# Calculating Ksp from Molar Solubilty

• JeweliaHeart
In summary, the molar solubility of magnesium fluoride, MgF2, is 1 x 10-3 in pure water. The Ksp for MgF2 is 4 x 10-9, as calculated using the solubility product constant formula, Ksp= [Mg2+][F-]2, where the concentrations of magnesium and fluoride ions are 1 x 10-3 and 2 x 10-3, respectively. This is the correct answer, as confirmed by the book.
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.

Write dissolution reaction and think about stoichiometry.

MgF2 (s) ----> Mg2+ + 2F-

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

JeweliaHeart said:
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?

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

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

JeweliaHeart said:
Ksp= [Mg2+][F-][F-]

JeweliaHeart said:
Ksp= [Mg2+][F-]

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?

That puts us several squares back. What is Ksp and how is it written for a XaYb 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.

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.

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).

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?

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

Ksp = [Mg2+][F-]2=

[1 x 10-3][2 x 10-3]2= 4 x 10-9

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

## 1. How do you calculate Ksp from molar solubility?

To calculate Ksp from molar solubility, you will need to use the solubility product constant equation, which is Ksp = [A+][B-]. The molar solubility of the compound (represented by [A+] and [B-]) can be found by dividing the number of moles of the compound that dissolve by the volume of the solution. Once you have both values, simply plug them into the equation to calculate Ksp.

## 2. What is the significance of calculating Ksp from molar solubility?

Calculating Ksp from molar solubility allows us to determine the maximum amount of a compound that can dissolve in a solution at a given temperature. This value is important for predicting the formation of precipitates and understanding the solubility of a compound in different conditions.

## 3. What units are used for molar solubility and Ksp?

Molar solubility is typically expressed in units of moles per liter (mol/L), while Ksp is unitless. This is because Ksp is a ratio of the concentrations of the ions in the solution, and therefore does not have units.

## 4. Can you calculate Ksp from molar solubility for all compounds?

No, not all compounds have a defined Ksp value. Ksp can only be calculated for compounds that dissociate into ions in solution, known as strong electrolytes. Compounds that do not dissociate, such as covalent compounds, do not have a Ksp value.

## 5. How does temperature affect the calculation of Ksp from molar solubility?

Temperature can have a significant impact on the solubility of a compound and therefore on the calculation of Ksp from molar solubility. As temperature increases, the solubility of most compounds also increases, resulting in a higher Ksp value. This is because increasing temperature provides more energy for the solute particles to overcome the attractive forces of the solvent and dissolve.

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