Aqueous Equilibria The Common-Ion Effect Consider a solution of acetic acid: NaC 2 H 3 O 2 Le Châtelier says the equilibrium will shift to the ______. As a result, what happens to [H + ]? pH? HC 2 H 3 O 2 (aq) + H 2 O (l) H 3 O + (aq) + C 2 H 3 O 2 − (aq)

Aqueous Equilibria The Common-Ion Effect Shift in equilibrium position that occurs because of the addition of an ion already involved in the equilibrium reaction

Aqueous Equilibria The Common-Ion Effect Calculate the pH and % dissociation of a 0.2M HF solution. K a = 7.2  10 −4 Calculate the pH and % dissociation of a solution containing 0.20 M HF and 0.10 M of NaF Because NaF is ionic, it will dissociate completely, so the initial [F - ] is not 0, but rather 0.10 M

Aqueous Equilibria Buffered Solutions Solutions of a weak conjugate acid-base pair. They are particularly resistant to pH changes, even when strong acid or base is added. After addition of strong acid or base, deal with stoichiometry first, then the equilibrium.

Aqueous Equilibria Buffers If a small amount of hydroxide is added to an equimolar solution of HF in NaF, for example, the HF reacts with the OH − to make F − and water.

Aqueous Equilibria Buffers If acid is added, the F − reacts to form HF and water.

Aqueous Equilibria Solving Problems with Buffered Solutions Copyright © Cengage Learning. All rights reserved 7

Aqueous Equilibria When Strong Acids or Bases Are Added to a Buffer… …it is safe to assume that all of the strong acid or base is consumed in the reaction.

Aqueous Equilibria Buffer example Calculate the pH of a solution containing 0.5M acetic acid (HC 2 H 3 O 2, K a =1.8x10 -5 ) and 0.5M sodium acetate (NaC 2 H 3 O 2 ).

Aqueous Equilibria Calculate the change in pH that occurs when mole of NaOH is added to 1.0 L of the previous solution. (0.5M acetic acid (HC 2 H 3 O 2, K a =1.8x10 -5 ) and 0.5M sodium acetate (NaC 2 H 3 O 2 )) Step 1 – use stoichiometry to calculate how much acetic acid remains in solution Step 2 – calculate [H + ] and pH

Aqueous Equilibria Buffer Capacity Amount of acid/base that can be neutralized before pH changes significantly A buffer with large capacity contains large concentrations of the buffering components ([HA] and [A – ]). 1M HC 2 H 3 O 2 & 1M NaC 2 H 3 O 2 vs..1M HC 2 H 3 O 2 &.1M NaC 2 H 3 O 2

Aqueous Equilibria Henderson–Hasselbalch equation So, pH = pK a + log [base] [acid] This is the Henderson–Hasselbalch equation. What happens when [base] = [acid]? K a [HA] [A − ] [H + ] =

Aqueous Equilibria Copyright © Cengage Learning. All rights reserved 13

Aqueous Equilibria Henderson–Hasselbalch Equation What is the pH of a buffer that is 0.12 M in lactic acid, HC 3 H 5 O 3, and 0.10 M in sodium lactate? K a for lactic acid is 1.4  10 −4.

Aqueous Equilibria Henderson–Hasselbalch Equation pH = pK a + log [base] [acid] pH = −log (1.4  10 −4 ) + log (0.10) (0.12) pH = (−0.08) pH = 3.77

Aqueous Equilibria What is the pH of a buffer solution that is 0.45 M acetic acid (HC 2 H 3 O 2 ) and 0.85 M sodium acetate (NaC 2 H 3 O 2 )? The K a for acetic acid is 1.8 × 10 –5. pH = 5.02 Copyright © Cengage Learning. All rights reserved 16 EXERCISE!

Aqueous Equilibria pH Range The pH range is the range of pH values over which a buffer system works effectively. It is best to choose an acid with a pK a close to the desired pH.

Aqueous Equilibria Calculating pH Changes in Buffers A buffer is made by adding mol HC 2 H 3 O 2 and mol NaC 2 H 3 O 2 to enough water to make 1.00 L of solution. The pH of the buffer is Calculate the pH of this solution after: a)0.020 mol of NaOH is added. b)0.020 mol of HCl is added.

