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### Course: AP®︎/College Chemistry>Unit 7

Lesson 4: Magnitude and properties of the equilibrium constant

# Properties of the equilibrium constant

The equilibrium constant for a reaction depends on how the balanced equation is written. If the equation is reversed, K is inverted. If the equation is multiplied by a factor n, K is raised to the nth power. If multiple equations are added together, K for the overall equation is the product of the K values for the equations that were summed. Created by Jay.

## Want to join the conversation?

• Is there an intuitive way of understanding the reason behind why we multiply the equilibrium constant of the 2 added reactions in order to get the resultant equilibrium constant of the new, combined reaction (the last problem tackled in the video)? Sorry, I just find it more satisfying to gain an intuitive "sense" as oppose to plainly memorizing formulae.
• This property of equilibrium constants is an extension of Hess's Law. Hess's Law states that the total change of energy of an overall reaction is the sum of the energy changes of the individual reactions. Equilibrium constants take into account thermodynamics and can be related to Gibbs free energies. And Hess's Law also applies to Gibbs free energy. So an overall reaction's equilibrium constant will be a combination of the individual reaction's equilibrium constants similarly how the change in Gibbs free energy of the overall reaction is the combination of the change in Gibbs free energy for the individual reactions.

Hope that helps.
• Why does Kc change when you multiply each coefficient by two? Isn't it just the same reaction written in a different way?
• An equilibrium expression, and therefore the equilibrium constant, depends on the coefficients of a chemical reaction. So if we change the coefficients, even by the same factor for all chemical species, the constant changes too.

For example a simple reaction like: A → B, yields an equilibrium expression of:
K1 = [B]/[A].
If we change to coefficients by doubling them then the reaction becomes: 2A → 2B. And so the equilibrium expression becomes:
K2 = [B]^(2)/[A]^(2), since we raise the terms by their coefficients in the chemical equation.
So [B]^(2)/[A]^(2) can be written as ([B]/[A])^(2), which is K1 squared or K1^(2). So K1^(2) = K2.

Hope that helps.
• The third problem seems to be the same as hess's law, except we are calculating for Kc instead of enthalpy of reaction. Is this the same principle going into play?
(1 vote)
• It’s similar, but I would say that they are different. Hess’s Law involves using a sum of different reaction’s quantities, but for equilibrium constants we combine them by multiplication instead. So it is similar in that we are combining different reaction’s quantities into a single quantity, but the operations are different.

Hope that helps.