DETERMINATION OF THE EQUILIBRIUM CONSTANT, Ka, OF A WEAK ACID

CHEM 1412 Lab – 7 Dr. Pahlavan

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DETERMINATION OF THE EQUILIBRIUM CONSTANT,

Ka, OF A WEAK ACID

EQUIPMENT and CHEMICALS

Beakers (50 mL, 100 mL, 400 mL) Graduated cylinder (25 mL, 50 mL) Buret (50 mL)

pH meter Buret clamp Ring stand Stirring rod

Plastic funnel 0.10 M NaOH Unknown acid Phenolphthalein

Purpose a) Determine the equilibrium constant of a weak acid

b) Using acid/base titration method to identify the unknown solid

INTRODUCTION In this lab you will investigate the qualitative and quantitative aspects of acid-base reactions, also known as

neutralization reactions. Using known concentrations of acid OR base in a neutralization reaction allows for

later determination of unknown molarities and/or volumes of the counterpart base or acid in the reaction.

Experimentally, this technique involves the process of titration (a titer refers to a known or fixed volume).

Thus we will be adding a fixed volume and concentration of base to an acid to find the acid concentration.

Generally, for titration, the operative definition of an acid follows the Brønsted-Lowry definition:

An acid is a proton donor (H+) and a base is a proton acceptor (-OH or other base). After reaction of the acid

and base, the reacting acid produces a base (its conjugate base). The base accepts the H+ thereby becoming an

acid (the conjugate acid for that base).

Therefore, every acid-base neutralization reaction involves an acid-base pair. Even diluting an acid with water

is an acid-base reaction, shown at the right.


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Neutralization reactions take the general form below. Generally stated, an acid plus base yields a salt and

water. In this case, the combination of H+ from the acid and OH- from the base forms the water. The counter

ion (cation) from the base serves as the ion pair for the resulting conjugate acid.

There are several factors which describe acids and bases. The simplest way is to classify each as strong or

weak, and related to the number of H+ or -OH each can accept (e.g. mono-, di- or triprotic acid). An acid that is

effectively 100% dissociated in water (all H+), it is considered a strong acid. Anything less than 100% can

be considered a weaker acid. A monoprotic acid dissociates into one mol of H+ per mol of acid molecules. A

diprotic acid produces two moles of H+, triprotic three moles of H+, etc. The profiles of each type of acid can

be investigated using titration.

Dissociation of Weak Acids

The relative strength of acids can be found by comparing their pKa values, obtained through experimental

measurement. The pKa is related to the Ka, defined as the equilibrium constant for acids (generally called the

acid dissociation constant).

The pKa can be found experimentally from the titration data using the Henderson-Hasselbalch equation below.

Graphically, an acid's pKa value is equal to the pH at the midpoint (1/2 equilibrium point) of the titration. The

mathematical justification for this fact is below:

Notice at this point in the reaction, [A-] = [HA], thus log10 = 0. Also recall that the -log10 [H+] = pH.

Therefore, at the midpoint (1/2 equilibrium point) of a titration, the pH = pKa.

Examine the following titration data generated from two kinds of acid. Data in this form is referred to as a

titration curve, each of which has distinguishing characteristics.


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In this experiment you will be using a pH meter. This small hand held device is an inexpensive instrument

commonly used in the chemistry laboratory to accurately measure the pH of a solution. While a complete

understanding of how a pH meter functions and the chemistry which takes place during a pH measurement are

beyond the scope of this course, a brief discussion regarding the operation of the pH is in order.

The pH consists of a liquid crystal display, calibrated in pH units, and a combination electrode. The

combination electrode is immersed in a solution and the pH of the solution is displayed in the liquid crystal

window. The combination electrode consists of a reference electrode and a sensing electrode. The reference

electrode has a known potential which is constant and independent of the solution in which it is immersed. The

sensing electrode is sensitive to the [H3O+] in the solution. The potential of this electrode depends upon the

concentration of H3O+ in the solution. When the combination electrode is immersed into a solution, a potential

difference develops between the reference and sensing electrodes. The potential difference is directly dependent

on the [H3O+] in the solution. This potential difference is measured by the pH and displayed by the meter as a

pH value.


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To be accurate, the pH must be calibrated with a solution of known pH. This is accomplished using a carefully

prepared buffer solution of known pH. Such solutions can be prepared in the laboratory or purchased from a

chemical supply company. When the combination electrode is immersed in the buffer solution, the meter will

display a measured pH. If the measured pH is not equal to the known pH of the buffer, then the displayed

reading must be adjusted by turning the calibration screw. When the pH reading equals the pH of the buffer and

the reading has become steady, the pH is calibrated and ready to measure the pH of unknown solutions.

