Hess's Law (Lesson)

Hess's Law

In this section, the calculation of enthalpy changes will be approached in a slightly different manner. As has been shown in previous lessons, enthalpy changes can be determined experimentally using calorimetry techniques. On some occasions, for various reasons, chemical reactions proceed in such a way that makes their enthalpy changes very difficult to determine using these techniques. As this lesson will show, enthalpy changes can oftentimes be calculated using other reactions whose enthalpy changes can be experimentally determined.

State Functions

A state function is a thermodynamic property that can be determined based on the present conditions of the system and is not dependent on how the system arrived at that state of conditions. In other words, if thinking in terms of a starting point A and an ending point B, it does not matter what path was taken between the two points, and the distance between those points is the same. Applying this idea to a chemistry scenario, essentially means that the enthalpy change for a reaction can be measured directly from a single step OR a series of reactions can be performed that will lead to the same result. An example to illustrate this thought is shown below.

Hess's Law

Hess's law states something very similar to the description of a state function. Essentially, Hess's law states that if a chemical reaction takes place in a series of steps, then the $LaTeX: \Delta$ $\Delta$ H for the overall process is equal to the sum of the enthalpy changes for the individual steps. The following example illustrates this idea.

Take the combustion of carbon below:

C (s) + $LaTeX: \frac{1}{2}$ $\frac{1}{2}$ O₂ (g) $LaTeX: \longrightarrow$ $\longrightarrow$ CO (g)

The following reactions and their $LaTeX: \Delta$ $\Delta$ H values can be utilized to determine the $LaTeX: \Delta$ $\Delta$ H for this reaction:

C (s) + O₂ (g) $LaTeX: \longrightarrow$ $\longrightarrow$ CO₂ (g) $LaTeX: \Delta$ $\Delta$ H = -393.5 kJ

CO (g) + $LaTeX: \frac{1}{2}$ $\frac{1}{2}$ O₂ (g) $LaTeX: \longrightarrow$ $\longrightarrow$ CO₂ (g) $LaTeX: \Delta$ $\Delta$ H = -283 kJ

When utilizing Hess's Law, the following principles are important to keep in mind:

When a thermochemical equation is written in the reverse direction, the sign of the enthalpy change is switched to the opposite sign. For example, an exothermic reaction (- $LaTeX: \Delta$ $\Delta$ H) written in one direction would be an endothermic reaction (+ $LaTeX: \Delta$ $\Delta$ H) when written in the opposite direction.
When the coefficients of a balanced thermochemical equation are multiplied by some factor, the enthalpy change is multiplied by that same factor. For example, if all of the coefficients are doubled (x2) then the enthalpy change would be twice as great and would therefore be doubled (x2) as well.

Utilizing the equations provided it can be seen that if the second equation is reversed and then added to the first equation their sum would be the same as the reaction for the combustion of carbon.

Reaction #1: C (s) + O₂ (g) $LaTeX: \longrightarrow$ $\longrightarrow$ CO₂ (g) $LaTeX: \Delta$ $\Delta$ H = -393.5 kJ

(notice that since no change was made to the chemical reaction there is no change to the enthalpy value)

Reaction #2: CO₂ (g) $LaTeX: \longrightarrow$ $\longrightarrow$ CO (g) + $LaTeX: \frac{1}{2}$ $\frac{1}{2}$ O₂ (g) $LaTeX: \Delta$ $\Delta$ H = +283 kJ

(In this case, the reaction has been written in reverse and the sign for $LaTeX: \Delta$ $\Delta$ H has been changed from positive to negative)

Once this has been done, the reactions can simply be added. Note that the Overall Reaction depicted is identical to the reaction shown above whose enthalpy was unknown.

The following video shows an additional example. Be sure your volume is turned on!

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