# Applications of Aqueous Equilibrium

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Applications of Aqueous Equilibrium
Chapter 15 Applications of Aqueous Equilibrium

The Common Ion Effect The Common Ion effect is when a weak acid is added to a salt which contains the same anion. Examples are HNO2 and NaNO2 OR HC2H3O2 and NaC2H3O2 When this occurs it reverses the dissociation of the acid if the acid had already dissociated or reduces the dissociation if the salt is added first. Either way, Ksp remains the same and there will be a lower % dissociation of the acid.

The Common Ion Effect # 2 The same principle applies to salts with the cation of a weak base. Examples are Fe(OH)2 and Fe(NO3)2 The calculations are the same as last chapter. Set up the ICE BOX

Buffered solutions A solution that resists a change in pH.
Either a weak acid and its salt or a weak base and its salt. We can make a buffer of any pH by varying the concentrations of these solutions. Same calculations as before. Calculate the pH of a solution that is .50 M HAc and .25 M NaAc (Ka = 1.8 x 10-5) Note: Ac is an abbreviation for Acetate. Chemists like to abbreviate. You must write it out completely. Other common ones are Benzoic Acid (HBen) and Citric Acid (HCit).

Adding a strong acid or base
Do the stoichiometry first. A strong base will grab protons from the weak acid reducing [HA]0 A strong acid will add its proton to the anion of the salt reducing [A-]0 Then do the equilibrium problem. What is the pH of 1.0 L of the previous solution when mol of solid NaOH is added ?

General equation and its manipulation.
Ka = [H+1] [A-1] [HA] so [H+1] = Ka [HA] [A-1] The [H+] depends on the ratio [HA]/[A-1] taking the negative log of both sides pH = - log(Ka [HA]/[A-1]) pH = - log(Ka)-log([HA]/[A-1]) pH = pKa + log([A-1]/[HA])

The Henderson - Hasselbach equation
This equation is VERY useful. pH = pKa + log([A-1] / [HA]) pH = pKa + log(base / acid) Calculate the pH of the following mixtures 0.75 M lactic acid (HC3H5O3) and 0.25 M sodium lactate (NaC3H5O3) (Ka = 1.4 x 10-4) 0.25 M NH3 and 0.40 M NH4Cl (Kb = 1.8 x 10-5)

Prove they’re buffers What would the pH be if .020 mol of HCl is added to 1.0 L of both of the preceding solutions. What would the pH be if mol of solid NaOH is added to each of the proceeding.

Buffer capacity The pH of a buffered solution is determined by the ratio [A-1]/[HA]. As long as this doesn’t change much the pH won’t change much. The more concentrated these two are the more H+1 and OH-1 the solution will be able to absorb. Larger concentrations bigger buffer capacity.

Buffer Capacity Calculate the change in pH that occurs when mol of HCl(g) is added to 1.0L of each of the following: 5.00 M HAc and 5.00 M NaAc 0.050 M HAc and M NaAc Ka= 1.8x10-5

Buffer capacity The best buffers have a ratio [A-]/[HA] = 1
This is most resistant to change This occurs when [A-] = [HA] Make pH = pKa (since log1=0)

Titrations Millimole (mmol) = 1/1000 mol Molarity = mmol/mL = mol/L
Makes calculations easier because we will rarely add Liters of solution. Adding a solution of known concentration until the substance being tested is consumed. This is called the equivalence point. Graph of pH vs. mL is a titration curve.

Strong acid with Strong Base
Do the stoichiometry. There is no equilibrium . They both dissociate completely. The titration of 50.0 mL of M HNO3 with M NaOH Analyze the pH

Weak acid with Strong base
There is an equilibrium. Do stoichiometry. Then do equilibrium. Titrate 50.0 mL of 0.10 M HF (Ka = 7.2 x 10-4) with 0.10 M NaOH

Titration Curves

Strong acid with strong Base
Equivalence at pH 7 7 pH mL of Base added

Weak acid with strong Base
Equivalence at pH >7 > 7 pH mL of Base added

Strong base with strong acid
Equivalence at pH 7 7 pH mL of Base added

Weak base with strong acid
Equivalence at pH <7 < 7 pH mL of Base added

Summary Strong acid and base just stoichiometry.
Determine Ka, use for 0 mL base Weak acid before equivalence point Stoichiometry first Then Henderson-Hasselbach Weak acid at equivalence point Kb Weak base after equivalence - leftover strong base.

Summary Determine Ka, use for 0 mL acid.
Weak base before equivalence point. Stoichiometry first Then Henderson-Hasselbach Weak base at equivalence point Ka. Weak base after equivalence - leftover strong acid.

Indicators Weak acids that change color when they become bases.
weak acid written HIn Weak base HIn  H+ + In clear red Equilibrium is controlled by pH End point - when the indicator changes color.

Indicators Since it is an equilibrium the color change is gradual.
It is noticeable when the ratio of [In-1] / [HI] or [HI] / [In-1] is 1/10 Since the Indicator is a weak acid, it has a Ka. pH the indicator changes at is. pH = pKa + log([In-1]/[HI]) = pKa +log(1/10) pH = pKa - 1 on the way up

Indicators pH = pKa + log([HI]/[In-1]) = pKa + log(10)
pH = pKa + 1 on the way down Choose the indicator with a pKa 1 less than the pH at equivalence point if you are titrating with base. Choose the indicator with a pKa 1 greater than the pH at equivalence point if you are titrating with acid.

