Adding equilibria is a powerful bookkeeping tool: if several reversible steps sum to a net chemical equation, their equilibrium constants combine predictably. This lets you relate an overall equilibrium position to equilibria of component reactions.

Core idea: summing reactions combines their K values

When two or more chemical equations are added to obtain a single overall reaction, the corresponding equilibrium constants multiply. Conceptually, each step establishes a reactant–product ratio; performing steps in sequence compounds those ratios.

When you are allowed to multiply K values

• The component reactions must be addable to give a meaningful net equation (species may cancel if they appear on both sides).

• Each $K$ must correspond to the reaction exactly as written in the set you are adding.

• The overall reaction is interpreted as the combined process of the individual equilibria.

Mathematical statement

This rule is consistent with the law of mass action: multiplying equilibrium-constant expressions corresponds to adding the stoichiometric equations, because the exponents in $K$ track stoichiometric coefficients.

Why multiplication makes chemical sense

Cancellation of intermediates

Often, a species is produced in one step and consumed in a later step.

When you add the equations, that species cancels from the net reaction, and it also cancels algebraically when the $K$ expressions are multiplied. The overall $K$ therefore depends only on species present in the final net equation.

Connection to reaction “strength”

This diagram summarizes how the equilibrium composition shifts as the magnitude of $K$ changes. Large $K$ corresponds to product-dominant mixtures at equilibrium, small $K$ corresponds to reactant-dominant mixtures, and intermediate $K$ gives appreciable amounts of both. Source

• If each step has $K>1$ (product-favoured), the product $\prod K_i$ tends to be even larger, indicating an even more product-favoured overall reaction.

• If one step has a very small $K$, it can dominate the product and make the overall reaction reactant-favoured, even if other steps are product-favoured.

Log form (useful for reasoning)

Because logarithms turn products into sums, chemists often reason about combined equilibria with logs (without needing any calculation details):

• $\ln(K_{\text{overall}})=\sum \ln(K_i)$

• $\log(K_{\text{overall}})=\sum \log(K_i)$

This additive property helps compare contributions of individual steps to the overall equilibrium position.

Practical workflow (no arithmetic required)

How to apply the rule reliably

• Write each reaction step with its given $K$.

• Add the reactions to obtain the overall reaction (cancel species that appear on both sides).

• Multiply the listed $K$ values to obtain $K_{\text{overall}}$ for the summed equation.

Common pitfalls to avoid

• Multiplying $K$ values for reactions that do not sum to the stated overall equation.

• Forgetting that the $K$ provided must match the reaction as written (direction and coefficients matter, even though those adjustment rules are handled separately).

• Treating $K$ like it adds directly; it is $K$ values that multiply, not add.

What this rule enables in equilibrium reasoning

• Building an overall equilibrium constant for a net transformation from chemically meaningful steps (e.g., coupling equilibria that share intermediates).

• Checking consistency: if an overall reaction can be obtained by two different sets of steps, both routes should yield the same $K_{\text{overall}}$ when the equations truly represent the same net process.