Chapter 16 Additional Aqueous Equilibria Buffer Solutions Buffer ...

8 downloads 205 Views 334KB Size Report
Buffer = chemical system that resists changes in pH. Example. Add 0.010 mol of HCl or NaOH to: Buffer Solutions. pH. 1 L Solution. Initial after HCl after NaOH.
Buffer Solutions John W. Moore Conrad L. Stanitski Peter C. Jurs http://academic.cengage.com/chemistry/moore

Chapter 16 Additional Aqueous Equilibria Stephen C. Foster • Mississippi State University

Buffer Action

Buffers are made with ~equal quantities of a conjugate acid-base pair. (e.g. CH3COOH + CH3COONa)

Buffer Action

1 L Solution

Initial

pH after HCl

after NaOH

pure H2O

7.00

2.00

12.00

[CH3COOH] = 0.5 M + [CH3COONa] = 0.5 M

4.74

4.72

4.76

A buffered solution

Added OH- removed by the acid: CH3COOH + OHCH3COO- + H2O Added H3O+ removed by the conjugate base: CH3COO- + H3O+ CH3COOH + H2O The equilibrium maintains the acid/base ratio. CH3COOH + H2O CH3COO- + H3O+ pH remains stable.

The pH of Buffer Solutions

Blood pH • Blood is buffered at pH = 7.40 ± 0.05.  pH too low: acidosis.  pH too high: alkalosis. • CO2 generates the most important blood buffer.

H2CO3(aq) + H2O(ℓ)

Example Add 0.010 mol of HCl or NaOH to:

Buffer Action

Buffers must contain: • A weak acid to react with any added base. • A weak base to react with any added acid. • These components must not react with each other.

CO2(aq) + H2O(ℓ)

Buffer = chemical system that resists changes in pH.

H2CO3(aq) H3O+(aq) + HCO3-(aq)

Depends on the [acid]/[base] – not absolute amounts. HendersonHenderson-Hasselbalch equation [H3O+] = Ka

[HA] [A-]

log [H3O+] = log Ka + log pH = pKa + log Note: pH = pK pKa

[A-] [HA]

[HA] [A-] With pKa = -log Ka

when [HA] = [A-]

1

The pH of Buffer Solutions

Common Buffers

What is the pH of a 0.050 M (monoprotic) pyruvic acid + 0.060 M sodium pyruvate buffer? Ka = 3.2 x 10-3.

pH

weak acid

weak base

Ka(weak acid) pKa

4 lactic acid

lactate ion

1.4 x 10-4

3.85

5 acetic acid

acetate ion

1.8 x 10-5

4.74

6 carbonic acid

hydrogen carbonate ion

4.2 x 10-7

6.38

= 2.49 + 0.08

7 dihydrogen phosphate hydrogen phosphate ion

6.2 x 10-8

7.21

= 2.57

8 hypochlorous acid

hypochlorite ion

3.5 x 10-8

7.46

9 ammonium ion

ammonia

5.6 x 10-10

9.25

carbonate ion

4.8 x 10-11 10.32

pH = – log(3.2 x

10-3)

+ log(0.060/0.050)

What is the HPO42-/H2PO4- ratio in blood at pH =7.40. Ka(H2PO4- ) = Ka,2(H3PO4) = 6.2 x 10-8. 7.40 = −log(6.2 x 10-8) + log([HPO42-]/[H2PO4-]) log([HPO42-]/[H2PO4-]) = 0.192 [HPO42-]/[H2PO4-] = 1.5

Addition of Acid or Base to a Buffer 1.0 L of buffer is prepared with [NaH2PO4] = 0.40 M and [Na2HPO4] = 0.25 M. Calculate the pH of: (a) the buffer (b) after 0.10 mol of NaOH is added. Ka (H2PO4-) = 6.2 x 10-8

pH = pKa + log

[A-] [HA]

pH = 7.21 + log 0.25 = 7.01 0.40

Buffer Capacity The amount of acid (or base) that can be added without large pH changes. [A-]/[HA] determines the buffer pH. Magnitude of [A-] and [HA] determine buffer capacity The buffer capacity for: • Base addition = nconjugate acid • Acid addition = nconjugate base

Useful buffer range: pH = pKa ±1 (10:1 or 1:10 ratio of [A-]/[HA]).