Aqueous Equilibria Calculating pH Changes in Buffers The mol NaOH will react with mol of the acetic acid: HC 2 H 3 O 2 (aq) + OH − (aq)  C 2 H 3 O 2 − (aq) + H 2 O (l) HC 2 H 3 O 2 C2H3O2−C2H3O2− OH − Before reaction0.300 mol mol After reaction0.280 mol0.320 mol0.000 mol

Aqueous Equilibria Calculating pH Changes in Buffers Now use the Henderson–Hasselbalch equation to calculate the new pH: pH = log (0.320) (0. 280) pH = pH = 4.80

Aqueous Equilibria Calculating pH Changes in Buffers The mol HCl will react with mol of the acetic ion: C 2 H 3 O 2 − (aq) + H 3 O + (aq)  HC 2 H 3 O 2 (aq) + H 2 O (l) C2H3O2−C2H3O2− H+H+ HC 2 H 3 O 2 Before reaction0.300 mol0.020 mol0.300 mol After reaction0.280 mol0.000 mol0.320 mol

Aqueous Equilibria Calculating pH Changes in Buffers Now use the Henderson–Hasselbalch equation to calculate the new pH: pH = log (0.280) (0. 320) pH = pH = 4.62

Aqueous Equilibria Acid-Base Titrations A known concentration of base (or acid) is slowly added to a solution of acid (or base). (titrant) (analyte)

Aqueous Equilibria Titration A pH meter or indicators are used to determine when the solution has reached the equivalence point, at which the stoichiometric amount of acid equals that of base.

Aqueous Equilibria Titration Curves Titrant volume vs. pH 4 regions: Initial pH Before equivalence point Equivalence point After equivalence point

Aqueous Equilibria Titration Curve Strong base added to strong acid From the start of the titration to near the equivalence point, the pH goes up slowly.

Aqueous Equilibria Titration Curve Strong base added to strong acid Just before (and after) the equivalence point, the pH increases rapidly.

Aqueous Equilibria Titration Curve Strong base added to strong acid At eq. point, moles acid = moles base. Solution contains only water & salt from the cation of the base and the anion of the acid.

Aqueous Equilibria Titration Curve Strong base added to strong acid As more base is added, the increase in pH again levels off.

Aqueous Equilibria Titration Curve Strong base added to weak acid Unlike in the previous case, the conjugate base of the acid affects the pH when it is formed. The pH at the equivalence point will be >7. Phenolphthalein is commonly used as an indicator in these titrations.

Aqueous Equilibria Titration of a Weak Acid with a Strong Base At each point below the equivalence point, the pH of the solution during titration is determined from the amounts of the acid and its conjugate base present at that particular time.

Aqueous Equilibria Titration of a Weak Acid with a Strong Base With weaker acids, the initial pH is higher and pH changes near the equivalence point are more subtle.

Aqueous Equilibria Weak base & strong acid

Aqueous Equilibria Titrations of Polyprotic Acids In these cases there is an equivalence point for each dissociation.

Aqueous Equilibria Marks the end point of a titration by changing color. The equivalence point is not necessarily the same as the end point (but they are ideally as close as possible). Copyright © Cengage Learning. All rights reserved 35 Indicators

Aqueous Equilibria The Acid and Base Forms of the Indicator Phenolphthalein Copyright © Cengage Learning. All rights reserved 36

Aqueous Equilibria The Methyl Orange Indicator is Yellow in Basic Solution and Red in Acidic Solution Copyright © Cengage Learning. All rights reserved 37

Aqueous Equilibria Useful pH Ranges for Several Common Indicators Copyright © Cengage Learning. All rights reserved 38

Aqueous Equilibria Solubility Equilibria Dissolution/precipitation reactions are heterogeneous. Consider the equilibrium that exists in a saturated solution of BaSO 4 in water: BaSO 4 (s) Ba 2+ (aq) + SO 4 2− (aq)

Aqueous Equilibria Solubility Products The equilibrium constant expression for this equilibrium is K sp = [Ba 2+ ] [SO 4 2− ] where the equilibrium constant, K sp, is called the solubility product.

Aqueous Equilibria Solubility Products K sp is not the same as solubility. Solubility is generally expressed as the mass of solute dissolved in 1 L (g/L) or 100 mL (g/mL) of solution, or in mol/L (M).

Aqueous Equilibria Factors that Affect Solubility The Common-Ion Effect  If one of the ions in a solution equilibrium is already dissolved in the solution, the equilibrium will shift to the left and the solubility of the salt will decrease. BaSO 4 (s) Ba 2+ (aq) + SO 4 2− (aq)

Aqueous Equilibria Factors Affecting Solubility pH  If a substance has a basic anion, it will be more soluble in an acidic solution.  Substances with acidic cations are more soluble in basic solutions.