Determining an Equilibrium Constant

At this point in your chemistry career, you should be able to predict the products of chemical reactions, the states of the products, and whether the reaction will occur spontaneously at any given set of conditions.  You should even be able to determine the rate at which the reactants are consumed and predict the amount of time it would take to produce a given amount of product.  While this is extremely useful information, it only applies to a limited set of reactions, namely those that occur in one direction only:

Here the reactants A and B collide with sufficient energy and the proper geometry to form the products C and D.  What about a reaction in which C and D now become reactants in the opposite direction and form the products A and B?

Initially, when A and B were mixed, the reaction proceeds in the forward direction to produce C and D.  However, as time progresses, the concentration of C and D increases causing an increase in the rate of the reverse reaction.  Concurrent with this increased rate of the reverse reaction is a reduction of the forward rate due to the decrease in the concentration of A and B.  At some point, the rate of the forward and reverse reactions will become the same and we will reach a state of dynamic equilibrium:

This state of dynamic equilibrium does not mean that the forward and reverse reactions have stopped.  Molecules of A and B are still reacting to form C and D and molecules of C and D are reacting to form A and B.  However, since the rate of the forward and reverse reactions are the same, it will appear that nothing is happening.  As such, all quantifiable physical and chemical properties such has pH, color, and concentration will remain constant.

For a general equilibrium equation in which 'a' moles of A react with 'b' moles of B to produce 'c' moles of C and 'd' moles of D,

We can specify an equilibrium constant, K_equil, that relates the concentrations of all product and reactant species,

where [A], [B], [C], and [D] are the molar concentration of all species present at equilibrium.  The exponents, a, b, c, and d represent the stoichiometry coefficients from the balance chemical reaction.  K_equil is really the ratio of the rate of the reverse reaction divided by the rate of the forward reaction and so is a dimension less constant at a given temperature (normally 25°C unless otherwise noted).

Purpose:

The purpose of this experiment is to familiarize you with the concept of an equilibrium reaction.  This will be achieved by determining the equilibrium constant for a reaction at room temperature.  Specifically, we will be studying the acid catalyzed (HCl) hydrolysis of an ester (ethyl acetate, EtAc), to form an alcohol (ethanol, EtOH) and an acid (acetic acid, HAc):

It is important to note, that this hydrolysis reaction will occur spontaneously at room temperature.  The addition of acid does not affect the equilibrium, just the amount of time it takes the reaction to reach equilibrium.

To determine the equilibrium constant we must first establish the stoichiometry for the reaction.  In this case, one mole of ethyl acetate reacts with one mole of water to generate one mole of ethanol and one mole of acetic acid.

In addition to the stoichiometry, we must know the concentration of all reacting species at equilibrium.  In practice it is often difficult to determine the equilibrium concentration of all these species.  However, we can calculate the equilibrium constant by determining the concentration of a single species at equilibrium, if we know the initial concentration of all species.  We do not have to be concerned about the concentration of the hydrochloric acid since it only serves as a catalyst.  For our specific reaction, the equilibrium constant will equal:

Since we will know the initial concentration of each component, we only need to determine the equilibrium concentration of one component to calculate the equilibrium constant.  Although we have several chemical species to choose from, we will monitor the acetic acid concentration since it can be very accurately determined via a simple titration with standardized base.

Method:

The acid catalyzed hydrolysis of ethyl acetate takes several days to reach equilibrium.  Therefore, the solutions you will need to carry out this experiment have already have been prepared for you.  The following table shows the composition of a 10.00 mL aliquot of each solution:  

In the above discussion, we decided to monitor the concentration of the HAc to determine the equilibrium constant.  However, the presence of the strong acid HCl complicates our task.  A simple titration with sodium hydroxide will neutralize all the acids that are present and we will not be able to differentiate the amount of base needed to neutralize the HCl versus the amount that was needed to neutralize the HAc.  This is a common problem in chemistry and is solved by titrating a blank, which only contains the HCl (Solution 1).  Since it contains a known amount of HCl and water, a simple titration will determine the amount of base needed to neutralize the HCl contained in the other solutions.  This amount of HCl will be constant in the other solutions because the HCl is a catalyst that is not consumed by the reaction.  Now that we know the amount of base needed to account for the HCl, any additional base used in the titration of Solution #2, Solution #3, and Solution #4, must represent the amount of HAc present.

