Hess's Law

Hess's law explains how to find the enthalpy change of a reaction by adding other reactions with known enthalpy changes. It works because the overall $\Delta H$ depends on the initial and final states, not on the route between them.

In short: if the chemical equations add up to the target reaction, their enthalpy changes add up too. This is only valid when the equations describe the same substances in the same physical states under the same conditions.

What Hess's law means in chemistry

Imagine taking the same chemical system from one set of reactants to one set of products by two different routes. If the initial and final states are the same, the total enthalpy change is the same as well.

That is why Hess's law is useful in thermochemistry. Some reaction enthalpies are hard to measure directly, but the same overall change can often be built from reactions whose $\Delta H$ values are already known.

The idea is usually written as

$$\Delta H_{overall} = \Delta H_1 + \Delta H_2 + \Delta H_3 + \cdots$$

This statement applies only when the adjusted equations really combine to give the target reaction.

How to calculate $\Delta H$ with Hess's law

Use this sequence:

1. Write the target reaction exactly.
2. Pick known reactions that can be rearranged to make it.
3. Reverse any reaction if needed, and reverse the sign of $\Delta H$.
4. Multiply any reaction if needed, and multiply $\Delta H$ by the same factor.
5. Add the equations and cancel species that appear on both sides.

The algebra with the equations and the algebra with $\Delta H$ must stay matched. If you change one, you must change the other in the same way.

Worked example: finding $\Delta H$ for forming $CO_2$

Suppose you want the enthalpy change for

$$C(graphite) + O_2(g) \rightarrow CO_2(g)$$

and you know these two reactions:

$$C(graphite) + \frac{1}{2}O_2(g) \rightarrow CO(g) \qquad \Delta H = -110.5\ \mathrm{kJ/mol}$$ $$CO(g) + \frac{1}{2}O_2(g) \rightarrow CO_2(g) \qquad \Delta H = -283.0\ \mathrm{kJ/mol}$$

Now add them:

$$\begin{aligned} C(graphite) + \frac{1}{2}O_2(g) &\rightarrow CO(g) \\ CO(g) + \frac{1}{2}O_2(g) &\rightarrow CO_2(g) \end{aligned}$$

The $CO(g)$ cancels because it appears on both sides. The two $\frac{1}{2}O_2(g)$ terms combine to give $O_2(g)$, so the overall reaction becomes

$$C(graphite) + O_2(g) \rightarrow CO_2(g)$$

Then add the enthalpy changes:

$$\Delta H = -110.5\ \mathrm{kJ/mol} + (-283.0\ \mathrm{kJ/mol}) = -393.5\ \mathrm{kJ/mol}$$

So the enthalpy change for forming $CO_2(g)$ from graphite and oxygen is

$$\Delta H = -393.5\ \mathrm{kJ/mol}$$

This is the core pattern of Hess's law. You do not need a new formula each time. You need equations that combine to the target reaction, plus careful sign changes and cancellation.

Why enthalpy can be added this way

Hess's law works because enthalpy is a state function. A state function depends on the state itself, not on how the system got there.

That is the main contrast with a path-dependent quantity. If two routes begin and end at the same states, their total enthalpy change must agree. If that were not true, you could create inconsistent energy cycles.

Common Hess's law mistakes

Forgetting to change the sign when reversing a reaction

If you flip a chemical equation, the corresponding $\Delta H$ must change sign. A reversed exothermic step becomes endothermic, and vice versa.

Forgetting to scale $\Delta H$

If you multiply a reaction by $2$, you must also multiply $\Delta H$ by $2$. The enthalpy change scales with the amount of reaction written.

Canceling the wrong species

Only cancel a species if it appears on opposite sides after the equations are arranged. If it appears on the same side in two equations, it does not cancel.

Ignoring physical states

States matter in thermochemistry. $H_2O(l)$ and $H_2O(g)$ are not interchangeable, and using the wrong state can give the wrong target reaction and the wrong enthalpy.

When Hess's law is useful

Hess's law is used when a reaction enthalpy is difficult to measure directly but related reactions are known. It often appears with enthalpies of formation, combustion data, and reaction cycles in introductory chemistry.

It is also a good check on thermochemical reasoning. If the equations do not combine cleanly into the target reaction, the enthalpy sum is not ready yet.

Try a similar thermochemistry problem

Try your own version by starting with a target reaction and three known thermochemical equations, then see whether you need to reverse or scale any of them before adding. If you want a related next step, compare this with enthalpy and entropy so the role of $\Delta H$ fits into the bigger thermodynamics picture.