[allotp]

Hi,

I have a problem with some calculations on tartrate solubility and etc.

Substances dissolved (in this order):
-1.0 g/l potassium hydrogen tartrate (KHT)
- 843.2 mg/l KCl
- adjust pH = 3.2 with tartartic acid (H2T).
- fill up the solution until 1 L.

Reactions:
1.  KHT  <---> K⁺  + HT^-
2.  H²T   <---> HT^-  +   H⁺
3.  HT^-    <--->  T^2-   +   H⁺

Reaction 2 and 3 are dependant on the pH. At pH=3.2 the relation is H2T : HT- : T2- = 43.7 : 54.0 : 2.3

pKa ( H²T   <---> HT^-  +   H⁺)= 2.98
pKa (HT^-    <--->  T^2-   +   H⁺)= 4.34

Data:
MW (KHT) = 188.18 g/mol
MW (H2T) = 150.09 g/mol
MW (HT-) = 149.0 g/mol
MW (KCl) = 74.55 g/mol

Solubility (KHT, at T=20*C) = 2.77 g/L


Calculation:
mol (KHT) = 2.77 / 188.18 = 1.47E-02 mol
mol (KHT) = mol (K+) = mol (HT-) = 1.47E-02 mol

Question A: HT- will react further according to reaction 2 and 3. When can I niggled  that?

Ksp = [K+] x [HT-]
Ksp = 1.47E-02 x 1.47E-02 = 2.16E-04


Real content KHT = 1.0/188.18 = 5.31E-03 mol
KHT will dissolve completely. mol (KHT) = mol (K+) = mol (HT-) = 5.31E-03 mol

At the solution with KHT is KCl added.
mol (KCl) = mol (K+) = mol (Cl- ) = 0.8432/74.55=1.13E-02 mol



Question B: What are the new equilibrium concentrations?
I 'll tried it but there is something not right.

Reaction 1. KHT  <---> K⁺  + HT^-
Start mol (KHT) = 0; mol (K+)= 5.31E-03 + 1.13E-02 = 1.66E-02; mol; mol (HT-) = 5.31E-03
Change +x; -x; -x;
Equilibrium 0 + x; 1.66E-02 – x; 5.31E-03 - x;

Complete formula Ksp = [K+] x [HT-]
Ksp = 2.16E-04 = (1.66E-02 – x) x (5.31E-03 - x)
x = 2.67E-02

This is impossible because both concentration, [K+] and [HT-], would turn out negative.

I 'll hope someone could help me out of this....

[allotp]

By the way: this is only about the first step: without looking to the H2T that will be dissolved later on.

[Borek]

Ksp = 2.16E-04 = (1.66E-02 – x) x (5.31E-03 - x)
x = 2.67E-02

This is impossible because both concentration, [K+] and [HT-], would turn out negative.

Just looking at the formula you wrote and not analysing anything else - this is a quadratic equation and it most likely has two zeros. x = 2.67E-02 is only one of them. Have you tried the other one?

[allotp]

Just looking at the formula you wrote and not analysing anything else - this is a quadratic equation and it most likely has two zeros. x = 2.67E-02 is only one of them. Have you tried the other one?

Yeah, the other one is negative. This would make the other concentration negative..

[Borek]

Just looking at the formula you wrote and not analysing anything else - this is a quadratic equation and it most likely has two zeros. x = 2.67E-02 is only one of them. Have you tried the other one?

Yeah, the other one is negative. This would make the other concentration negative..

I am still not sure if I understand the question (what does it ask in A?) but isn't -x change in amount of solid dissolved? And as such it must be negative if there was dissolution?

[allotp]

Actually, it is quite simple if you see it like this. The way I did it is just completely wrong.

KHT will be split in K+ and HT-. Furthermore, HT- will be split in H2T, HT- and T2- according to the relation that is given. So the actual Ksp value is the one that is calculated with the "K+ concentration" and "the second HT- concentration".

To be short: forget my way of calculating the Ksp!