Lets work through an example (NOTE:  this is an EXAMPLE, your numbers WILL be DIFFERENT!).  Suppose a student titrates Solution #1 and Solution #3  from the table above with 1.000 M NaOH.  Solution #1 requires 28.90 mL, and Solution #3 requires 42.16 mL.  What is the equilibrium constant for this reaction?

First, we must determine the number of moles of HCl in the blank (Solution #1):

This means that both Solution #1 and Solution #3 contain 0.02890 moles of HCl.

The amount of total acid in Solution #3 is calculated using the same procedure:

However, the blank (Solution #1) showed us that 0.02890 moles of this total is HCl.  Therefore,  the remainder represents the HAc present:

We have now acquired all of the experimental data we need to calculate the equilibrium constant.  To complete our task we must calculate the initial concentration (or amounts) of the reactants (we don't need to worry about the products, because none have been formed at the start of the reaction).  Recall that we used 4.00 mL of EtAc in the reaction.  Using its density (0.893 g/mL) and its molecular weight (88.0 g/mol), we can calculate the number of moles of EtAc:

The other reactant is H₂O.  We added 1.00 mL of H₂O to the reaction, but there is also H₂O from the HCl solution and we must account for all sources of H₂O. To determine the amount of H₂O in the HCl solution we must first determine how much HCl is present:

Since we are given that the density of the HCl solution is 1.11 g/mL, we can calculate the weight of the HCl solution:

Therefore, the amount of H₂O in 5.00 mL of the HCl solution is the total weight of the solution, minus the weight of the HCl:

Adding this to the 1.00 g of H₂O that was in Solution #3 (assuming the density of water at room temperature is 1.00 g/mL), we obtain a total of 5.495 g of H₂O, which can be converted to moles of H₂O:

The table below summarizes all of the information we have generated from these two solutions:  

This table represents the amounts (moles) of the various species in this equilibrium, however, to calculate the equilibrium constant, we need to know the molar concentration of each compound.  This is easily accomplished by remembering that each of these solutions had a total volume of 10 mL (0.01L).  We simply divide the moles by the volume to determine the molarity:  

Now we can calculate the equilibrium constant for this reaction as:

Procedure:

Titration of Solution #1 (Blank):

1. Clean and dry three 125 mL Erlenmeyer flasks.
2. Using a pipet, add 10.00 mL of Solution #1, and 3 drops of phenolphthalein indicator to a flask  Now add approximately 20 mL of water to increase the volume.  You may be concerned that the extra 20 mL of water that you just added will shift the equilibrium according to LeChatelier's principle.  However, remember that the equilibrium for this reaction takes several days to be established.  This means that on the time scale of your titration, the equilibrium will not have time to shift so that extra 20 mL of water will not effect your results.
3. Put a magnet stirring bar in the flask and set the stir plate to a moderate rate.
4. Titrate the sample with standardized sodium hydroxide to the first faint pink color.
5. Repeat Steps 2 - 4 two more times and average your results.  If your three results do not agree within 0.2 mL, you will have to run additional titrations.

1. Clean and dry three 125 mL Erlenmeyer flasks.
2. Using a pipet, add 10.00 mL of a Solution #2, and 3 drops of phenolphthalein indicator to a flask  Now add approximately 20 mL of water to increase the volume.
3. Put a magnet stirring bar in one of the flask and set the stir plate to a moderate rate.
4. Titrate the sample with standardized sodium hydroxide to the first faint pink color.
5. Repeat Steps 2 - 4 two more times and average your results.  If your three results do not agree within 0.2 mL, you will have to run additional titrations.
6. Repeat Steps 1 - 5 for Solution #3, and Solution #4.

Results/Calculations:

• Using your titration data and your calculated concentrations of EtAc, EtOH, HAc, and H₂O, calculate the equilibrium constant, K_equil.
• How reproducible were your titrations from each Solution?
• Does the equilibrium constant differ between Solution #2, Solution #3, and Solution #4?  Why?
• In the analysis, we added 20 mL of  water to a sample before titrating.  Does this have an impact on the equilibrium?  What does LeChatelier's principle suggest?
• During the titration, we neutralized the acetic acid.  This is one of the products of the reaction.  How does this affect the equilibrium?
• Suggest at least two other chemical or physical properties that we could have taken advantage of to monitor the course of this equilibrium reaction.

(Updated 6/5/07 by C.R. Snelling)