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Titrations with Weak Acids or Weak Bases

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  • 0:03 Titration
  • 1:55 Titration Curves
  • 3:30 pH During Weak…
  • 11:08 Lesson Summary
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Lesson Transcript
Instructor: Elizabeth (Nikki) Wyman

Nikki has a master's degree in teaching chemistry and has taught high school chemistry, biology and astronomy.

Learn about titrations with weak acids or weak bases in this lesson. Study their titration curves and learn about some of their important characteristics. Learn how to calculate pH during titrations involving weak acids and strong bases.

Titrations

Have you ever taken an antacid like Tums or Rolaids to quell the effects of a spicy or acidic meal? The antacids are bases that react with the acids in your stomach to produce a neutral product that will help decrease the burning sensation in your stomach. The type of chemical reaction that occurs is called a neutralization reaction.

Chemists use neutralization reactions to analyze acidic or basic solutions in a technique called titration. During titration, a solution of known properties (called the titrant) is used to analyze properties of an unknown solution. Titrations may be done to determine the initial concentration of the unknown solution or to measure changes in pH as the titration occurs.

Imagine that you have to take three antacid tablets to neutralize the acid in your stomach. The point at which neutralization occurs is called the equivalence point. This is best described chemically as the point at which equal amounts of acid and base have been added together to create a neutral solution. The equivalence point is the most important point of a titration because it gives us information about how much unknown is present. Ideally, the equivalence point is the same as the endpoint, or stopping point of a titration.

Unfortunately, we can't just feel the endpoint of a titration like we can when we're taking antacids. Instead, we either need to use an indicator solution or do some math to predict the pH at equivalence point. An indicator solution is a special chemical solution that changes color within specific pH ranges. If we know what kinds of acids or bases we're titrating, we can choose a specific indicator to help us find our endpoint. If we know the identity of the acids and bases we're titrating and their concentrations, we can do math to predict the pH at equivalence point.

Titration Curves

Data collected during titration can be used to create a titration curve, or a graph of pH vs. milliliters of titrant added. All titration curves have similar characteristics; to me, they all kind of look like slides. Like many slides, titration curves begin with a slope that is gentle and gradual initially, dramatic in the middle, and then gentle at the end. The equivalence point occurs in the middle of the dramatic slope.

A titration in which a weak acid is titrated with a strong base will look like this:

Titration curve for weak acid with strong base
weak acid and strong base titration curve

A slide modeled from this curve would be a more mellow ride. Starting pH values are lower, ending pH values are higher, the slopes of the lines are not as dramatic, and the equivalence point is higher than seven.

A titration in which a weak base is titrated with a strong acid will look very similar to the previous titration curve, except backwards. The starting pH will be relatively high and the ending pH will be relatively low, but not as extreme as if this was a titration between a strong base and strong acid. The slopes of the lines aren't as steep and the equivalence point occurs below seven.

Notice that when an acid is titrated with a base, the pH increases from left to right. When a base is titrated with an acid, the pH decreases from left to right. If a weak acid or base is present in titration, the slopes will always be more mellow than if both substances are strong acids and bases. If you want to learn more about strong acid-base titrations, please check out our video!

pH During Weak Acid/Strong Base Titration

Determining the pH of a weak acid or base that is titrated by a strong acid or base is kind of a labor-intensive process. If you've watched the video on titrations with strong acids or strong bases, you are already familiar with most of this process. To determine the pH in a titration that involves a weak acid or weak base we will:

  1. Determine the number of moles of each reactant present
  2. Determine which reactant is in excess
  3. Then, use stoichiometry and Ka values (or Kb values) to determine hydrogen ion concentration and pH (we'll break this step into three smaller steps later)

Imagine we're titrating a sample of acetic acid (HC2H3O2, Ka 1.8 * 10^-5), with NaOH as our titrant. Our acetic acid sample is 1.5 M and 50 mL; our NaOH has a concentration of 1 M. We want to know what our pH will be after 5 mL of titrant has been added. Acetic acid reacts with NaOH in a 1:1 ratio to produce water and sodium acetate. The acetate ion is a relatively strong conjugate base and affects pH.

Step 1. Determine the number of moles of each reactant present:

The initial number of moles for our reactants can be found by multiplying molarity by volume. For simplicity's sake, I'll refer to the compound HC2H3O2 as acetic acid.

1.5 M acetic acid * 0.050 L acetic acid = 0.075 moles of acetic acid

1 M NaOH * 0.005 L NaOH = 0.0050 moles NaOH

To simplify, I'm just going to just call NaOH, OH-.

Step 2. Determine which reactant is in excess:

We have significantly less OH- than acetic acid, so pH will be based on the amount of acetic acid remaining. Like in the previous problem, the base added will react completely with the weak acid. This will leave us with no OH- and 0.070 moles of acetic acid.

0.075 moles acetic acid - 0.005 moles acetic acid <=> OH- = 0.070 moles remaining

Now, things are going to get a little complicated! We have determined the amount of acetic acid in solution and identified that species as the major contributor to pH. But acetic acid is a weak acid, so it only dissociates a tiny bit! Plus, the reaction between acetic acid and NaOH produced the acetate ion, which affects pH.

To tackle the third step, we will use an ICE table to help us organize our calculations and concepts. An ICE table stands for Initial (concentration), Change (in concentration), and Equilibrium (concentration). It looks like this:

Reaction
Initial
Change
Equilibrium

I often augment my ICE tables with an additional row on top where I write my reactants and products. It helps me keep track of what chemical species are involved. The goal of an ICE table is to figure out the equilibrium concentration of a species after it has undergone a change. In this case, the change is the dissociation of acetic acid. The species we're interested in is the hydrogen ion.

Step 3 can be broken into three parts:

3a. Filling in the ICE table

3b. Writing the equilibrium expression for the dissociation of the acid

3c. Plugging in the equilibrium concentrations determined in the ICE table into the equilibrium expression and solving for the concentration of hydrogen ions

The expression for the dissociation of acetic acid is HC2H3O2 <=> H+ + C2H3O2-. I put all this information into the top row of my ICE table:

Reaction HC2H3O2 H+ C2H3O2-
Initial
Change
Equilibrium

I know from Step 2 that I have 0.070 moles of acetic acid. I also know that the initial reaction between NaOH and acetic acid produced some of the acetate ion. Because NaOH and acetic acid react in a 1:1 ratio, the amount of acetate ion produced should be equal to the amount of OH that reacted, 0.0050 moles. ICE tables express amounts of chemicals in terms of concentration. To find concentration, I divide moles by total volume, 0.055 L.

Reaction HC2H3O2 H+ C2H3O2-
Initial (0.070 mol / 0.055 L) ~0 (0.0050 mol / 0.055 L)
Change
Equilibrium

Initially, we have no hydrogen ions, but not for long! The dissociation of acetic acid will produce hydrogen ions. The amount produced is contingent upon the dissociation constant and the presence of the acetate ion. The presence of the acetate ion will discourage acetic acid from dissociating as much.

To fill in the next row, we'll let the number of hydrogen ions produced from the dissociation of acetic acid equal x. Since dissociation happens in a 1:1 ratio, the number of hydrogen and acetate ions produced will both equal the number of acetic acid particles.

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