K a of a Weak Acid by pH Measurements Lab Report

Determination of Ka of a Weak Acid by pH Measurements

Introduction

In this experiment, we will use a weak acid to determine the equilibrium constant of the weak acid, HAn. The ionization equation of an aqueous solution of HAn is given below.

HAn (aq) + H2O (l) equilibrium An(aq) + H3O+ (aq) (1)

An is the conjugate base of the acid and H3O+ is the conjugate acid of H2O. H2O acts as the Bronsted-Lowry base and the proton from the weak acid HAn is donated to H2O molecule and it becomes a hydronium ion H3O+.

According to the Bronsted-Lowry (B-L) definition, an acid is defined as a proton (H+) donor and a B-L base is defined as a proton acceptor. In the following reaction, hydrochloric acid (HCl) donates a hydrogen ion to a water molecule, which acts as the B-L base. A hydronium ion (H3O+) and the conjugate base Cl are produced.

 

HCl(aq) + H2O(l) H3O+(aq) + Cl(aq) (2)

In the following reaction, HF donates a hydrogen ion to a water molecule generating fluoride and hydronium ions.

HF(aq) + H2O(l) H3O+(aq) + F(aq) (3)

The difference between the two acid-base reactions above is the strength of the acids. HCl is a strong acid, meaning that when HCl dissociates completely into chloride ions and hydronium ions, whereas HF, a weak acid, ionizes only partially into hydronium ions and fluoride ions (approximately 1-2%). The extent of ionization of a weak acid is indicated by the magnitude of its acid dissociation constant, Ka. Ka is the acid dissociation constant and for the ionization of HF is given by the following expression.

(4)

Ka is the concentration of products divided by the concentration of reactants. The stoichiometric coefficients become the exponents to which the concentrations are raised. Concentrations of species in the reaction are in mol/L. The equilibrium constant expression does not include concentration of water, as it is considered a pure liquid and its concentration is essentially constant. Ka is temperature dependent and is a unit less quantity. If the dissociation constant of an acid is greater than 1 x 10-2 the acid is considered a strong acid and if the Ka < 1 x 10-3 the acid is considered to be a weak acid. As Ka increases, the strength of the acid also increases.

The acid dissociation constants for some weak acids @ 25C are listed in Table 1.

Table 1: Acid Dissociation Constants @ 25C

Acid

Ka

Acetic acid, CH3CO2H

1.7 x 10-5

Boric acid, H3BO3

5.8 x 10-10

Nitrous acid, HNO2

4.5 x 10-4

Hypochlorous acid, HOCl

3.5 x 10-8

Hydrocyanic acid, HCN

4.0 x 10-10

Hydrofluoric acid, HF

7.2 x 10-4

Potassium Hydrogen Phthalate (KHP)

4.0 x 10-6

In today’s lab you will determine the equilibrium constant of a weak acid HAn by measuring the pH values of several solutions. The equation below describes the dissociation of a generic weak acid HAn in water to produce the hydronium ion and An.

HAn(aq) + H2O(l) H3O+(aq) + An(aq) (1)

The Ka expression for the reaction above can be seen in Equation 5.

(5)

We can calculate the Ka for HAn if we know the equilibrium concentrations of the dissociated and undissociated species in Equation 5. We will determine the H3O+ concentration by pH measurements using a pH meter.

pH = -log [H3O+] (6a)

Rearranging equation 6a gives us:

[H3O+] = 10-pH (6b)

[An]e = [H3O+]e. If we know the original concentration of the acid, HAn, we can calculate the undissociated [HAn]e. Knowing [H3O+], [An], and [HAn] at equilibrium, we can calculate the Ka using Equation 5.

In this experiment, four solutions are prepared by varying the [OH] and keeping the [HAn]i fixed. The solutions contain H3O+, An, and HAn and have partially neutralized unknown weak acid. Due to partial neutralization of HAn, [H3O+] and [An] are no longer equal; instead, a buffer solution is produced with appreciable concentrations of HAn and An. Hydroxide ion is a strong base and the reaction of OH ions with HAn essentially goes to completion and the number of moles of An ions formed is equal to the number of moles of NaOH used. The amount of acid neutralized and conjugate base produced are calculated from the initial amount of the acid and the amount of added base. pH measurements give the [H3O+]e. Essentially an ICE table is prepared, where I lists the initial number of moles of acid and NaOH added, C lists the change in moles of acid as NaOH neutralizes the acid and E lists the equilibrium moles of acid, and conjugate base. The following equation helps determine the amount of HAn consumed and An- formed.

HAn (aq) + OH(aq) H2O (l) + An(aq) (7)

[HAn]e and [An]e are calculated from the equilibrium number of moles and total volume of the solutions.

Steps required to calculate [HAn] e and [An] e

  1. Calculate the initial number of moles of acid and number of moles of OH from molarity and volumes used.
  2. Calculate the number of moles of HAn left after hydroxide is added by subtracting moles OH from moles HAn.

