9 Acid-Base Titration Curves

Yu Kay Law

Purpose

To compare and contrast acid-base titration curves for different acid-base titrations.

Learning Outcomes

  • Identify the features of different types of acid-base titration curves.
  • Determine the concentration of analyte present, as well as the acid ionization constant K_a and base ionization constant K_b.
  • Select appropriate indicators for use in a titration.

Textbook Reference

Tro, Chemistry: Structure and Properties, Ch. 17.4

The write-up below covers merely the very basics of what the lab entails; more details are covered in your textbook which you are expected to refer to.

Introduction

A buret (a long tube with a tap at the bottom) with an Erlenmeyer flask underneath.
An illustration
of the setup for
a titration.

Acid-base titrations involve the dropwise addition of one solution-phase reagent (using a buret) into a carefully measured amount of another reagent (in an Erlenmeyer flask). There are three main classes of titrations that can be studied:

  • Strong acid-strong base
  • Weak acid-strong base
  • Weak base-strong acid

In this experiment, you will examine the titration curves for each of these types of titrations.  In each case, we are studying an acid-base neutralization reaction.

Equivalence Points

One particularly important point in a titration curve is the equivalence point. The equivalence point is the point in the acid-base titration at which each molecule of HA is neutralized by one OH– ion, causing the acid to be converted to its conjugate base.  Or, if a base is the analyte, the point where each molecule of the base A– is neutralized by one H3O+ ion, causing the base to be converted to its conjugate acid.

Types of Titration Curves and its Features

Strong Acid-Strong Base Titrations

When titrating a strong acid, such as hydrochloric acid with sodium hydroxide, you are reacting the HCl directly with NaOH

(1)   \begin{equation*} \textrm{HCl}(aq) + \textrm{NaOH}(aq) \to \textrm{H}_2\textrm{O}(l) + \textrm{NaCl} \end{equation*}

The titration curve is shown below.  In this case, there is a very sharp transition in pH at the equivalence point. Furthermore, as the salt formed in the neutralization reaction is neutral, the solution at the equivalence point is neutral.

Two graphs are shown. The first graph on the left is titled “Titration of Weak Acid.” The horizontal axis is labeled “Volume of 0.100 M N a O H added (m L).” Markings and vertical gridlines are provided every 5 units from 0 to 50. The vertical axis is labeled “p H” and is marked every 1 unis beginning at 0 extending to 14. A red curve is drawn on the graph which increases steadily from the point (0, 3) up to about (20, 5.5) after which the graph has a vertical section from (25, 7) up to (25, 11). The graph then levels off to a value of about 12.5 from about 40 m L up to 50 m L. The midpoint of the vertical segment of the curve is labeled “Equivalence point p H, 8.72.” The second graph on the right is titled “Titration of Strong Acid.” The horizontal axis is labeled “Volume of 0.100 M N a O H added (m L).” Markings and vertical gridlines are provided every 5 units from 0 to 50. The vertical axis is labeled “p H” and is marked every 1 units beginning at 0 extending to 14. A red curve is drawn on the graph which increases gradually from the point (0, 1) up to about (22.5, 2.2) after which the graph has a vertical section from (25, 4) up to nearly (25, 11). The graph then levels off to a value of about 12.4 from about 40 m L up to 50 m L. The midpoint of the vertical segment of the curve is labeled “Equivalence point p H, 7.00.”
Two types of acid-base titration curves.  Source: OpenStax Chemistry: Atoms First 2e.

Weak Acid-Strong Base Titrations

An example of such a titration would be acetic acid (CH3COOH) with sodium hydroxide. In this case, the reaction is

(2)   \begin{equation*} \ce{CH3COOH} (aq) + \ce{NaOH} (aq) \to \ce{CH3COONa}(aq) + \ce{H2O}(l) \end{equation*}

or, for the net ionic equation,

(3)   \begin{equation*} \ce{CH3COOH}(aq) + \ce{OH-} (aq) \to \ce{CH3COO-}(aq) + \ce{H2O}(l) \end{equation*}

In this case, there is one important aspect to note. As the neutralization takes place, there will be appreciable amounts of both CH3COOH, a weak acid, and CH3COO–, its conjugate base, present in the solution.  This mixture is a buffer solution.  As a result, a gradual transition in the pH is observed in this solution as shown in the figure above, as opposed to the very sharp transition observed for strong acid-strong base solutions.

