To begin a discussion about acid-base titrations, we must first recall that there are several definitions of acids and bases. For the purpose of this exercise, we will consider the Arrhenius definition of acids and bases, in which an acid is a proton (H+) donor and a base produces hydroxide (OH-) in solution. When an acid reacts with a base, the products of this reaction are water and a salt. Note that salt here does not only mean table salt (NaCl), but can refer to any ionic compound. For an example, consider the reaction of hydrochloric acid (HCl) with the base, potassium hydroxide (KOH):
HCl(aq) + NaOH(aq) -> KCl(aq) + H2O(l)
As this equation shows, the reaction between HCl and NaOH forms water and the salt, KCl. The concentration of an acid, specifically H3O+, or a base, specifically OH-, in a solution will cause that solution to have a specific pH. Recall that pH is a logarithmic scale that is based on the concentration of H3O+ in solution. The pH scale ranges from 0-14, with an acidic solution having a pH lower than 7 on the pH scale and a basic solution having a pH greater than 7 on the pH scale.
A titration is a controlled addition of one substance into another substance. In an acid-base titration, the experimenter will add a base of known concentration to an acid of unknown concentration (or vice-versa). The goal of the titration is usually to use the substance of known concentration to determine the concentration of the other substance. In order to run a titration, the following materials are needed:
• A burette filled with the base (or acid) of known concentration
• A beaker or flask containing a measured volume of acid (or base) of unknown concentration
• Several drops of a chemical indicator, which will be added into the flask with the acid
The titration is performed by slowly dripping the basic solution from the burette into a beaker or flask containing a measured amount of the acidic solution and several drops of a chemical indicator. An indicator is a chemical that will respond to changes in its environment. In the case of an acid-base titration, the experimenter will most often use an indicator that will change color when the endpoint of the titration is reached. In an acid-base titration the experimenter is trying to determine the equivalence point of the reaction, which is the point when the amount of base added was exactly the correct amount to have the moles of base completely react with the moles of acid. If the experimenter chooses the correct indicator, the endpoint of the reaction will be as close as possible to the actual equivalence point.
There are several different types of acid-base titrations. To understand the difference, we must briefly review what a strong acid/base vs. a weak acid/base is. A strong acid is an acid that is said to completely dissociate, meaning that every molecule of that acid in solution gives off an H+ in solution. A strong base is also characterized by complete dissociation. A weak acid or weak base by contrast, is an acid or base in which only some of the molecules in solution dissociate into their respective ions. We will consider two types of acid-base titrations, including the following topics, in this tutorial1:
1. Strong acid titrated with strong base
a. Finding the unknown concentration of the solution
b. Finding the pH of a solution during a titration
2. Weak acid titrated with strong base
a. Finding the number of mL required to reach the equivalence point of an acid
b. Finding the pH of a weak acid-strong base solution that has reached the equivalence point with no additional
When a strong acid is titrated with a strong base, we will expect the equivalence point to be at a pH of 7, as the strong base will neutralize the strong acid. The acidic starting solution will be of a low pH and, as the base is added, it will raise the pH. The titration curve of this system looks like the one shown in Figure 1.
Figure 1: Titration Curve of Acid-Strong Base
To understand calculations that can be done from strong acid-strong base systems, consider the following question.
Question: A 100 mL volume of HCl of unknown concentration is titrated with 0.20 M NaOH. It takes 200 mL of NaOH to reach the endpoint of the reaction.
a. What is the concentration of HCl?
b. What is the pH of the solution after 100 mL of NaOH has been added to the solution?
Part A Approach: The first step in tackling this problem would be to write and balance the chemical equation for the reaction taking place.
HCl + NaOH -> NaCl + H2O
Since there is a 1:1 stoichiometry in the chemical reaction, we know that for every one molecule of base that was needed to react with the acid, one molecule of acid was present in the solution to react with it. In order to figure out the concentration of acid; therefore, we must first figure out the moles of base that was added to the solution. This can be done by multiplying the concentration in Molarity (moles/L) by the volume of the base in liters, as shown below.
Because the stoichiometry of the reaction is 1:1, this means that the moles of HCl reacted is also 0.040 moles, as shown below:
Now that the number of moles of HCl are known, to figure out the initial concentration of HCl, we just divide the number of moles by the initial volume of HCl in L, which is 0.1 L.
Part A Solution: The concentration of HCl was 0.40 M.
Part B Approach: To determine the pH of the solution at any point in the titration, we need to know the [H3O+] of the solution at that time. For instance, the initial pH of the HCl solution before it is titrated is –log[H3O+] = -log(0.40 M) = 0.40. How can we say that the [H3O+] is 0.40 M? We must recall that when HCl dissociates, it does so according to the following reaction.
HCl + H2O(l) -> H3O+(aq) + Cl-(aq)
Because HCl dissociates in a 1:1 ratio and dissociates fully, we know that the concentration of HCl initially will equal the concentration of H3O+. We will expect the pH of the solution once the NaOH is added to be higher than this because adding base will raise the pH.
To determine the [HO+] after 100 mL NaOH has been added, we first need to determine how many moles of NaOH reacted. Using the stoichiometry of the reaction, we can convert this to moles of acid reacted, as seen below:
If 0.02 moles of HCl reacted, than this means that the remainder of the HCl is still unreacted. The initial number of moles of HCl was:
Subtracting the number of moles of HCl reacted from the initial number of moles yields 0.020 mol unreacted HCl.