Titration curves: pH Experimentally Determined Titration Curve for a Monoprotic

Weak Acid

If, during a titration, one plots a graph of the pH of the solution being titrated against the volume of acid (or

base) added to a given volume of base (or acid), one obtains titration curves. Some sample titration curves are

shown below:


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Example 1 - 0.3400 g sample of a monoprotic unknown acid was quantitatively transferred to a 50.0 mL

volumetric flask, approximately 10 mL of 95 % aqueous ethanol and 10 mL of distilled water were added to the

flask. The solution was mixed to dissolve the solid, and then brought to volume with distilled water and mixed

well. The data for the titration curve shown below (Figure 1) was generated by titrating a 5.00 mL sample of the

unknown acid with a 0.04924 M NaOH solution. The NaOH was added using a 10.00 mL volumetric buret and

the pH was recorded on a standard pH meter that had been calibrated between pH 4 and pH 7 at 23 oC.

Experimentally from graph at half-equilibrium approximately is 8.50. Therefore, pKa = pH = 8.50 and the Ka

value will be calculated as follow:

Ka = 10 – pKa = 10 – 8.50 = 3.16 x 10 -9

Example 2 – A solution was prepared by dissolving 0.02 moles of acetic acid (HOAc; pKa = 4.8) in water to

give 1 liter of solution.

a) What is the pH?

b) To this solution was then added 0.008 moles of concentrated sodium hydroxide (NaOH). What is the new

pH? (In this problem, you may ignore changes in volume due to the addition of NaOH).

c) An additional 0.012 moles of NaOH is then added. What is the pH?

Solution a)

HOAc H+ + OAc- pKa = 4.8 Ka = 1.6 x10-5 M

Initial Conc 0.02 M ~0 0

Change -X +X +X

Equilibrium 0.02-X X

Ka = [H+][OAc- ] / [HOAc] = ( X.X / 0.02 – X) = 1.6 x10-5

[HOAc]initial > 100 x Ka, so... X can be ignored in the denominator.


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X2/0.02 = 1.6 x10-5 ; X2 = 3.2 x10-7 , X = 5.6 x10-4 M = [H+] , pH = -log(5.6 x10-4) = 3.25

b) NaOH is a strong base. It will react nearly quantitatively with HOAc to produce OAc-.

HOAc + OH- OAc- + H2O

0.008 moles HOAc + 0.008 moles OH- 0.008 moles OAc-

Amount of HOAc remaining = 0.02 - 0.008 = 0.012 moles. Thus,

[HOAc] = 0.012 M and [OAc-] = 0.008 M

Since both [HOAc] and [OAc-] are present, this is a class 3 problem.

pH = pKa + log [ OAc / HOAc] = 4.8 + log [0.008 / 0.012] = 4.8 + log(0.67) = 4.8 - 0.17, pH = 4.63

c) After the addition of another 0.012 moles of NaOH, all of the HOAc has been converted to NaOAc. thus,

[OAc-] = 0.02 M. Since only the "base form" of the HOAc is now present.

OAc- + H2O HOAc + OH-

Initial Conc. 0.02 M [H2O] ~0 ~0

Change -X -X +X +X

Equilibrium 0.02-X [H2O] X X

Keq = Kw[H2O]/Ka , Kw/Ka =[HOAc][OH-] / [OAc-] = X.X. / (0.02- X) = 10-14 / 1.6x10-5

Neglecting the denominator gives, X2/0.02 = 6.25 x10-10 , X2 = 12.5 x10-12 , X = 3.5 x10-6 M = [OH-]

[H+] = 10-14/(3.5 x10-16) = 2.9 x10-9 M , pH = 8.54

THE pKa BOX

The pKa of an acid is a very useful number, as you will see in the math below. The pKa is the negative log of the

Ka, the pKa is the negative log of the Kb, and the pKa plus the pKb equal fourteen. The ka box is the same as the

pH box, but substitute ka for [H+], pKa for pH, Kb for [OH-], and pKb for pOH.


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Procedure

Conditioning and calibrating the pH

1. Conditioning the pH: Remove the cap and soak the electrode for at least 30 minutes in either a pH 4.0

or 7.0 buffer solution. Immerse the electrode end in the buffer solution to a depth of one and a half inches.

2. Calibrating the pH: This can be done by using a buffer solution having a pH close to that of the solution you

are measuring. For a pH titration, use a pH 7.0 buffer. Immerse the pH in the buffer to a depth of one and a

half inches and stir gently for a few seconds. Allow the reading to stabilize. If the display does not agree with

the known pH of buffer solution turn the screw located on the back of the pH until the digital display shows

the correct pH value. Since the electrode response changes with time, you should periodically recalibrate

the pH.

