Determining The Ionization Constant Of A Weak Acid

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 (same as K_c), that relates the concentration 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 stoichiometric coefficients from the balance chemical reaction.  K_equil is a constant for all conditions 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.  The ionization of a weak acid or weak base is a typical example of an equilibrium process.  Consider the reversible ionization of the classic weak acid, acetic acid:

The reversible arrows tell us that the ionization reaction does not go to completion.  Some time after the acetic acid (CH₃CO₂H or HAc) is mixed with water, the reverse of the ionization process (combination) will begin to occur as the concentrations of the hydronium ion (H₃O⁺ or H ⁺) and acetate ion (CH₃CO₂^- or Ac ^-) increase.  At some time, the opposing reactions will be occurring at the same rate and the concentrations of all reactants and products will remain constant.  Once we have reached this state of dynamic equilibrium, we can define the equilibrium constant as:

In dilute aqueous solutions, the concentration of H₂O is essentially constant at 55.5 M.  Since it is a constant, we can rearrange the equilibrium equation and define an new equilibrium constant for the ionization of weak acids,  K_a:

To calculate the ionization constant, K_a, for a acetic acid, it is necessary to experimentally determine the equilibrium concentrations of H⁺, Ac^-, and HAc.

Method:

Based on the discussion above, if we want to determine the K_a for any weak acid (HA), we need to determine the equilibrium concentration of  H⁺, A^- , and HA.  The most straight forward of these is [H⁺ ], because we know that the pH = -log[H⁺].  So if we measure the pH of the equilibrium solution, we will not only know the concentration of the hydrogen ion, [H⁺], but the concentration of the weak acid's conjugate, [A^-], as well.  As an example, lets assume that the pH of this solution was 2.37.  This means that the value for both [H⁺] and [A^-] is:

However, we still need to determine the equilibrium concentration of HA.  Unfortunately, this is difficult to determine since most methods of analysis will change the concentration of the HA and cause the equilibrium to shift.  Since we can not directly determine the [HA] , we need to find the initial concentration of HA.  To do this we need to neutralize all of the HA present by titrating it with a strong base of known concentration.  As the H⁺ from the weak acid is neutralized by the strong base, the equilibrium will shift to the right generating more H⁺.  This process will continue as the strong base is added until all of the HA has been converted to H ⁺ and A^- (equivalence point).  This is no longer an equilibrium solution, it only contains A^-_(aq), Na ⁺_(aq), and H₂O_(l).  For example, if 23.6 mL of 0.321 M NaOH were required to neutralize 50.0 mL of the HA solution, then the initial concentration of HA would have been:

Now we can calculate the equilibrium concentration of HA, by subtracting the equilibrium [H⁺] concentration from the initial HA concentration:

Now we have all of the equilibrium concentrations necessary to calculate the K_a for our weak acid!

But wait!  What if we don't know the concentration of the strong base we used to titrate the weak acid?  No problem...we will standardize it!  Standardization is a process of comparing an unknown against a known or standard.  In this case, we will titrate a known quantity of standard acid with our unknown base.  Using our M₁ V₁ = M₂V₂ relationship, we will be able to determine the exact concentration of our base.

As with all standardization procedures, the real problem is picking an appropriate standard.  A primary standard is a substance that is readily available in a pure form (<0.02% impurities), it is stable, easy to dry, is not hydroscopic, and should have a fairly high equivalent weight to minimize the consequences of errors in mass determination.  We are fortunate that such a standard exists for our situation, the mono potassium salt of the organic di-acid, phthalic acid (KHC₈H₄O ₄, or KHP, mw = 204.223 g/mole). 

For example, if we dissolve 1.000 g of KHP in 50 mL of water and titrate this solution with 31.6 mL of our unknown base, what is the molarity of our base?  First we need to remember that at the equivalence point (where the indicator changes color), the moles of KHP equal the moles of NaOH:

Since 31.6 mL of our base solution contained 0.0049 moles, the molarity of our base is:

Now that we know the concentration of our base, we can titrate our unknown weak acid to determine its initial concentration, and use the pH meter to determine the equilibrium [H ⁺], and [A^-].  With these measurements, it is a simple matter to calculate the K_a for any weak acid.  [Pssst....there are also other ways of determining the K_a for a weak acid, but that is a story for another day.]

