Acid-Base Reactions - Titration Curves

Part B: Weak Acid and Strong Base

© Silvia Kolchens

Pima Community College

B. Titration of a Weak Acid with a Strong Base

When tritrating a weak acid with a strong base we obtain an acid-base titration curve with the following characteristic features (Figure 2):

How to calculate pH values for weak acid/strong base titration curves:

Example: Titrate 50 mL 0.1 M acetic acid (CH3COOH) with 0.1 M NaOH solution:

CH3COOH + NaOH ó CH3COO- + H2O + Na+
 
 

(1) What is the pH of the acetic acid before any base is added?

When dealing with weak acids in aqueous solutions, we can no longer assume total dissociation. In fact, the equilibrium lies predominantly on the left hand side of the equation:

CH3COOH(aq) + H2O(l) ç CH3COO- (aq) + H3O+(aq)

In this case, the hydronium ion concentration is not immediately known, but can be determined from an iCe table:

iCe table
 
 
CH3COOH(aq) H2O(l) CH3COO- (aq) H3O+(aq)
i 0.1 M - 0 0
C -x - +x +x
e 0.1-x - x x


We make the approximation that x is much smaller than the initial concentration (x<<0.1) and can be neglected. This will greatly simplify our expression and we can solve for "x", the hydronium ion concentration:

The value for Ka of acetic acid is 1.8x10-5 and we obtain

x=[H3O+] = 0.003 M

The pH of the 0.1 M acetic acid solution is then

pH=-log 0.003 =2.52



(2) What is the pH value at the equivalence point:

At the equivalence point we have equivalent amounts of acids and bases are present. In our example this means that 50 mL of 0.1 M CH3COOH and 50 mL of 0.1 M NaOH solution have been combined. The total volume is now 100 mL.

At this point, all acid has been neutralized, i.e. all CH3COOH has been converted to CH3COO-. The acetate ion (CH3COO-) itself is a weak base and will react with water (hydrolysis):

CH3COO- (aq) + H2O(l) ó CH3COOH + OH-(aq)

This hydrolysis reaction will produce hydroxide ions, hence the equivalence point will be higher than pH 7. We can calculate the pH at the equivalence point using an iCe table and the base dissociation constant (Kb) for the acetate ion:

First, we have to calculate the molar concentration of the acetate ion:


 
 

Now we can use this concentration in the iCe table:


CH3COO- (aq)  H2O(l)  CH3COOH OH-(aq)
i 0.05 - 0 0
C -x - +x +x
e 0.05-x - x x

We assume that x is much smaller than 0.05, and 0.05-x~0.5. The expression for Kb can then be written

Kb for the acetate ion is 5.6x10-10 and we solve for x;

x= [OH-] = 5.29 x 10-6

pOH = 5.27

pH = 14-pOH = 8.72

The equivalence point is in the basic range.

(3) What is the pKa value of the acid?

What is a pKa value? The pKa value is the negative logarithm of the acid dissociation constant Ka:

pKa = -log Ka

The midpoint can be determined from the equivalence point: it is located where just half the volume of titrant has been used to neutralize the acid. Consequently the solution contains equal amounts of acid (CH3COOH) and its conjugated base (CH3COO-) or

[CH3COOH] = [CH3COO-]

Using this equation in the equilibrium constant and solving for H3O+ yields

Taking the negative logarithm on both sides yiels

Which can also be expressed as

or



This last equation is known as the Henderson Hasselbach equation. What does the equation mean?

If the concentrations of acid (CH3COOH) and its conjugated base (CH3COO-) are the same, then the ratio CH3COO-/CH3COOH will be "1". Since the logarithm of "1" equals zero, this equation simplifies to

pH = pKa

At the mid point the pKa value of an acid equals the measured pH. Thus we have a very simple method to determine acid dissociation constants.

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© copyright Silvia Kolchens, Pima Community College 2000

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