Solubility Equilibria
Will it all dissolve, and if not, how much?

Ksp Equilibrium All dissolving is an equilibrium and depends on the concentration of the materials. As more solid is added the solution will become saturated. Solid  dissolved ions AND The solid will precipitate as fast as it dissolves .

General equation M+1 stands for the cation (usually metal).
N-1 stands for the anion (a nonmetal). MaNb(s)  a M+1(aq) + b N-1 (aq) K = [M+]a[N-]b/[MaNb] But the concentration of a solid doesn’t change. Ksp = [M+1]a [N-1]b Called the solubility product for each compound.

Watch out Solubility is not the same as solubility product.
Solubility product is an equilibrium constant. It doesn’t change except with temperature. Solubility is an equilibrium position for how much can dissolve. A common ion can change this.

Calculating Ksp The solubility of iron (II) oxalate FeC2O4 is 65.9 mg/L Remember what solubility is equal to in our algebra equation. The solubility of Li2CO3 is 5.48 g/L

Calculating Solubility
The solubility is determined by equilibrium. Its an equilibrium problem. Calculate the solubility of SrSO4, with a Ksp of 3.2 x 10-7 in M and g/L. Calculate the solubility of Ag2CrO4, with a Ksp of 9.0 x in M and g/L.

Relative solubilities
Ksp will only allow us to compare the solubility of solids that dissociate into the same number of ions. The larger the value of Ksp , the more soluble the species is.

Common Ion Effect If we try to dissolve the solid in a solution with either the cation or anion already present less will dissolve. Calculate the solubility of SrSO4, with a Ksp of 3.2 x 10-7 in M and g/L in a solution of M Na2SO4. Calculate the solubility of SrSO4, with a Ksp of 3.2 x 10-7 in M and g/L in a solution of M SrNO3.

Solubility v. Reactivity # 1
A confusing idea is the difference between solubility and reactivity. SOLUBILITY is when a substance dissolves in water. NaCl and Strong Acids/Bases are very soluble. PbSO4 and Weak Acids/Bases are not very soluble. REACTIVITY is when a material combines chemically with another element.

Solubility v. Reactivity # 2
How does this come into play ? A weak acid dissociates only a few H+1 ions in water, where as HCl dissociates a lot. BUT, when both are added to a base, they are both equally a source of H+1 ions for the base to grab onto. The base actively grabs onto H+1 ions from any source and does not only react with H+1 ions in solution.

pH and solubility OH-1 can be a common ion.
For other anions if they come from a weak acid they are more soluble in a acidic solution than in water. CaC2O4  Ca+2 + C2O4-2 H+1 + C2O4-2  HC2O4-1 Reduces C2O4-2 in acidic solution.

Precipitation Ion Product, Q =[M+]a[N-]b
If Q > Ksp a precipitate forms. If Q < Ksp No precipitate. If Q = Ksp equilibrium. A solution of mL of 4.00 x 10-3M Ce(NO3)3 is added to mL of x 10-2M KIO3. Will Ce(IO3)3 precipitate and if so, what is the concentration of the ions? (Ksp= 1.9 x 10-10M)

Selective Precipitations
Used to separate mixtures of metal ions in solutions. Strategically select ions that will only precipitate certain metals at a time. We can determine these with their Ksp values. Used to purify mixtures. Often use H2S because in acidic solution Hg+2, Cd+2, Bi+3, Cu+2, Sn+4 will precipitate.

Selective Precipitation
In Basic adding OH- solution S-2 will increase so more soluble sulfides will precipitate. Co+2, Zn+2, Mn+2, Ni+2, Fe+2, Cr(OH)3, Al(OH)3

Selective precipitation
Here is a sample sequence used for a Selective Precipitation. Follow the steps first with insoluble chlorides (Ag, Pb, Ba) Then sulfides in Acid. Then sulfides in Base. Then insoluble carbonate (Ca, Ba, Mg) Alkali metals and NH4+1 remain in solution.

Complex ion Equilibria
A charged ion surrounded by ligands. Ligands are Lewis bases using their lone pair to stabilize the charged metal ions. Common ligands are NH3, H2O, Cl-1,CN-1 Coordination number is the number of attached ligands. Cu(NH3)4+2 has a coordination # of 4

Ligands and Ksp The theory is similar to the Ksp found in Polyprotic Acids such as H3PO4. The addition of each ligand has its own equilibrium. Usually the ligand is in large excess. And the individual K’s will be large so we can treat them as if they go to equilibrium. The complex ion will be the biggest ion in solution.

Ksp and Ligands Calculate the concentrations of Ag+, Ag(S2O3)-, and Ag(S2O3)-3 in a solution made by mixing mL of 3.00 M AgNO3 with mL of 5.00 M Na2S2O3 Ag+1 + S2O3-2  Ag(S2O3)-1 K1=7.4 x 108 Ag(S2O3)-1 + S2O3-2  Ag(S2O3)-3 K2=3.9 x 104