Chapter 16: Applications of Aqueous Equilibrium Part 3. Solubilities of Ionic Compounds and K sp

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1 Chapter 16: Applications of Aqueous Equilibrium Part 3 Solubilities of Ionic Compounds and K sp You ve already learned that not all ionic compounds are water soluble. You memorized the solubility rules (page ) which tell you which salt is soluble or not. But just exactly how soluble are different ionic compounds? Well, the dissolving process is an equilibrium process, so we can write an equilibrium expression for it. CaCO 3 (s) H 2 O Ca 2+ (aq) + CO 2-3 (aq) You can easily write the equilbrium expression for the above: The K for the dissolution or water solubility of ionic comounds is called K sp, or the solubility product constant. For calcium carbonate, K sp = 6.2x10-12 This may seem low compared to the weak acids and bases we were just working with, but if you look at Tables of K sp values (see page A-16), you will see values as low as 10-40! Practice: Write the K sp expressions for MnCrO 4 and for Pb 3 (PO 4 ) 2 K sp Problems: Finding K sp and using K sp to find Solubilities or Concentrations There are several typical problems involving K sp : Typical Problem 1) Find K sp when a salt is dissolved in pure water: A saturated solution (remember this means that as much is dissolved as is possible) of Pb 3 (PO 4 ) 2 is found to contain [Pb 2+ ] = 2.32x10-9 M. Find K sp. (Assumption: as nothing is said, the solvent is water with no other source of lead or phosphate.)

2 Typical Problem 2) Find the water solubility of a salt from its K sp : What is the solubility in M and in g/l of silver sulfate if its K sp = 1.5x10-5? What are the final [Ag + ] and [SO 4 2- ]? Factors Which Affect Solubility: Common Ion, ph, Complex Ion Formation Common Ion Effect You ve learned about this before, with respect to adding a common ion to an acid or base solution. As before, adding a common ion will shift the equilibrium to the opposite side. This is Le Chatelier s Principle in action. Typical Problem 3) Find the solubility of a salt in a common ion sln from its K sp : What is the molar solubility of barium sulfate in a 0.10 M sodium sulfate sln? What are the final [Ba 2+ ] and [SO 4 2- ]? Typical Problem 4) Add slns together and determine how much is needed to form a ppt (and which one forms first). This combines common ion effect with selective ppt.: A solution contains 1.0 mole of Cl - ion and 1.0 mmole of CrO 4 2- ion per liter. Tl + ion in the form of solid TlNO 3 is added to this solution. Solubility product constants: TlCl 1.8x10 4; Tl 2 CrO 4 9.8x10 13 a) Calculate the concentration of Tl + ion necessary to start the precipitation of TlCl. b) Calculate the concentration of Tl + ion necessary to start the precipitation of Tl 2 CrO 4. c) Which precipitate is formed first when the TlNO 3 is added to the above solution?

3 ph Effect on Solubility The ph of a sln will often affect the solubility of ionic compounds if the anion is basic (anion creates a basic sln). Ex: CaS Ca 2+ + S 2- But S 2- + H 2 O HS - + OH - a basic sln Comment 1: The very fact that the anion reacts with water to produce a basic sln in itself tends to raise the solubility of the compound over what the K sp alone predicts. Again, this is Le Chatelier s Principle. But this is VERY complicated math with 5 equations and 5 unknowns, so we will generally ignore this. Comment 2: You can also see from the above coupled rxns, that if there is another source of hydroxide (i.e. the CaS is added to an already basic sln), that the solubility would decrease as the second rxn would shift to the left, causing the first rxn to shift to the left. Comment 3: Likewise, if the CaS is added to an already acidic sln, the solubility would increase due to more coupled rxns: OH - + H + H 2 O and S 2- + H + HS - In this case, the hydroxide produced would be removed by the hydronium, forcing all of the rxns to shift to the right. Problem: Which of the following salts will show an increase in solubility for decreasing ph? AgCl, AgF, PbCO 3, Ba(NO 3 ) 2 Complex Ion Formation Effect on Solubility The solubilities of some ionic compounds increases dramatically when the sln also contains a Lewis Base like hydroxide, cyanide, and ammonia. The cation may then form a complex ion with this base, thus pushing the K sp rxn to the right. The complex ion formation rxn has its own equilibrium constant called K f. Ex: silver ion forms a complex ion with 2 ammonia molecules If we add silver chloride to a sln containing ammonia, you can see the 2 coupled rxns: If you add the 2 rxns together, you get the overall rxn and an overall K:

4 Problem: Determine the solubility of silver chloride in pure water and in 1.5 M ammonia. Look how the solubility of silver chloride has increased! Ionic Compound Precipitation An earlier problem posed the question of how much Tl cation was needed to precipitate out as Tl 2 CrO 4 or TlCl, and which would ppt first. Here is another common ppt problem, where you mix 2 aqueous slns together and have to determine whether a ppt forms. Typical Problem 5) Do a double displacement rxn and determine whether a ppt forms. Will a ppt form upon mixing 125 ml of a mm Ca(NO 3 ) 2 sln with 50.0 ml of a M NaF sln? K sp for calcium fluoride is 1.5x Just like you did in Ch 15, you can calculate a Q for this sln. If Q > K sp, ppt will occur, while if Q K sp, no ppt will occur.

5 If a salt does ppt, you can calculate the final [ ] and the %-salt which is dissolved. For the above problem, calculate the final [Ca 2+ ] and %-CaF 2 dissolved. Take-Home Problem: See handout.