Procedure:

Preparing the Sodium Hydroxide Solution:

1. Add approximately 400 mL of distilled water to a clean 600 mL beaker.
2. Weigh out approximately 6.0 grams of sodium hydroxide pellets and add them to the 600 mL beaker.  NOTE:  Handle the sodium hydroxide pellets with care . Sodium Hydroxide is very hydroscopic and can cause burns if it comes in contact with your skin.  Be sure to use weighing boats or weighing paper to determine the mass and to deliver the sodium hydroxide pellets to the beaker.  When removing the sodium hydroxide pellets from the reagent container replace the cap of the container as quickly as possible.  Clean up any spilled sodium hydroxide pellets immediately.
3. Stir the solution until the pellets have completely dissolved.

1. Accurately weigh approximately 1.5 g (to 0.001 g) of KHP directly into a 150 mL Erlenmyer flask.
2. Add approximately 50 mL of distilled water to the flask and gently swirl until all of the KHP has dissolved.  Use distilled water to make sure all of the KHP has been rinsed off the sides of the flask.
3. Add 2 drops of phenolphthalein indicator to the flask.
4. Put a magnet stirring bar in the flask and set the stir plate to a moderate rate (avoid splashing).
5. Rinse and fill a 50 mL burette with your prepared sodium hydroxide solution.
6. Titrate the KHP sample with your sodium hydroxide solution until a faint pink color remains for 30 seconds.
7. Repeat Steps 1 - 6, for two additional KHP samples.
   
8. Calculate the concentration of your sodium hydroxide solution from each of the three trials.  They must agree to within 0.01 N.  If they do, then average them and use this as the normality of your sodium hydroxide for the rest of the experiment.  If they do not, repeat Steps 1 - 6 until you have three trials that do agree to within 0.01 N.
   

1. Pick one of the of the unknown weak acids and be sure to record its number.
2. Using the repipetter, transfer 20.00 mL of this acid to a clean 100 mL Erlenmyer flask.  Use distilled water to make sure all of the acid has been rinsed off the sides of the flask. 
3. Add 2 drops of phenolphthalein indicator to the flask.
4. Put a magnet stirring bar in the flask and set the stir plate to a moderate rate (avoid splashing).
5. Fill your 50 mL burette with your standardized sodium hydroxide solution.
6. Titrate the unknown weak acid with your standardized sodium hydroxide solution until a faint pink color remains for 30 seconds.
7. Repeat Steps 2 - 6, for two additional 20 mL aliquots of the same unknown weak acid and average your results.
8. Once you are satisfied with your results you may pour any remaining sodium hydroxide solution down the sink with copious water.

1. Add approximately 20 mL of the unknown acid to a clean 50 mL beaker.
2. Remove the pH electrode from its buffer solution and rinse it off with distilled water.
3. Submerge the pH electrode into the unknown acid and wait 10-30 seconds for the meter to stabilize.
4. Record the pH and the temperature of the unknown acid solution.

• From your titration data, calculate the molarity of your sodium hydroxide solution.
• How reproducible were your results for the molarity?
• From your titration of the weak acid, calculate the its initial concentration.
• How reproducible were your results for this concentration?
• Knowing the initial concentration of the weak acid and its pH, calculate the K_a for this acid.
• In the back of your textbook is a list of K_a values for several weak acids, from your analysis what is the identity of your unknown acid?
• The K_a values in the back of your textbook have been very accurately determined using a process similar to the one you have used.  One major difference is that all water used in the analysis is freshly boiled before use.  Why?
• Phenolphthalein was used as the indicator in this experiment.  What is the role of the indicator?  Why was phenolphthalein used and not some other indicator (see your textbook for other indicators)?

(Updated 8/23/07 by C.R. Snelling)