Topic 6.9 Notes – Hess’s Law

1. Hess’s Law

Many chemical and physical processes can be broken into a series of steps, and each step has its own enthalpy change $\Delta H$.

Here’s a simple example. The formation of nitrogen dioxide can happen directly:

$$\ce{N2(g) + 2O2(g) -> 2NO2(g)}$$

Or in steps:

$$\ce{N2(g) + O2(g) -> 2NO(g)}$$

$$\ce{2NO(g) + O2(g) -> 2NO2(g)}$$

Both pathways start with $\ce{N2}$ and $\ce{O2}$ and end with $\ce{NO2}$. The total enthalpy change is the same either way.

That works because of the First Law of Thermodynamics:

• Energy is conserved.
• It cannot be created or destroyed.
• At constant pressure, heat flow equals $\Delta H$.

Each step transfers heat to or from the surroundings. When you add the steps together, the total heat transferred is just the sum of each step’s heat.

The key idea:
The enthalpy change depends only on the initial and final substances, not on how you get there.

On the AP exam, you won’t be asked to use formal “state function” language, but this idea is exactly what makes Hess’s Law valid.

2. The Three Hess’s Law Rules

These rules always go together. Every Hess problem uses some combination of them.

a. Reversing a Reaction

If you flip a reaction:

• Reactants and products switch sides.
• The sign of $\Delta H$ changes.
• The magnitude stays the same.

Example:
If $\Delta H = -120 \text{ kJ}$, reversing makes it $+120 \text{ kJ}$.

You are reversing the direction of heat flow.

b. Multiplying a Reaction by a Coefficient

If you multiply the entire reaction by a factor $c$:

• Multiply every coefficient by $c$.
• Multiply $\Delta H$ by the same factor.

If you double a reaction, you double the heat released or absorbed.

c. Adding Reactions

When you add reactions:

• Add the equations algebraically.
• Cancel species that appear on both sides.
• Add their enthalpies.

$$\Delta H_{\text{overall}} = \Delta H_{1} + \Delta H_{2} + \Delta H_{3} + \dots$$

Think of intermediate substances like algebra terms. If something appears on both sides, it cancels.

Whatever you do to the equation, you must do to $\Delta H$.

3. Using Hess’s Law Step by Step

This is how it usually appears on a quiz or FRQ.

1. Write the Target Reaction

This is the reaction you are trying to create.
Check coefficients carefully.

2. Compare with the Given Reactions

For each substance in the target:

• Is it on the correct side?
• Does it have the correct coefficient?

Decide which reactions need to be:

• Flipped
• Multiplied
• Left alone

Do this before touching any numbers. Most mistakes happen when students rush into arithmetic.

3. Manipulate Carefully

Apply one change at a time.

If you:

• Flip → change the sign of $\Delta H$
• Multiply → multiply $\Delta H$

Write the new $\Delta H$ immediately. Don’t wait.

4. Add and Cancel

Add all manipulated equations together.

Cancel intermediates. For example, if $\ce{CO(g)}$ appears on both sides, it disappears in the sum.

If something refuses to cancel, go back. The algebra is wrong.

5. Add the Enthalpies

Add the adjusted $\Delta H$ values.

Keep track of signs. Many wrong answers come from adding a negative incorrectly.

Include units in kJ.

Why the Math Matches the Chemistry

Every reaction involves:

• Breaking bonds (energy absorbed)
• Forming bonds (energy released)

Each step changes the system’s potential energy. When you add steps, the intermediate bond changes cancel out just like intermediate species do.

Only the energy difference between the starting substances and final substances remains.

That’s why the pathway does not matter.

Common Traps

• Flipping a reaction but forgetting to flip $\Delta H$.
• Changing only one coefficient instead of the whole equation.
• Forgetting to multiply $\Delta H$ when scaling.
• Adding enthalpies before confirming the equations actually sum to the target reaction.
• Leaving an intermediate species in the final equation.

On FRQs, they sometimes ask you to justify why adding reactions works. The scoring point usually comes from stating that energy is conserved, so the total heat change equals the sum of the stepwise heat changes.