Addition of Acid or Base to a Buffer 1.00 L Buffer: [NaH2PO4]= 0.40 M ; [Na2HPO4] = 0.25 M. (b) calculate pH after 0.10 mol of NaOH is added. Ka (H2PO4-) = 6.2 x 10-8

(b) 0.10 mol of NaOH, converts conj. acid to base: H2PO4- + OH0.40 0.10 (0.40 – 0.10) 0

ninitial nadded nafter

pKa = -log(6.2 x 10-8) = 7.21 (a) No base added:

10 hydrogen carbonate

pH = pKa + log

[A-] [HA]

→ HPO42- + H2O 0.25 (0.25 + 0.10)

Use n directly. [ ] = n/ V and V is the same for both (cancels)

pH = 7.21 + log 0.35 = 7.28 0.30

Acid-Base Titrations • Standard solution (titrant titrant) is added from a buret. • The equivalence point occurs when a stoichiometric amount of titrant has been added. • Use a pH meter. • An indicator is used to find an end point. point • Color change observed. • End point ≠ equivalence point (should be close...). ntitrant = nanalyte

ntitrant = Vtitrant [titrant] nanalyte= Vanalyte[analyte]

2

Detection of the Equivalence Point Acid-Base Indicator = weak acid that changes color with changes in pH. HIn(aq) + H2O(ℓ) color 1

H3O+(aq) + In-(aq) color 2

Observed color will vary (depends on [HIn] and [In-] in solution). Ka =

Detection of the Equivalence Point The acidic form dominates when the [HIn] >> [In-] If

pH = pKa -1

Basic color shows when [In-] >> [HIn] [In-] = 10 [HIn]

Ka =

- pKa = 1 - pH

Detection of the Equivalence Point

[H3O+][In-] [H3O+] = [HIn] 10

Ka =

- pKa = - pH - 1

If

[H3O+][In-] [HIn]

[HIn] = 10 [In-]

[H3O+][In-] = 10 [H3O+] [HIn]

pH = pKa +1

Titration of Strong Acid with Strong Base AcidAcid-base titration curve = plot of pH vs Vtitrant added. Titrate 50.0 mL of 0.100 M HCl with 0.100 M NaOH

Red pH ≤ 4

Yellow pH ≥ 6

Initial pH = -log(0.100) = 1.000 (fully ionized acid)

Moles of acid = 0.0500 L Methyl Red

Bromothymol blue

Phenolphthalein

0.100 mol L

= 5.00 x 10-3 mol

Titration of Strong Acid with Strong Base

Titration of Strong Acid with Strong Base

After 40.0 mL of base added (before equivalence) Base removes H3O+ : H3O+ + OH2 H2O

After Equivalence (50.2 mL added) All acid consumed.

original nacid – total nbase added [H3O+] = Vacid (ℓ) + Vbase added (ℓ) -3 -3 [H3O+] =(5.00 x 10 – 4.00 x 10 ) mol= 0.0111 M (0.0500 + 0.0400) L pH = -log(0.0111) = 1.95

At Equivalence (50.0 mL added) All acid and base react. Neutral salt. pH = 7.00.

nOH- added = 0.0502 L

0.100 mol = 5.02 x 10-3 mol L

original nacid = 0.0500 L 0.100 mol L

= 5.00 x 10-3 mol

nOH- remaining = 0.02 x 10-3 mol

Vtotal = (0.0500 + 0.0502) L = 0.1002 L pOH = - log(0.02 x10-3 / 0.1002) = 3.70 pH = 14.00 – 3.70 = 10.30

3

Titration of Strong Acid with Strong Base Vtitrant/mL Vexcess/mL Vtotal/mL

[OH-]/mol L-1

Titration of Strong Acid with Strong Base

pH

50.0

0

100.0

0

7.00

50.1

0.1

100.1

0.0001

10.00

50.2

0.2

100.2

0.0002

10.30

51

1

101.0

0.0010

11.00

55

5

105.0

0.0048

11.67

60

10

110.0

0.0091

11.96

70

20

120.0

0.0167

12.22

80

30

130.0

0.0200

12.30

0.1 mL of base increased the pH by 3 units!

