Understanding Equilibrium Constants With No Denominator

[yougene]

Lets say you have something like
CaSO4 (s) <-----> Ca (aq) + SO4(aq)

The equilibrium constant would then have no denominator. That makes no sense to me!

K would equal [ Ca ][ SO4 ].

Wouldn't that then represent a constant amount of moles no matter how much CaSO4 is present?

Lets say K = 4 in this case
and [ Ca ] = 2 and [ SO4 ] = 2

Because K isn't a fraction, there is no way to reach equilibrium by balancing the reactant and products. K would then suggest the maximum molarity for a given solution, no matter how much solid reactant is in the solution.

That's how I'm interpreting it but it just seems wrong. Can someone clarify for me?

Thanks

 

[chemisttree]

The concentration of CaSO4 in solid CaSO4 is a constant. Multiplying the inverse of that constant by [ Ca ][ SO4 ] gives you your K. Sometimes the constant is not shown (like in solubility products).

 

[Blueshift5]

for your question! I can understand your confusion about equilibrium constants with no denominator. Let me try to clarify this concept for you.

First, it's important to understand that equilibrium constants (K) represent the ratio of product concentrations to reactant concentrations at equilibrium. In the case of the reaction you provided, CaSO4 (s) <-----> Ca (aq) + SO4(aq), the equilibrium constant would be K = [Ca][SO4], where [Ca] and [SO4] represent the molar concentrations of Ca and SO4 ions in the solution at equilibrium.

Now, let's break down the reaction and look at it step by step. Initially, when the reaction starts, there is only solid CaSO4 present. As the reaction proceeds, some of the CaSO4 will dissolve and form Ca and SO4 ions in solution. At equilibrium, there will be a certain concentration of Ca and SO4 ions in the solution, and the equilibrium constant will be equal to the ratio of these concentrations.

So, what does this mean in terms of the equilibrium constant having no denominator? It simply means that the concentration of the solid CaSO4 does not affect the equilibrium constant. The equilibrium constant only depends on the concentrations of the ions in solution, not on the amount of solid CaSO4 present.

To address your example, let's assume that the initial concentration of CaSO4 is 4 moles and that the reaction goes to completion. This means that all 4 moles of CaSO4 will dissolve and form 4 moles each of Ca and SO4 ions in solution. In this case, the equilibrium constant would be K = [Ca][SO4] = (4 moles/L)(4 moles/L) = 16 L/mol, which is a constant value regardless of the initial concentration of CaSO4. This value represents the maximum molarity for the given solution, as you correctly mentioned.

In summary, equilibrium constants with no denominator are not wrong or incorrect. They simply represent the ratio of product concentrations to reactant concentrations at equilibrium, and the concentration of the solid reactant does not affect this ratio. I hope this helps to clarify the concept for you.