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Acid-Base Titrations

Introduction

Recall that titration is the quantitative measurement of an analyte in solution by reacting it completely with a standardized reagent. Acids and bases react until one of the reactants is consumed completely. A solution of base of known concentration can therefore be used to titrate an acid solution of unknown concentration. Likewise, an acid solution of known concentration can be used to titrate a base solution of unknown concentration.


Strong Acid and Strong Base

The point at which all of the analyte is consumed by titrant is called the equivalence point. The following figure shows the titration of a strong acid with 0.100 M NaOH. For titration of a strong acid with a strong base, the equivalence point occurs at a pH of 7. To reach the equivalence point in this example required 0.0350 mL of titrant, or 0.00350 moles of OH-. The titration shows that there were 0.00350 moles of acid in the original solution.

titration curve

We can identify three different regions in this titration experiment. Before the equivalence point the pH is determined by the concentration of unneutralized strong acid. At the equivalence point the pH, 7, is determined by the dissociation of water. After the equivalence point the pH is determined by the concentration of excess strong base that we are adding.


Weak Acid Titration

The following plot shows the titration curves of 0.1 M solutions of a strong acid and a weak acid (acetic acid).

titration curves

First note the initial pH of these solutions (the initial pH of the 0.1 M acetic acid is 2.9). For the strong acid, the dominant pH-determining species were described above. For the weak acid titration, we can also identify three dominant equilibria as titrant is added. Before the equivalence point the dominant species are acetic acid and acetate ion. The presence of these two species form a buffer, and the pH could be calculated by the Henderson-Hasselbalch equation. At the equivalence point, all of the acetic acid has been neutralized and only acetate ion remains in solution. The pH is therefore determined by the base hydrolysis reaction of the acetate with water. The pH is approximately 8.8 (not 7!). After the equivalence point, the situation is the same as for a strong acid and the pH is determined by the concentration of excess strong base.

An alternate plot to find the equivalence point is the first derivative of the data as shown below. The slope of the titration curve is steepest at the equivalence point, and the first derivative plot shows a maximum.

titration 1st derivative

Adding sufficient titrant to neutralize one-half of the weak acid results in a solution with equal amounts of the weak acid and its conjugate base. At this halfway point in the titration, the pH equals the pKa of the acid. Plotting pH versus log([base]/[acid]) produces a line with a y-intercept equal to the pKa. This is a plot of the Henderson-Hasselbalch equation:

pH = pKa + log{V/(E-V)}

where E is the titrant volume at the endpoint and V is the variable for titrant added. This equation is the same as the one in the Exp. 5, which uses Ve and Vb for E and V respectively. This plot is only linear from about 20% to 80% of the endpoint volume. The Henderson-Hasselbalch equation does not predict accurate results outside of this range due to the assumptions in the equation. The plot shown below uses the pH data from 5.0 mL to 20.0 mL on the weak acid titration curve from above.

titration 1st derivative


Acid-Base Indicators

In an acid-base titration, addition of titrant near the equivalence point causes the solution pH to change drastically. This pH change is detectable with indicators that change color as a function of pH. Indicators are weak acids that change color when they gain or lose their acidic proton(s). The table lists a few common indicators with the color of their acidic and basic forms and the pH range over which the color change occurs. (The listed endpoint color assumes titration of an acid with base, i.e., increasing pH.)

IndicatorColorpH Range
 acidicendpointbasic 
bromocresol greenyellowgreenblue4.0-5.6
methyl redredyellowyellow4.4-6.2
bromothymol blueyellowgreenblue6.2-7.6
phenolpthaleincolorlesslight pinkred8.0-10

We call the point at which the indicator changes color the end point. The end point might differ slightly from the equivalence point, and the difference between the equivalence point and the end point is called the titration error. The titration error will usually be negligible if a suitable indicator is available for use.


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