At the equivalence point, all of the CH3COOH is converted to CH3COO– , a weak base. Therefore, the solution is basic at the equivalence point.

Remember that at the equivalence point, an acid is converted to its conjugate base.  Furthermore, the conjugate base of a weak acid is a weak base (not a strong base).

Beyond this point, as additional OH– is added, a sharp transition in the pH curve is observed.

Importance of the Half-Equivalence Point: Finding K_a

To identify the half-equivalence point of a solution, you start by identifying the equivalence point of the titration curve and then halving the volume.  Then, you find the point on the curve where this volume of the titrant was added.

Example

Consider the weak acid-strong base titration curve shown above.  The equivalence point is at 25 mL and hence the volume of NaOH added at the half-equivalence point is \frac{1}{2} \times 25\textrm{ mL} = 12.5 \textrm{ mL}.  At this point, the pH is 4.9.

As mentioned before, in this region the mixture behaves as a buffer solution, where we can use the Henderson-Hasselbalch equation

(4)   \begin{equation*} \mbox{pH} = \mbox{p}K_a + \log_{10} \left(\frac{[\ce{A-}]}{[\ce{HA}]}\right) \end{equation*}

At the half-equivalence point, as [\ce{A-}]=[\ce{HA}],

(5)   \begin{equation*} \mbox{pH} = \mbox{p}K_a \end{equation*}

from which you can find K_a.

Example

From above, we saw that the pKa of the analyte in the weak acid-strong base titration curve above is 4.9.  Therefore,

(6)   \begin{equation*} K_a = 10^{-\textrm{p}K_a} = 10^{-4.9} = 1 \times 10^{-5} \end{equation*}

Weak Base-Strong Acid Titration Curves

A plot of pH vs volume of titrant added. The curve goes gradually downwards at first, and then drops suddenly.
A weak base-strong acid titration curve.

This type of titration would yield a curve with decreasing pH, given that you’re neutralizing base with a strong acid:

(7)   \begin{equation*} \ce{A-} (aq) + \ce{H3O+}(aq) \to \ce{H2O}(l) + \ce{HA}(aq) \end{equation*}

where HA is the conjugate acid of the original weak base A– and is therefore a weak base.  A few features can be found … the flip side of the weak acid-strong base titration curve:

  • At the equivalence point, we have a solution of HA, the weak acid.  As a result, you would have an acidic solution (pH < 7) at the equivalence point.
  • Before you hit the equivalence point, you would have a mixture of HA and A–.  Similarly, you would have a buffer solution in that region, leading to the gradual decrease in pH there.

Similarly, therefore, we can use the half-equivalence point to find the Kb of the weak base.  In this case, the pH is the pKa of the conjugate acid of the weak base.

Example

Examining the curve above, the pH at the half-equivalence point (as defined for weak acid-strong base titration curves) is approximately 7.5.  Given this, \textrm{p}K_a = 10^{-7.5} = 3\times 10^{-8} for the conjugate acid.  Therefore, we can relate this to the K_b of the weak base as follows:

    \begin{align*} K_a \times K_b &= K_W \\ K_b &= \frac{K_W}{K_a} \\ &= \frac{1.0\times 10^{-14}}{3\times 10^{-8}} \\ &= 3\times 10^{-7} \end{align*}

 

Experimental Procedure

  • Before doing this experiment, please review the section on Using ChemCollective Virtual Labs.
  • For your lab notebook, you must:
    • Record, in handwriting on your regular lab notebook, your purpose, procedure, and results similar to a face to face experiment.
    • Include a set of screenshots as directed below.
  • If you think that a change to the procedure would help, then feel free to do so.  Just make sure it is documented in your lab notebook.  Feel free to consult with your lab instructor if you’re unsure, but remember there are no safety implications.
  • A separate report form will be provided in MS Word format.

Strong Acid-Strong Base Titration

You will use the ChemCollective Strong Acid and Base Problems virtual lab to perform this virtual titration.  For further details on how to do this on the electronic platform, please see: Using ChemCollective Virtual Labs.

