Why are Concentrations Squared in Solubility Equilibrium Constants?

[JFS321]

Hi all,

I'm trying to understand -- really visualize -- the concept of solubility equilibrium constants. But, I can't understand WHY a stoichiometric value, say 2Ag+, is written in an equilibrium constant as [Ag+]^2.

I understand that in a rate law, squaring the concentration makes sense because you may have data indicating that the rate of reaction has increased by a factor of 4.

But, I can't make the mental connection here for solubility equilibrium or any other equilibrium constant. Can anyone help me visualize? Thanks--

 

[gadong]

The justification is quite involved, and proceeds from the concept of the chemical potential. Textbooks on physical chemistry (Levine, Atkins) work through it in full, but you probably won't find it in general chemistry textbooks.

 

[JFS321]

So basically, this is not something that I should intuitively be able to visualize? I think I can put it to rest if that's the case...

 

[Office_Shredder]

If you think it's intuitive that a reaction that includes A+B gives a reaction rate proportional to [A], then when A happens to equal B you should be willing to believe it's still proportional to [A]

 

[LudusRex]

The use of squared concentrations in equilibrium constants is based on the principles of thermodynamics and the concept of equilibrium. In thermodynamics, the equilibrium constant (K) represents the ratio of the products to the reactants at equilibrium. This means that the concentration of the products must be raised to a power in order to match the stoichiometric ratio of the reaction. In other words, if the reaction has a stoichiometric value of 2 for the products, the concentration must be squared in order to match this ratio. This is why we see squared concentrations in equilibrium constants.

In the case of solubility equilibrium, the equilibrium constant (Ksp) represents the ratio of the dissolved ions to the undissolved ions in a saturated solution. This means that the concentration of the dissolved ions must be raised to a power in order to match the stoichiometric ratio of the reaction. For example, if the reaction is 2Ag+ <--> Ag2S, the equilibrium constant would be [Ag+]^2[S^-]^2, as the stoichiometric ratio of the products is 2:2. This helps us understand the relationship between the concentration of the dissolved ions and the undissolved ions at equilibrium.

Additionally, using squared concentrations in equilibrium constants helps to simplify the equations and make them more manageable. It allows us to represent the equilibrium constant with a single value, rather than having to write out multiple terms for each individual ion. This is especially useful in more complex equilibrium reactions.

In summary, the use of squared concentrations in equilibrium constants is based on the principles of thermodynamics and helps us understand the relationship between the concentrations of products and reactants at equilibrium. It also simplifies the equations and makes them easier to work with.