Because enthalpy is a state property, the enthalpy change between fixed initial and final states is independent of the route taken between them. Applied to chemical reactions, this is Hess's law.

If an overall reaction can be written as the sum of several reactions,

$$R_1+R_2+\cdots\longrightarrow R_{\mathrm{overall}},$$

then

$$\boxed{\Delta H_{\mathrm{overall}}=\Delta H_1+\Delta H_2+\cdots}.$$

Reaction equations may therefore be manipulated algebraically together with their enthalpy changes:

• reversing a reaction reverses the sign of $\Delta H$;
• multiplying all coefficients by a factor multiplies $\Delta H$ by the same factor;
• adding reactions causes species appearing on both sides to cancel.

Example

Suppose

$$\mathrm{C(s)+\tfrac12O_2(g)\rightarrow CO(g)}\qquad \Delta H_1=-110.5,\mathrm{kJ}$$

and

$$\mathrm{CO(g)+\tfrac12O_2(g)\rightarrow CO_2(g)}\qquad \Delta H_2=-283.0,\mathrm{kJ}.$$

Adding the equations cancels $\mathrm{CO(g)}$:

$$\mathrm{C(s)+O_2(g)\rightarrow CO_2(g)}.$$

Therefore

$$\Delta H=\Delta H_1+\Delta H_2 =-110.5-283.0 =-393.5,\mathrm{kJ}.$$

The result does not require the physical reaction to proceed through carbon monoxide. The intermediate equations form a thermochemical cycle: they provide an alternative bookkeeping path between the same initial and final states.

Hess's law is especially valuable when a desired enthalpy change is difficult to measure directly. It also provides the basis for calculating reaction enthalpies systematically from tabulated standard enthalpies of formation.