Lesson: Chapter - 9

Hess’s Law

The total enthalpy of a reaction is independent of the reaction pathway. This means that if a reaction is carried out in a series of steps, the enthalpy change (DH) for the overall reaction will be equal to the sum of the enthalpy changes for the individual steps. This idea is also known as Hess’s law. Here are some rules for using Hess’s law in solving problems:

1. Make sure to rearrange the given equations so that reactants and products are on the appropriate sides of the arrows.
2. If you reverse equations, you must also reverse the sign of DH.
3. If you multiply equations to obtain a correct coefficient, you must also multiply the DH by this coefficient.

Finally, in doing Hess’s law problems, it’s often helpful to begin by working backward from the answer that you want. In other words—write the final equation first. Try it out.

Example

Given the following equations
H₃BO_3(aq) ? HBO_2(aq) + H₂O_(l) DH_rxn = -0.02 kJ
H₂B₄O_7(aq) + H₂O_(l) ? 4HBO_2(aq) DH_rxn = -11.3 kJ
H₂B₄O_7(aq)?2B₂O_3(s) + H₂O_(l) DH_rxn = 17.5 kJ
find the DH for this overall reaction:
2H₃BO_3(aq) ? B₂O_3(s) + 3H₂O_(l)

Explanation

Multiply the first equation by 4:
4H₃BO_3(aq) ? 4HBO_2(aq) + 4H₂O_(l) DH_rxn = 4(-0.02 kJ) = -0.08
Reverse the second equation:
4HBO_2(aq) ? H₂B₄O_7(aq) + H₂O_(l) DH_rxn = +11.3 kJ
Leave the last equation as is:
H₂B₄O_7(aq) ? 2B₂O_3(s) + H₂O_(l) DH_rxn = 17.5 kJ
Cross out common terms and you are left with:
4H₃BO_3(aq) ? 2B₂O_3(s) + 6H₂O_(l) DH_rxn = 28.8 kJ

Divide the above equation and the enthalpy by 2 and you see that the answer is 14.4 kJ (the reaction is endothermic).

Bond Energies

As we mentioned earlier, another way of calculating the enthalpy change in a chemical reaction is by using bond energies. You are probably aware that energy must be added or absorbed to break bonds and that energy is released when bonds are formed. Therefore, you can calculate the total enthalpy of the reaction using the following formula:

DH = bonds broken - bonds formed

Example

Using bond energies, calculate the change in energy that accompanies the following reaction:

Explanation

If the problem you’re trying to solve involves more complex molecules, be sure to draw out their structures to determine how many bonds of each type you have.

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