Calculating Ksp from Molar Solubilty

[JeweliaHeart]

Homework Statement

The molar solubility of magnesium fluoride, MgF₂ is 1 x 10^-3 in pure water. What is the Ksp for MgF₂?

a)4 x 10^-3
b)4 x 10^-6
c)4 x 10^-9
d)2 x 10^-3
e)1 x 10^-3

My book says the correct answer is C in bold.

Homework Equations

Ksp= [Mg2+][F-][F-]

The Attempt at a Solution

Ksp= [Mg2+][F-][F-]=[1 x 10^-3][1 x 10^-3][1 x 10^-3]=

1 x 10^-9



I think this should be the correct answer. For some reason the book multiplies by four. It says:

"The relationship between the solubility product constant and molar solubility for a compound that produces 3 moles of ions for every mole of solid dissolved is as follows:

Ksp=4x³= 4(1 x 10^-3)³= 4 x 10^-9 "

I don't understand why to multiply by four.

 

[Borek]

Write dissolution reaction and think about stoichiometry.

 

[JeweliaHeart]

MgF₂ (s) ----> Mg²⁺ + 2F^-

There is 1 x 10^-3 moles/liter of each ion. What did I do wrong? :(

 

[Borek]

MgF₂ (s) ----> Mg²⁺ + 2F^-

There is 1 x 10^-3 moles/liter of each ion.

That would mean exactly the same number of fluoride and magnesium ions. Take a look at the reaction equation - are they produced in 1:1 ratio?

 

[JeweliaHeart]

Oh, I think I see. So I shouldn't have divided up the fluoride ions into individual concentrations:

The total fluoride ion concentration is 2 x (1 x 10^-3)= 2 x 10^-3

So, the Ksp= [Mg²⁺][F-]

[1 x 10^-3][(2 x 10^-3]= 2 x 10^-6

 

[JeweliaHeart]

...Oops I forgot to include, but that's not an answer choice.

 

[Borek]

Compare your two posts:

Ksp= [Mg2+][F-][F-]

Ksp= [Mg²⁺][F-]

 

[JeweliaHeart]

The only way I could see arriving at an answer of 4 x 10^-9 is by squaring (2 x 10^-3) before multiplying it by (1 x 10^-3), which would mean that the concentration of [F-] is squared.

It doesn't make sense to me square the concentration of F-. If there are two moles of F- ions, per MgF₂, why not just multiply 2 times the [MgF₂] to get [F-].

Where does [F-]² come into all this or am I not supposed to square it at all?

 

[Borek]

That puts us several squares back. What is Ksp and how is it written for a X_aY_b type salt?

Or perhaps I should ask more general question - do you know what the reaction quotient is? Ksp is a just a specific case.

 

[JeweliaHeart]

Yes. I know about both solubility product constants and equilibrium constants.

I guess what's happening here is something I've been trying to avoid all along: understanding why reaction orders match the coefficients in a balanced chemical equation. I've kind of just accepted it without really knowing why. I've heard that it has something to do with number of collisions or something like that, but I've never really gotten into depth.

 

[Borek]

No, you don't have to dig into kinetics, it is enough that you learn the definition of the reaction quotient.

(Actually reaction quotient can be easily derived from the thermodynamics, but it is still not necessary, definition is perfectly enough).

 

[JeweliaHeart]

Borek, why do I have to square the concentration of [F-] once I've already multiplied it by two to account for the double F- ions?

 

[Borek]

There is no "why" here, simply apply the definition. Concentration calculation is one thing, properly written Ksp is another.

 

[JeweliaHeart]

K_sp = [Mg²⁺][F^-]²=

[1 x 10^-3][2 x 10^-3]²= 4 x 10^-9


Okay, thanks... I understand how to write a K_sp, just not why it is written as such, but oh well...