Assuming the volume of the NaOH is additive to the volume of HCl initial, the new volume of the solution will be 200 mL after adding the NaOH. This makes the concentration of HCl:
Because HCl dissociates completely into H+ and Cl-, this is also the [H3O+] at this point in the titration. To find the pH:
Solution: The pH of the solution after 100 mL of NaOH was added was 1.
In a titration of a weak acid with a strong base, the titration curve changes slightly, as is seen in Figure 2. The equivalence point of the titration will now be at a pH higher than 7. This is because when the weak acid reacts, its anion is a base.
Figure 2: Titration Curve of Weak Acid with Strong Base
To understand what happens in a system where a weak acid is titrated with a strong base, we must recall that weak acids only dissociate partly in solution. They are in a dynamic equilibrium with their conjugate base. For the purposes of discussion, let’s consider the hypothetical weak acid, HA. HA reacts with water according to the following equation:
To determine the pH of a 0.1 M solution of HA, it is no longer possible to assume that the [H3O+] is 0.1 M because the acid does not dissociate completely. In order to determine the pH of this solution, the Ka of the acid must be given. To determine the [H3O+], the equilibrium expression for this acid would be written, and then the concentration of H3O+ would be solved for. Assuming the Ka for the hypothetical acid is 1 x10-10,
*Note: The –x can be dropped because the Ka is so small the change in concentration won’t have an effect. To understand where the “x” values and “0.1-x” comes from, review the concept of equilibrium reactions.
When adding a strong base to a weak acid, the strong base completely dissociates and will react completely with all available weak acid. To understand the different information that we can determine from these titrations, consider the following question.
Question: Assuming we have 100 mL of 0.100 M HA being titrated with 10.0 mL 0.100 M NaOH, what is the final pH of this solution?
Approach: First, we must find the moles of NaOH and the moles of HA available to react, keeping in mind that the HA will fully react with any NaOH available to form A-. Then, the moles of HA remaining after the reaction with NaOH has taken place must be determined.
HA + OH- -> A- + H2O
To find the molarities of each substance, divide by the total L in solution, 0.110 L:
At this point, we know how much of the acid and conjugate base we have in the solution, but we don’t know how much H3O+ is present in the solution. For a situation like this, we must use the Henderson-Hasselbalch Equation,
Solution: The pH of the resultant solution would be 9.05.
Other information that can be determined from a weak acid-strong base titration is addressed in the following questions:
a. How many mL of 0.3 M NaOH are required to reach the equivalence point when being titrated into 20 mL 0.1 M HA?
b. What is the pH of this solution after the equivalence point has been reached? The Ka of HA is 1 x 10-10.
Approach Part A: Recall that the equivalence point of an acid base reaction is the point where the moles of base have completely reacted with the moles of acid. To determine how many mL of NaOH we need, we first need to figure out how many moles of HA we have.
HA + OH- -> A- + H2O
Using the 1:1 stoichiometry of OH- to HA:
Using the molarity of OH-:
Solution: 6.67 mL of 0.3 M NaOH are needed to titrate 20 mL 0.1 M HA to the equivalence point.
Approach Part B: To figure out the pH, we must realize that the NaOH completely reacted with HA to leave 0.002 mol of A- in the solution. This A- will now react with the water in the solution to form HA according to the equation:
If the Ka of HA is 1x10-10, then the Kb for this expression is 1 x 10-4 because KaKb=Kw.
The concentration of A- initially (before the reaction proceeds to equilibrium) would be:
The Kb expression for this reaction would be:
Solving for x:
To find pOH:
Solving for pH:
Solution: The pH of the solution would be 11.4.
1 It should be noted that there are other possible titration systems, such as a weak base titrated with a strong acid, or a weak acid-weak base titration. The weak base-strong acid titration calculations are similar to the strong acid-weak base titrations. The acid and base are just switched and, therefore, the equivalence point will be at a pH below 7 for this system. Weak acid-weak base titration curves differ from those discussed this tutorial in that the equivalence points will not be as sharp. We did not discuss these in this tutorial because these are not commonly performed in the laboratory.
True or False: The equivalence point of a strong acid-strong base titration is always at a pH of 7.
What is the pH of a solution that has a [OH-] of 0.0500 M?
In a titration of 50.0 mL HBr of unknown concentration with 0.125 M LiOH, 75.0 mL of LiOH had to be added to the HBr solution to reach the endpoint. The concentration of the initial HBr solution is:
The pH of the above titration system after only 25 mL of LiOH has been added would be:
True or False: In a weak acid-strong base titration, the equivalence point is always below 7.
Consider a titration between 100 mL of 0.100 M acetic acid and 0.0600 M potassium hydroxide solution. How many mL of KOH needs to be added to this solution to reach the equivalence point?
True or False: At the moment when the equivalence point is reached, all of the initial acetic acid has now been converted into the conjugate base?
What is the concentration of [OH-] after the solution in questions 6 and 7 is allowed to establish equilibrium? Some Hints: This is when equilibrium is established after all of the OH- from the potassium hydroxide had been initially reacted. You will need to draw the reaction occurring and then have to look up the pKa or Ka of acetic acid and convert this to Kb.
What is the pH of the above solution at the equivalence point?
True or False: The equivalence point of a weak base-strong acid titration should be less than 7.