3.6: ACIDS AND BASES … Equilibrium Constants…K a and K b

HOW DO WE MEASURE PH? For less accurate measurements, one can use Litmus paper “Red” paper turns blue above ~pH = 8 “Blue” paper turns red below ~pH = 5 Or an indicator.

HOW DO WE MEASURE PH? For more accurate measurements, one uses a pH meter, which measures the voltage in the solution.

PRACTICE Calculate the pH of a M solution of HI and a M solution of Ca(OH) 2 (aq). HI solution: pH = Ca(OH) 2 (aq) : pH = 13.18

EQUILIBRIUM CONSTANTS FOR ACIDS AND BASES: Facts about acid and base concentrations: For a strong monoprotic acid, [H 3 O + ] in solution is equal to the original acid concentration. Likewise, for a strong monoprotic base, [OH - ] will be equal to the original base concentration For a weak acid, [H 3 O + ] will be much less than the original acid concentration. [H 3 O + ] will be smaller than it would have been if it were a strong acid For a series of weak monoprotic acids (of the type HA) of the same concentration, [H 3 O + ] will increase (and the pH will decline) as the acids become stronger. Likewise, for a series of weak bases, [OH - ] will increase (and the pH will increase) as the bases become stronger

EQUILIBRIUM CONSTANTS FOR ACIDS AND BASES: Relative strength of an acid or base can be expressed quantitatively with an equilibrium constant Ionization Constant Still a constant… still the same thing… we’re just talking about the ionization of acids and bases… so we give it a specific term… why? To make your life more difficult, that’s why

EQUILIBRIUM CONSTANTS FOR ACIDS AND BASES: Write the equilibrium constant for the following reaction, where HA represents a generic acid: But this is for an acid… so we call the equilibrium constant is called the acid- dissociation constant, K a [H 3 O + ] [A - ] [HA] K c = HA (aq) + H 2 O (l) A - (aq) + H 3 O + (aq)

EQUILIBRIUM CONSTANTS FOR ACIDS AND BASES: The greater the value of K a, the stronger is the acid.

EQUILIBRIUM CONSTANTS FOR ACIDS AND BASES: Calculating the K a from the pH: The pH of a 0.10 M solution of formic acid, HCOOH, at 25  C is Calculate K a for formic acid at this temperature. Use the pH to calculate the hydronium ion concentration [H 3 O + ] [COO - ] [HCOOH] K a =

EQUILIBRIUM CONSTANTS FOR ACIDS AND BASES: pH = -log [H 3 O + ] 2.38 = -log [H 3 O + ] = log [H 3 O + ] = 10 log [H 3 O + ] = [H 3 O + ] 4.2  = [H 3 O + ] = [HCOO - ] [4.2  ] [0.10] K a = = 1.8  10 -4

EQUILIBRIUM CONSTANTS FOR ACIDS AND BASES: Calculate the pH of a 0.100M solution of HF. K a = 6.8 x Use an ICE table to calculate the [H + ]. Then use the [H + ] to calculate the pH. [H + ] = pH = 2.1 HF (aq) + H 2 O (l) F - (aq) + H 3 O + (aq)

EQUILIBRIUM CONSTANTS FOR ACIDS AND BASES: Similarly, we can write equilibrium constants for weak bases: But this is for an base… so we call the equilibrium constant is called the base- dissociation constant, K b [HB] [OH - ] [B - ] K b =

EQUILIBRIUM CONSTANTS FOR ACIDS AND BASES: K b can be used to find [OH - ] and, through it, pH.

EQUILIBRIUM CONSTANTS FOR ACIDS AND BASES: What is the pH of a 0.15 M solution of NH 3 ? ICE TABLE TIME!!! NH 3 (aq) + H 2 O (l) NH 4 + (aq) + OH - (aq) [NH 4 + ] [OH - ] [NH 3 ] K b = = 1.8  10 -5

EQUILIBRIUM CONSTANTS FOR ACIDS AND BASES: (1.8  ) (0.15) = x  = x  = x 2 [OH - ] = 1.6  M pOH = -log (1.6  ) pOH = 2.80 pH = pH = (x) 2 (0.15) 1.8  =

POLYPROTIC ACIDS: …have more than one acidic proton If the difference between the K a for the first dissociation and subsequent K a values is 10 3 or more, the pH generally depends only on the first dissociation.

AQUEOUS SOLUTIONS OF SALTS Anions that are conjugate bases of strong acids (things like Cl - ) will have effect on the solution pH. There are numerous basic anions (CO 3 -2 ). All are conjugate bases of weak acids. The acid-base behavior of anions of polyprotic acids depends on the extent of deprotonation. For example, a fully deprotonated anion (like CO 3 -2 ) will be basic. A partially deprotonated anion (such as HCO 3 - ) is amphiprotic – its behavior will depend on the other species in the reaction. Alkali metal and alkaline earth cations have no measurable effect on solution pH. Basic cations are conjugate bases of acids cations [Al(H 2 O) 6 ] +3. Acidic cations are limited to metal cations with +2 or +3 charges and to ammonium ions (and their organic derivatives) All metal cations are hydrated in water. They form ions such as [M(H 2 O) 6 ] +3. However, only when M is a +2 or +3 ion, particularly a transition metal ion, does the ion act as an acid

© 2009, Prentice-Hall, Inc. EFFECT OF CATIONS AND ANIONS 1. An anion that is the conjugate base of a strong acid will not affect the pH. 2. An anion that is the conjugate base of a weak acid will increase the pH. 3. A cation that is the conjugate acid of a weak base will decrease the pH.

© 2009, Prentice-Hall, Inc. EFFECT OF CATIONS AND ANIONS 4. Cations of the strong Arrhenius bases will not affect the pH. 5. Other metal ions will cause a decrease in pH. 6. When a solution contains both the conjugate base of a weak acid and the conjugate acid of a weak base, the affect on pH depends on the K a and K b values.

EFFECT OF CATIONS AND ANIONS Cliff’s Summary: Salts made of the anion of a strong acid and the cation of a strong base will be neutral salts, pH = 7. Example – Sodium Chloride Salts made of the anion of a strong acid and the cation of a weak base will be acidic salts. Example – Ammonium Chloride Salts made of the anion of a weak acid and the cation of a strong base will be basic salts. Example – Sodium Bicarbonate

K A AND K B K a and K b are related in this way: K a  K b = K w

PK A How are the values of K a used to compare acid strength? pK a ! pK a = -log K a Like pH, as the value of pK a becomes smaller the acid strength increases

K A AND K B K a for lactic acid is 1.4 x What is the K b for the conjugate base of this acid? K b =7.1 x