## Lesson 10 Video 5

ArielM
Posts: 52
Joined: Mon Oct 02, 2017 9:15 pm

### Lesson 10 Video 5

This is about Lesson 10 Video 5 Slide 2.

This video is about solubility and my question is about writing the Ksp, the solubility constant.

I understand that equilibrium constants are always written as K = [Products]/[Reactants]. And in general, we omit solids (s) and liquids (s) from the equilibrium formula.

On slide 2 (at 1:38) Brian states the importance of setting up the equations right. He states that the stoichiometric coefficient should be place inside the brackets and also as the exponent. So, given the example in the video, Solving for Molar Solubility using Ksp, the dissociation equation is:
( x Mg3(PO4)2 (s) + H2O (l) <--> 3x Mg^2+ (aq) + 2x PO4^3- (aq) )

The Ksp should look like this:
Ksp = [3x Mg^2+]^3 * [2x PO4^3-]^2

And simplifying, the Ksp is:
Ksp = [3x]^3 * [2x]^2

________________________________________________________________________________________________________________________________________________________
*Herein lies my confusion*

I looked at this Khan Academy video to get further clarification about Ksp. Mid video, the instructor uses an ICE table (5:51) to obtain the Ksp. The dissociation equation is stated as being:

( 1 PbCl2 (s) <--> 1 Pb^2+ (aq) + 2 Cl- (aq) )

The Khan Academy Ksp appears as follows (8:20):
Ksp = [Pb^2+]^1 * [Cl-]^2

The "2" in 2Cl- is not placed in the brackets, it is only represented as the exponent. This is NOT consistent.

Shouldn't the molar coefficient be placed inside the bracket and in the exponent, also? Please help me to understand.

Sincerely,
-Ariel Morrow
NS_Tutor_Andrew
Posts: 520
Joined: Mon May 23, 2016 1:47 pm

### Re: Lesson 10 Video 5

Hi Ariel,

Thanks for the excellent question! Believe it or not, these two examples are actually consistent. Let me break Bryan's example down in a little bit more detail to show what's going on here, because he sort of skips a step by directly including the variable x in the Ksp equation.

So, for the equation we're given, the Ksp = [Mg^2+]^3 * [PO4^3-]^2. This is consistent with the Khan Academy example, and it might actually help to spell this out in words: the Ksp equals the concentration of magnesium ions to the third power times the concentration of phosphate ions to the second power.

Now, the question is whether we can say anything else about the concentration of magnesium ions and phosphate ions. This is where stoichiometry comes in! From the dissolution reaction Mg3(PO4)2 (s) <--> 3 Mg^2+ (aq) + 2x PO4^3- (aq), we can conclude that each mole of solid trimagnesium phosphate that dissolves will yield 3 moles of magnesium ions and 2 moles of phosphate ions. In other words, if we have x moles of Mg3(PO4)2 (s), we will have 3x moles of Mg^2+ and 2x moles of PO4^3-. In other words, the term [Mg^2+] will be 3x and the term [PO4^3-] will be 2x.

Once we have these algebraic values for the concentrations of magnesium and phosphate ions, we can substitute them back into the Ksp expression:

Ksp = [3x]^3 * [2x]^2

This brings us up to speed with the final step in Bryan's example.

This is an excellent question because it's really important to understand how these two steps apply in different situations.

The "pure" Ksp expression, Ksp = [Mg^2+]^3 * [PO4^3-]^2, is true for this reaction no matter what. It's inherent in the definition of what Ksp means.

The "algebraic" Ksp expression, Ksp = [3x]^3 * [2x]^2, is a bit of extra insight we can get if the dissolution reaction is the only source of Mg^2+ and PO4^3-. If some magnesium or phosphate is already floating around in the solution, then this trick won't yield an accurate estimation, because the dissolution reaction is not the only source of these ions and therefore we have to take other circumstances into account when calculating [Mg^2+] and [PO4^3-]. This specific situation is what happens in the common ion effect. This blog post (which is about the PCAT, not the MCAT, but the common ion effect is tested on both tests) briefly discusses the issue.

Hope this helps clarify matters!
Andrew D.
Content Manager, Next Step Test Prep.
ArielM
Posts: 52
Joined: Mon Oct 02, 2017 9:15 pm

### Re: Lesson 10 Video 5

Ah, okay I understand now. The stoichiometry and how the molar coefficients were presented threw me off. Also, I read the blog about Solutions and the Common Ion Effect, very insightful. Awesome post, thank you very much.

Sincerely,
-Ariel Morrow
ArielM
Posts: 52
Joined: Mon Oct 02, 2017 9:15 pm

### Re: Lesson 10 Video 5

Dear Andrew,

If possible, could you please answer my question in the post entitled "Lesson 6 video 4"? I just had a simple question about S & R configurations in chemistry.

Sincerely,
-Ariel M.
NS_Tutor_Andrew