Equilibrium moles HAn = (initial moles of HAn) – (initial moles of OH)

  1. The number of moles of the conjugate base An is the same as the number of moles of OH added.
  2. Calculate the [HAn]e and [An]e
  3. Use equation 6b to calculate [H3O+]e from the measured pH values of the four solutions at varying amounts of NaOH.
  4. Use equation 5 to determine Ka

Supplies:

  • ~0.5 M NaOH solution
  • Phenolphthalein indicator soln.
  • Distilled water
  • Burette (2)
  • Burette clamp
  • Burette funnel (2)
  • Ring stand
  • 50 mL Graduated cylinder
  • 400 ml beaker
  • 100 ml Beaker
  • 250 mL beaker
  • 30 mL or 50 mL beaker
  • 250 mL volumetric flask.
  • Vernier LabQuest
  • pH probe
  • Utility clamp
  • pH 7 Buffer
  • pH 4 Buffer

Procedure:

  1. Calibrate the pH meter with the instructions provided at your workstation, ask your instructor for help with this part if you have questions.
  2. Obtain ~100 mL of a ~1.00 M unknown weak acid solution. Record the unknown code of your unknown and the exact molarity of the solution on the data sheet.
  3. Measure the pH of the undiluted unknown solution.
  4. Condition a burette with ~ 10 mL of your unknown acid, transfer the washes into a beaker labeled “unknown acid and sodium hydroxide waste”. Fill the 50 mL burette with the weak acid solution and label as unknown acid.
  5. Obtain ~100 mL of ~0.500 M NaOH solution. Record the exact molarity on your datasheet.
  6. Condition a second burette with ~ 10 mL of the ~0.500 M NaOH solution, transfer the washes into a beaker labeled “unknown acid and sodium hydroxide waste”. Fill the conditioned 50 mL burette with the NaOH solution and label as ~0.500 M NaOH.
  7. To prepare solution 1
    1. Deliver 16.00 mL of the unknown acid solution from the burette into to a clean 100 mL volumetric flask. Record the initial reading and final readings of the burette to the nearest 0.01 mL.
    2. Deliver 5.00 mL of the ~0.500 M NaOH solution from the second burette to the acid solution in the 100 mL volumetric flask. Record the initial and final burette readings to the nearest 0.01 mL.
    3. Add DI water to this flask up to the base of the neck of the flask, stopper it tightly, hold the stopper with your finger and invert the flask 10 times to thoroughly mix the solution.
    4. Next, add DI water up to the graduation mark in the neck of the flask, stopper and thoroughly mix the solution as in step c.
  8. Prepare Solutions 2, 3 & 4 as per the volumes specified in the table below, following steps a-d.
  9. Pour about 50 mL of solution 1 into a clean 100 mL beaker and measure the pH of the solution. Record the pH on your data sheet.
  10. Discard the solution in the beaker into the “Discarded Beaker”, rinse the electrode and beaker with Soln. 2 and record the pH of the solution as in step above.
  11. Measure the pH of each solution and record the pH on the datasheet.
  12. At the end of the experiment, rinse the electrode with DI water and leave the electrode immersed in DI water. Switch the instrument off.
  13. Discard the solutions in the “Discarded Beaker” into the sink and run copious amounts of water.

Table 2:

Solution #

Volume ~1.0 M

Weak Acid, mL

Volume NaOH, mL

1

16.00

5.00

2

16.00

10.00

3

16.00

15.00

4

16.00

20.00

NAME: _____________________________ Date: _______________

Partner: _______________________________

Data sheet

Unknown Code:

Molarity of unknown acid

pH of undiluted unknown acid ___________________

Molarity of NaOH

 

Solution 1

Solution 2

Solution 3

Solution 4

Unknown Acid Solution

Final burette reading, mL

    

Initial burette reading, mL

    

Volume of unknown acid, mL

    
 

NaOH Solution

Final burette reading, mL

    

Initial burette reading, mL

    

Volume of NaOH solution, mL

    

Total Volume of Solution, mL

100.00

100.00

100.00

100.00

pH of Partially Neutralized unknown acid solution

pH

    

Calculating Ka of your unknown acid

 

Sample 1

Sample 2

Sample 3

Sample 4

Initial number of moles of HAn (before mixing)

Show calculations

Initial number of moles of OH (before mixing)

Show calculations for two flasks

HAn(aq)

    

OH(aq)

    

Number of moles of HAn(aq) and An(aq)at equilibrium after mixing

Show calculations:

 

HAn(e)

    

An(e)

    

Equilibrium concentrations, mol/L

Show example calculation for sample 1 Here:

HAn(e)

    

An(e)

    

H3O+(e)

    

Show complete calculations for Ka for all the solutions.

Ka

    

Average Ka _____________________

Average pKa _____________________

Identify your unknown weak acid from Table 1 _________________________

Compare the experimental value with the true value.

Calculate % error

 

NAME: ____________________________ Date: ________________

Post Laboratory Questions

  1. Why do the solutions that you prepared act as buffers?
  2. Show calculation to calculate Ka and pKa for data for one of the solutions using Henderson-Hasselbalch equation.
  3. The accepted dissociation constant for your unknown is 1.8 x 10-5. Calculate the percent error for the average Ka of the unknown acid.
  4. Calculate the percent error for the dissociation constant determined from each individual solution
  5. Describe any sources of error for this experiment.

NAME: ___________________________ Date: ________________

Partner: __________________________

Pre-Lab Questions

  1. Complete the calculations below based on the following student data. A student following the procedure similar to that in this lab prepared four solutions by adding 12.25, 23.00, 25.50, and 34.50 mL of 8.25 x 10-2 M NaOH solution to 50.00 mL of a 0.152 M solution of weak acid. The solutions were labeled 1, 2, 3, and 4 respectively. Each of the solutions was diluted to a total volume of 250 mL with DI water. The pH readings of these solutions were: (1) 6.64 (2) 6.98 (3) 7.04 (4) 7.23
 

Sample 1

Sample 2

Sample 3

Sample 4

Initial number of moles of HAn (before mixing)

Show calculations for 2 samples:

Moles of OH(before mixing)

HAn(i)

    

OH(i)

    

Number of moles of HAn at equilibrium

Show calculations for 2 samples:

Number of moles of An- at equilibrium

HAn(e)

    

An(e)

    

Equilibrium concentrations, mol/L

[HAn]e

[An]e

Concentration of H+ from pH values

[HAn]e

    

[An]e

    

[H3O+]e

    

Ka

    

Average Ka _____________________

Unknown weak acid from Table 1: _____________________

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