Titration of Weak Acid with Strong Base

Titration of Weak Acid with Strong Base

More complicated. • Weak acid is in equilibrium with its conjugate base. Example Titrate 50.0 mL of 0.100 M acetic acid with 0.100 M NaOH. What is the pH after the following titrant additions: 0 mL, 40.0 mL, 50.0 mL, and 50.2 mL?

40.0 mL added

0 mL added

HA + H2O

Ka = 1.8 x 10-5 =

2 [H3O+][A-] ≈ x [HA] (0.100)

50 mL of 0.100 M

ninitial nadded nleft

HA(aq) + OH-(aq)

+

H2O(ℓ)

0.00500 0.00400 0.00100

0.00400

Each OH- removes 1 HA… nleft = 0.00500 - 0.00400

H3O+ + A-

A-(aq)

…and makes 1 A40 mL of 0.100 M

x= 0.0013 Vtotal = (50.0 + 40.0) mL = 90.0 mL = 0.0900 L

pH = -log(0.0013) = 2.88

Titration of Weak Acid with Strong Base

Titration of Weak Acid with Strong Base

40.0 mL added

(c) 50.0 mL added Equivalence. All HA is converted to A-.

Henderson-Hasselbalch: pH = -log(1.8 x 10-5) + log

[A-] = nA-/ V

(0.00400/0.0900) (0.00100/0.0900) [HA] = nHA/ V

HA(aq) + OH-(aq) ninitial nadded nleft

A-(aq)

+

H2O(ℓ)

0.00500 0.00500 0

0.00500

Note: V cancels (could be omitted)

pH = 4.74 + log

0.0400 = 5.34 0.0100

Vtotal= 100.0 mL, so [A-] = 0.00500 mol/0.100 L = 0.0500 M A- is basic!

4

Titration of Weak Acid with Strong Base

Titration of Weak Acid with Strong Base

Use Kb to solve for the [OH-] generated by [A-]:

(c) 50.2 mL added 0.2 mL of “extra” OH- dominates pH. Ignore any contribution from A-.

Kb =

[OH-][HA] [A-]

A+ (0.0500 - x)

Kb = Kw / Ka = 5.6 x 10-10 H2 O

Kb = 5.6 x 10-10 ≈ pOH = 5.28

HA x

x2 0.0500

+

OHx

x = 5.3 x 10-6 M

[OH-] = (0.0002 L x 0.100 mol/L) / 0.1002 L = 2.0 x 10-4 M pOH = 3.7 pH = 14.0 – 3.7

= 10.3

pH = 14 - pOH = 8.72

Titration of Weak Acid with Strong Base

Titration of Weak Base with Strong Acid

Titrate of 50.0 mL of 0.100 M acetic acid with 0.100 M NaOH.

Volume of 0.100 M HCl added (mL)

pH = pKa at 50% titration (25 mL) pKa (acetic acid) = 4.74. Short vertical section compared to strong acid/strong base.

Solubility Equilibria and KSP Some ionic compounds are slightly water soluble. Saturation occurs at low concentration. AgCl(s)

50.0 mL of 0.100 M ammonia titrated with 0.100M HCl. • pH = pKa at 50% to equivalence (pKa = 9.25).

Solubility Equilibria and KSP Example Ksp(AgCl)=1.8 x 10-10. Calculate the solubility (mol/L).

