HBr is a strong acid, so the reaction goes to completion.

8-1 Strong Acids and Bases

HBr + H2O H3O3+ + Br-

pH = -log[H+] = -log(0.10) = 1.00

Chapter 8 Monoprotic Acid-Base Equilibria

The figure shows a Raman spectrum of solutions of nitric acid of increasing concentration.

Box 8-1 Concentrated HNO3 Is Only Slightly Dissociated2

KOH is a strong base (completely dissociated), so [OH-] = 0.10 M.

pH = -log[H+] = 13.00

Relation between pH pH + pOH = -logKW = 14.00 at 250C (9-1)and pOH:

The Dilemma

Step 2 Charge balance. The species in solution are K+, OH-, and H+. So,

Step 3 Mass balance. All K+ comes from the KOH, so [K+] = 1.0 X 10-8 M.

Step 4 Equilibrium constant expression. KW = [H+][OH-] = 1.0 X 10-14.

Step 5 Count. There are three equations and three unknowns ([H+], [OH-], [K+]), so we have enough information to solve the problem.

The Cure

[H+] = KW/(1.0 X 10-8) = 1.0 X 10-6M pH = 6.00

Step 1 Pertinent reactions. The only one is H2O = H+ + OH-.KW

[K+] + [H+] = [OH-] (9-2)

Step 6 Solve. Because we are seeking the pH, let’s set [H+] = x. Writing [K+] = 1.0 X 10-8 M in Equation 9-2, we get

[OH-] = [K+] + [H+] = 1.0 X 10-8 + x

[H+] = 9.6 X 10-8 M pH = -log[H+] = 7.02

1. When the concentration is “high” (≥10-6M), pH is calculated by just considering the added H+ or OH-. That is, the pH of 10-5.00M KOH is 9.00.

2. When the concentration is “low” (≤10-8M), the pH is 7.00. We have not added enough acid or base to change the pH of the water itself.

3. At intermediate concentrations of 10-6 to 10-8M, the effects of water ionization and the added acid or base are comparable. Only in this region is a systematic equilibrium calculation necessary.

Let’s review the meaning of the acid dissociation constant, Ka, for the

acid HA:

A weak acid is one that is not completely dissociated. That is, Reaction 9-3 does not go to completion. For a base, B, the base hydrolysis constant, Kb, is defined by the reaction

A weak base is one for which Reaction 9-4 does not go to completion.pK is the negative logarithm of an equilibrium constant:

8-2 Weak Acids and Bases

Weak-acid equilibrium:

Weak-base equilibrium:

pKW = -log KW

pKa = -log Ka

pKb = -log Kb

The acid HA and its corresponding base, A-, are said to be a conjugate acid-base pair, because they are related by the gain or loss of a proton.

The conjugate base of a weak acid is a weak base. The conjugate acid of a weak base is a weak acid.

Weak Is Conjugate to Weak

Relation between Ka and Ka · Kb = Kw (9-5)

Kb for conjugate pair:

Appendix G lists acid dissociation constants. Each compound is shown in its fully protonated form.

Using Appendix G

Names refer to neutral molecules.

8-3 Weak-Acid Equilibria

A Typical Weak-Acid Problem

x2 + (1.07 X 10-3) x – 5.35 X 10-5 = 0x = 6.80 X 10-3 (negative root rejected)

[H+] = [A-] = x = 6.80 X 10-3 M[HA] = F – x = 0.0432 M

pH = -logx = 2.17

Reactions:Charge balance:

Mass balance:

Equilibrium expressions:

[A-] (from HA dissociation) = 6.8 X 10-3 M

[H+] from HA dissociation = 6.8 X 10-3 M

[OH-] (from H2O dissociation) = 1.5 X 10-12 M

[H+] from H2O dissociation = 1.5 X 10-12 M

The fraction of dissociation, α, is defined as the fraction of the acid in the form A-:

Weak electrolytes (compounds that are only partially dissociated) dissociate more as they are diluted.

The Essence of a Weak-Acid Problem

Fraction of Dissociation

Fraction of dissociation of an acid:

Equation for weak acids:

Box 8-2 Dyeing Fabrics and the Fraction of Dissociation

Dyes are colored molecules that can form covalent bonds to fabric. For example, Procion Brilliant Blue M-R is a dye with a blue chromophore (the colored part) attached to a reactive dichlorotriazine ring:

Cellulose ㅡ CH2OH = cellulose ㅡ CH2O- + H+

ROH RO-

Ka≈10-15

Fraction of dissociation

fraction of dissociation

A handy tip: Equation 9-11 can always be solved with the quadratic formula. However, an easier method worth trying first is to neglect x in the denominator.

