AP® Chemistry · Unit 7 · Topic 7.6
Properties of the Equilibrium Constant
Reversing a reaction inverts K, and multiplying all its coefficients by n raises K to the nth power, because both moves flip or rescale every exponent in the equilibrium expression.
The equilibrium expression is a ratio of products over reactants, each raised to its coefficient. Reverse the reaction and products become reactants, so the whole ratio flips upside down: K_reverse = 1/K_forward. Nothing about the actual position of equilibrium changes, only which side you're calling the top.
Scaling the equation works differently. If you multiply every coefficient by n, every exponent in the expression gets multiplied by n too. Raising a whole expression's exponents by a factor of n is the same as raising the original expression to the nth power. So K_new = (K_old)n. Double the equation and K gets squared, not doubled; triple it and K gets cubed. This trips people up because it feels like coefficients and K should scale the same way, but K depends on concentrations raised to powers, and powers multiply, they don't add.
This is why combining equilibrium constants for a multistep target reaction mirrors Hess's law for enthalpies. With enthalpies you reverse a step by flipping the sign of delta H and scale a step by multiplying delta H by the same factor, then add the delta H values. With K you reverse a step by taking the reciprocal and scale a step by raising K to that power, then multiply the K values together. Addition of steps becomes multiplication of equations in Hess's law; the log of K behaves like an enthalpy, which is exactly why ln K connects to delta G in later equilibrium work.
Key terms
- Equilibrium constant (K)
- The ratio of product concentrations to reactant concentrations, each raised to its coefficient, at equilibrium.
- Reciprocal relationship
- Reversing a reaction's direction inverts its equilibrium expression, so K_reverse equals 1 divided by K_forward.
- Exponent scaling
- Multiplying every coefficient in a balanced equation by n multiplies every exponent in the K expression by n as well.
- Hess's law analogy
- Combining reactions by addition multiplies their K values, just as combining reactions by addition adds their delta H values.
Watch it explained
- How it worksHow does doubling every coefficient square the value of K?
- Worked exampleFind K for a target reaction built by reversing one known reaction and doubling another.
- Common mistakeWhy isn't K multiplied by two when the equation is multiplied by two?
- Ties togetherHow does combining equilibrium constants mirror the way Hess's law combines enthalpies?
Check yourself
End of topic.