Ag+(aq) + Cl-(aq) Ksp = [Ag+][Cl-] = 1.8 x 10-10

The solubility product constant is: Ksp = [ Ag+] [ Cl-]

At equilibrium,

[Ag+] = [Cl-] = S

Then:

1.8 x 10-10 = (S)(S) = S2 S = 1.3 x 10-5 M

As always, [ ] of solid is omitted

Solubility = 1.3 x 10-5 mol/L.

5

Factors Affecting Solubility

Common Ion Effect

pH and Dissolving Slightly Soluble Salts Using Acids Insoluble salts containing anions of Bronsted-Lowry bases dissolve in acidic solutions.

AgCl is slightly soluble in water:

Ca2+(aq) + CO32- (aq) Ksp = 8.7 x 10-9

Pure water: CaCO3(s) Acid:

Add more Ag+ or Cl-. Equilibrium will move left.

Called the common ion effect. CO3

HCO3

Ag+(aq) + Cl-(aq)

AgCl(s)

-(aq)

2-(aq)

+ H3

+ H3

O+(aq)

O+(aq)

H2CO3(aq)

HCO3

-(aq)

+ H2O(ℓ)

H2CO3(aq) + H2O(ℓ) CO2(g) + H2O(ℓ)

K ≈ 105

e.g. AgCl is less soluble in a NaCl solution than in water. The “common ion” is Cl-.

Solubility and the Common Ion Effect

Solubility and the Common Ion Effect

Example Calculate the solubility of PbI2 in (a) water (b) 0.010 M NaI. Ksp (PbI2) = 8.7 x 10-9.

(b) NaI supplies I - lowering the PbI2 solubility.

(a) Pure water:

Pb2+ S

PbI2

+

2 I2S

PbI2 [ ]initial (from NaBr) [ ]change (from PbBr2) [ ]equil

Pb2+ 0 S S

+

2 I0.010 2S 0.010 + 2S

Ksp = 8.7 x 10-9 = [Pb2+][I -]2 = S(2S + 0.010)2 Ksp = [Pb2+][I -]2 = (S)(2S)2 = 4S3 = 8.7 x 10-9 S = 1.3 x

10-3

M

Assume S Ksp • Q must decrease. • remove ions, precipitate solid.

If Q = Ksp • at equilibrium (saturated solution).

If Q < Ksp • Q must increase. • dissolve more solid (if present). Form more ions.

Precipitation: Will It Occur?

Precipitation: Will It Occur?

Mix 25.0 mL of 0.0025 M HCl and 10.0 mL of 0.010 M AgNO3. Will AgCl precipitate? Ksp (AgCl) = 1.8 x 10-10.

Slowly add HCl(aq) to a solution that is 0.010 M in Cu+ and 0.500 M in Pb2+. Which salt will precipitate first? Ksp for PbCl2 and CuCl are 1.7 x 10-5 and 1.9 x 10-7.

nCl-

= 0.0250 L (0.0025 mol/L)

nAg+ = 0.0100 L (0.010 mol/L)

= 6.25 x 10-5 mol = 1.0 x 10-4 mol

CuCl: KSP= 1.9 x 10-7 = [Cu+][Cl-] = 0.010[Cl-]

Vtotal = (0.0250 + 0.0100) = 0.0350 L. [Cl-] = 6.25 x 10-5 mol/ 0.0350 L = 1.79 x 10-3 mol/L [Ag+]

= 1.0 x

10-4

mol / 0.0350 L = 2.86 x

10-3

mol/L

Q = [Ag+][Cl-] = (1.79 x 10-3)(2.86 x 10-3) = 5.1 x 10-6 Q > KSP

Find the minimum [Cl-] that will cause precipitation:

[Cl-] = 1.9 x 10-5 M

Least soluble, precipitates 1st

PbCl2: KSP = 1.7 x 10-5 = [Pb2+][Cl-]2 = 0.500[Cl-]2 [Cl-] = 5.8 x 10-3 M

Precipitation will occur

7