  1. Obtain a buret (from Glassware > Other) and the 0.1 M sodium hydroxide.
  2. Fill the buret with the 0.1 M sodium hydroxide to about the 10.00mL mark. Read and record the volume reading on the buret, paying attention to the (a) direction that the numbers are graduated and (b) the number of significant figures.Data
  3. Obtain a 0.1 M hydrochloric acid solution, a 10 mL volumetric pipet, and a 250 mL Erlenmeyer flask.
  4. Withdraw 10.00 mL of the hydrochloric acid solution into the pipet.  When this is done, obtain a screenshot of the interface.
  5. Move the pipet away from the flask of 0.1 M hydrochloric acid solution and put it on top of the empty 250 mL Erlenmeyer flask.  Dispense the hydrochloric acid from the pipet into the Erlenmeyer flask.
  6. Select the Erlenmeyer flask and record the pH of the solution.
  7. Put the buret on top of the Erlenmeyer flask, and dispense approximately 0.5 mL of the sodium hydroxide solution into the Erlenmeyer flask.  Record the volume in the buret.  Record the pH of the solution in the Erlenmeyer flask.
  8. Repeat step 7 until the pH remains relatively constant.

A video demonstration of how to do this experiment (somewhat badly) is shown below:


Data Analysis

The use of Excel or another spreadsheet program to perform data analysis is recommended.  For plots, it is important that you have gridlines.

 

To plot the titration curve, first find the total volume of NaOH added at each step of the titration above.  Then, plot the pH as a function of the volume of sodium hydroxide added.  It’s not critical how the curve is fitted; however, it is important that you have a rather dense set of gridlines.  How this can be done with Excel is demonstrated below:

Weak Acid-Strong Base Titration

You will perform an unknown weak acid-strong base titration using the ChemCollective Unknown Acid and Base Problem simulation.

Complete the experiment following the same procedure as for the strong acid-strong base titration, except you need to use the unknown acid instead of hydrochloric acid.

Take a screenshot of your titration setup at some point during the titration procedure (i.e. with the buret above the Erlenmeyer flask).

Make a plot of the acid-base titration curve as above.

You will use the same simulation setup for the final part.  You are urged to either refresh the screen or clear the workbench before proceeding.

Finding the Molarity of the Unknown Solution

To find the molarity of the unknown solution, remember that at the equivalence point the number of moles of acid initially present equals the number of moles of base added for a monoprotic acid.  Therefore, you can perform a stoichiometry problem by using the definition of molarity, similar to what is described in Tro, Chemistry – Structures and Properties, 2nd Ed, Ch. 8.7.  An example of how this is done is explained in the following video:

https://iu.mediaspace.kaltura.com/id/1_7pl9o19p?width=400&height=285&playerId=26683571

pH at the Equivalence Point

Remember that at the equivalence point, all of the acid would have converted to its conjugate base.  We therefore have a solution of the conjugate base of the weak acid.  This is therefore a weak base problem.

  1. Find the concentration of the weak base solution at the equivalence point by performing a dilution problem using M_1V_1 = M_2 V_2, where
    • M1 is the molarity of the original unknown solution, found as described above.
    • V1 is the volume of the unknown solution in the Erlenmeyer flask (analyte).
    • M2 is the molarity of the diluted solution
    • V2 is the volume of the mixture in the Erlenmeyer flask including all components, which we will approximate to be the sum of the volumes of acid and base added.
  2. Given the value of Ka, find the value of Kb using the formula K_a \times K_b = K_W.
  3. This then becomes a weak base pH calculation similar to that calculated in the regular course.  As a refresher, the following video outlines how to solve this type of problem:

https://iu.mediaspace.kaltura.com/id/1_ldt19iip?width=400&height=285&playerId=26683571

Weak Base-Strong Acid Titration

Using the ChemCollective Unknown Acid and Base Problem simulation that you used for the previous part, repeat the procedure but use the unknown base as the analyte and the 0.1 M HCl as the titrant instead.  Similar approaches to find the pH at the equivalence point to the above can be found, except that this would now be an acidic salt.

License

Virtual Chemistry Experiments Copyright © by Yu Kay Law. All Rights Reserved.

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