8-4 Weak-Base Equilibria

Equation for weak base:

B + H2O = BH+ + OH-Kb

[B] = F – [BH+] = F-x

A Typical Weak-Base Problem

What fraction of cocaine has reacted with water? We can formulate α for a base, called the fraction of association:

B + H2O = BH+ + OH-

0.0372-x x x

[H+] = KW/[OH-] = 1.0 X 10-14/3.1 X 10-4 = 3.2 X 10-11

pH = -log[H+] = 10.49

Fraction of association of a base:

Earlier, we noted that the conjugate base of a weak acid is a weak base, and the conjugate acid of a weak base is a weak acid.

Conjugate Acids and Bases-Revisited

Isomer of hydroxyl benzoic acid Ka Kb(= Kw/Ka)

ortho 1.07 X 10-3 9.3 X 10-12

para 2.9 X 10-5 3.5 X 10-10

pH of 0.050 0 M o-hydroxybenzoate = 7.83pH of 0.050 0 M p-hydroxybenzoate = 8.62

A buffered solution resists changes in pH when acids or bases are added or when dilution occurs. The buffer is a mixture of an acid and its conjugate base.

If you mix A moles of a weak acid with B moles of its conjugate base, the moles of acid remain close to A and the moles of base remain close to B.

8-5 Buffers

Mixing a Weak Acid and Its Conjugate Base

HA = H+ + A- pKa = 4.000.10-x x x

Fraction of dissociation

HA dissociates very little, and adding extra A- to the solution will make the HA dissociate even less. Similarly, A- does not react very much with water, and adding extra HA makes A- react even less.

A- + H2O = HA + OH- pKb = 10.00 0.10-x x x

Fraction of dissociation

The central equation for buffers is the Henderson-Hasselbalch equation, which is merely a rearranged form of the Ka equilibrium expression.

Henderson-Hasselbalch Equation

Henderson-Hasselbalch equation for an acid:

Henderson-Hasselbalch equation for a base:

Properties of the Henderson-Hasselbalch Equation

Regardless of how complex a solution may be, whenever pH = pKa, [A‑] must equal [HA]. This relation is true because all equilibria must be satisfied simultaneously in any solution at equilibrium. If there are 10 different acids and bases in the solution, the 10 forms of Equation 9-16 must all give the same pH, because there can be only one concentration of H+ in a solution.

Challenge Show that, when activities are included, the Henderson-Hasselbalch equation is

A Buffer in Action

Notice that the volume of solution is irrelevant, because volume cancels in the numerator and denominator of the log term:

moles of B/L of solution

moles of BH+/L of solution

moles of B

moles of BH+

Box 8-3 Strong Plus Weak Reacts Completely

H+ + OH- = H2OStrong Strong acid base

B + H+ = BH+

Weak Strong base acid

Ka(for BH+)

OH- + HA = A- + H2OStrong Weak base acid

Kb(for A-)

Ka(for HA)

Demonstration 9-2 How Buffers Work

Percentage of reaction completed

Calculated pH

Procedure: All solutions should be fresh. Prepare a solution of formaldehyde by diluting 9 mL of 37 wt% formaldehyde to 100 mL. Dissolve 1.5 g of NaHSO3

10 and 0.18 g of Na2SO3 in 400 mL of water, and add ~1 mL of phenolphthalein solution (Table 11-4). Add 23 mL of formaldehyde solution to the well-stirred buffer solution to initiate the clock reaction. The time of reaction can be adjusted by changing the temperature, concentrations, or volume.

We see that the pH of a buffer does not change very much when a limited amount of strong acid or base is added.But why does a buffer resist changes in pH? It does so because the strong acid or base is consumed by B or BH+.

1. Weigh out 0.100 mol of tris hydrochloride and dissolve it in a beaker containing about 800 mL of water.

2. Place a calibrated pH electrode in the solution and monitor the pH.

3. Add NaOH solution until the pH is exactly 7.60.

4. Transfer the solution to a volumetric flask and wash the beaker a few times. Add the washing to the volumetric flask.

5. Dilute to the mark and mix.

Preparing a Buffer in Real Life!

Buffer capacity, β, is a measure of how well a solution resists changes in pH when strong acid or base is added. Buffer capacity is defined as

Buffer capacity reaches a maximum when pH = pKa.

That is, a buffer is most effective in resisting changes in pH when pH = pKa

(that is, when [HA] = [A-]).

In choosing a buffer, seek one whose pKa is as close as possible to the desired pH. The useful pH range of a buffer is usually considered to be pKa ±1 pH unit.

The correct Henderson-Hasselbalch equation, 9-18, includes activity coefficients.

Buffer Capacity14

Buffer pH depends on Ionic Strength and Temperature

Buffer capacity:

When What You Mix Is Not What You Get

Mass balance: FHA + FA- = [HA] + [A-]Charge balance: [Na+] + [H+] = [OH-] + [A-]

[HA] = FHA – [H+] + [OH-] (9-20) [A-] = FA- + [H+] – [OH-] (9-21)

The Henderson-Hasselbalch equation (with activity coefficients) is always true, because it is just a rearrangement of the Ka equilibrium expression.