Study Guide
Chapter 15 Titration Curves for Complex Acid Base Systems
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University:
Kentucky State University -
Course:
CHE 102 | General Chemistry II Academic year:
2022
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Views:
201
Pages:
41
Author:
Tyshawn Shaffer
Chapter 15
Titration Curves for Complex
Acid/Base Systems
In this chapter; we describe methods for calculating titration curves for complex acid/base
systems. For the purpose of this discussion, complex systems are defined as solutions made
up of
(1) two acids or two bases of different strengths,
(2) an acid or a base that has two or more acidic or basic functional groups, or
(3) an amphiprotic substance, which is capable of acting as both an acid and a base.
Equations for more than one equilibrium are required to describe the characteristics of any
of these systems. MIXTURES OF STRONG AND WEAK
ACIDS OR STRONG AND WEAK BASES
• Strong acid and a weak acid (or a strong base and
a weak base)
– the concentrations of the two are of the same order of
magnitude and
– the Ka or Kb for the weak acid or base is somewhat less
than about 10-4
– Assume all [H2O+] = comes from strong acid • assume that [A-] < < CHCl and [H30+] = CHCI
• The approximation employed in Example 15-1 can be shown to
apply until most of the HCl has been neutralized by the titrant.
• the curve in this region is identical to the titration curve for a
solution of a strong acid by itself.
• the presence of HA must be taken into account as the first end
point in the titration is approached The shape of the curve for a
mixture of weak and strong acids,
and hence the information
obtainable from it, depends in
large measure on the strength of
the weak acid.
Figure 15-1 Curves for the
titration of strong acid/weak acid
mixtures with 0.1000 M NaOH.
Each titration is on 25.00 mL of a
solution that is 0.1200 M in HCI
and 0.0800 M in HA.
The composition of a mixture of a
strong acid and a weak acid can
be determined by titration with
suitable indicators if the weak
acid has a dissociation constant
that lies between 10-4 and 10-8
and the concentrations of the two
acids are of the same order of
magnitude. POLYFUNCTIONAL ACIDS AND BASES
• Several species are encountered in analytical chemistry that
have two or more acidic or basic functional groups. Generally,
the two groups differ in strength and, as a consequence,
exhibit two or more end points in a neutralization titration. The Phosphoric Acid System
With this acid, as with other polyprotic acids
Ka1> Ka2> Ka3. The Carbon Dioxide Carbonic Acid System
The first reaction describes the hydration of aqueous CO2 to form carbonic acid. Note that
the magnitude of Khyd indicates that the concentration of CO2( aq) is much larger than the
concentration of H2CO3 (that is, [H2CO3] is only about 0.3% that of [CO2(aq)]. Thus, a more
useful way of discussing the acidity of solutions of carbon dioxide is to combine 1st and 2nd
Equations gives: BUFFER SOLUTIONS INVOLVING
POLYPROTIC ACIDS
• Two buffer systems can be prepared from a weak dibasic acid and
its salts. The first consists of free acid H2A and its conjugate base
NaHA, and the second makes use of the acid NaHA and its
conjugate base Na2A. The pH of the latter system is higher than that
of the former because the acid dissociation constant for HA-is
always less than that for H2A.
• only one of the equilibria is important in determining the
hydronium ion concentration of the solution.
• the dissociation of HA- to yield A2-is neglected. • For a buffer prepared from NaHA and Na2A, the second
dissociation will ordinarily predominate, and the equilibrium
is disregarded. The concentration of H2A is negligible compared
with that of HA- or A2-. The hydronium ion concentration can be
calculated from the second dissociation constant, again employing
the techniques for a simple buffer solution. To test the assumption,
we compare an estimate of the H2A concentration with the
concentrations of HA- and A2-. CALCULATION OF THE pH OF
SOLUTIONS OF NaHA
• Salts that have both acidic and basic properties (salts that are
amphiprotic).
– Salts are formed during neutralization titration of polyfunctional acids and
bases
• 1 mol of NaOH is added to a solution containing 1 mol of the acid
H2A, 1 mol of NaHA is formed. The pH of this solution is
determined by two equilibria established between HA-and water:
1
2 • mass-balance expression.
3
• charge-balance equation
• Since the sodium ion concentration is equal to the molar analytical concentration
of the salt, the last equation can be rewritten as
•
4
We now have four algebraic equations (Equations 3 and 4 and the two dissociation
constant expressions for H2A) and need one additional expression to solve for the five
unknowns. The ion-product constant for water serves this purpose:
• We first subtract the mass-balance equation from the charge-balance equation. • We then rearrange the acid-dissociation constant expressions for H2A to obtain
and for HA-to give
• Substituting these expressions and the expression for Kw into Equation 15-12 yields
• Multiplying through by [H30+J gives
• We collect terms to obtain
• Finally, this equation rearranges to
5
• Under most circumstances, we can make the approximation that • Introduction of this relationship into Equation 5 gives
6
• The approximation shown as Equation 3 requires that [HA -] be much larger than any of
the other equilibrium concentrations in Equations 3 and 4 . This assumption is not valid
for very dilute solutions of NaHA or when Ka2 or Kw/Ka1 is relatively large.
• Frequently, the ratio CNaHA/Ka1 is much larger than unity in the denominator of Equation 6,
and Ka2CNaHA is considerably greater than Kw in the numerator. With these assumptions,
the equation simplifies to TITRATION CURVES FOR POLYFUNCTIONAL ACIDS
• Compounds with two or more acid
functional groups yield multiple end
points in a titration provided that
the functional groups differ
sufficiently in strength as acids.
• Figure 15-2 Titration of 20.00 mL of
0.1000 M H2A with 0.1000 M NaOH.
– For H2A, Ka1 = 1.00 X 10-3 and
Ka2 = 1.00 X 10-7. The method
of pH calculation is shown for
several points and regions on
the titration curve. TITRATION CURVES FOR POLYFUNCTIONAl BASES TITRATION CURVES FOR AMPHIPROTIC SPECIES
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Chapter 15 Titration Curves for Complex Acid Base Systems
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