3. To measure the pH of a solution, immerse the pH to a depth of one and a half inches above the electrode.

Stir gently for a few seconds before recording the reading.

4. After all the readings have been recorded, rinse the pH with deionized water to remove residue from the

electrode. Wet the base of the cap with the buffer solution used to condition the pH and then close the pH

cap firmly. This will help to prolong the life of the pH electrode.

PART I. Standardization of the NaOH Solution with KHP

Weigh out approximately 0.400- 0.500 g of potassium acid phthalate (KHP) using a laboratory balance. Weigh

the sample using an aluminum weighing pan, watch glass or weighing paper and carefully transfer the sample to

a 125 mL Erlenmeyer flask. Dissolve the solid in 50 mL of deionized water. Make sure that all of the KHP has

dissolved before continuing. Add 2 or 3 drops of phenolphthalein indicator solution.

Obtain 100 mL of NaOH solution. Rinse a buret with deionized water and then with a 5 mL sample of the

NaOH solution. Be sure that both the deionized water and the NaOH solution run through the buret tip. Discard

both of these solutions. Attach a buret clamp to a ring stand. Insert the cleaned buret into the buret clamp and

fill the buret with NaOH solution. Open the stopcock to allow a few mL of the solution to drain from the buret .

As it is draining, check the buret tip to be sure no bubbles of air are trapped in the tip. Refill the buret with the

NaOH solution to a volume just between 0.00 mL and 1.00 mL. Read the initial volume of the buret to ±0.01

mL and record the initial volume of NaOH.

Place the flask containing the dissolved KHP under the buret and adjust the height of the clamp so the buret tip

is below the lip of the flask. Place a sheet of white paper under the container to make the color change of the

indicator more noticeable. Begin adding the NaOH solution from the buret slowly, swirling the solution in the

beaker or flask to insure proper mixing. The point at which the NaOH solution contacts the KHP solution will

show a pink color which will disappear upon swirling. As you approach endpoint, greater portions of the

solution will be pink. Titrate drop-by-drop so as not to miss the endpoint. Rinse the sides of the flask with small

amounts of deionizer water to insure that no drops of NaOH are left clinging to the walls of the container.

Remember the endpoint of the titration occurs when a pale pink color persists throughout the solution for

45 - 60 seconds. Record the volume of NaOH required to reach the endpoint.


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Calculate the concentration of the NaOH from your data. Show your work in the space provided. Repeat the

titration with two more samples of KHP. Before doing the each of the next two titrations, calculate the volume

of the NaOH solution required to neutralize the mass of KHP.

This way you will know approximately what volume of base will need to reach the endpoint before beginning

the titration. Calculate the normality of NaOH solution.

Nb = N (NaOH) = [ mass (g) of KHP / VL(NaOH)x 204.23 g/mol]

Average the three measured NaOH concentrations.

You may use the collected data and calculated average normality of NaOH (Nbase ,Vave) from experiment 5 in

the unknown acid titration calculations.

Nacid .Vacid = Nbase . Vbase , Nacid = (Nbase . Vbase / Nacid )

Part II. Determination of Ka of unknown acid

Add 5.0-mL of unknown acid solution into a 250-ml beaker and add 25.0-mL of distilled water ( CO2 free) and

2-3 drops phenolphthalein indicator. Place the pH electrode in the solution and read and record the initial pH of

solution before adding NaOH solution. Begin gentle stirring and record the initial pH and then after every 0.5 -

1.0 mL of base added. Near the endpoint record pH readings every 0.25 mL or less. Titrate at least 3-4 mL

beyond the endpoint. Repeat the same procedure for two more 5-ml unknown acid solutions. From these data

plot a titration curve of pH versus mL of NaOH added. From these titration curves calculate the ionization

constant, Ka, of unknown acid.

Part III. Determination of concentration of unknown acid

Determine the volume of base used at equilibrium point and average molarity of base; calculate the

concentration of the unknown acid.

NOTE- To clean the pH electrode, rinse with distilled water, wipe with a paper towel, and

place it properly on pH meter.

After collecting the data, plot a titration curve for each sample. Use a full sheet of graph paper for each curve.

Place pH on the y-axis, and mL of base added on the x-axis. Draw a smooth curve through the data points. Your

curves should be almost "S"- shaped and resemble pH curves found in your chemistry text.

Locate the area of the curve where the pH is changing most rapidly with small changes in the amount of base

added. This area of the curve should be almost vertical. The equivalence point is the point in the exact center of

the vertical section of the curve. Mark the equivalence point on each of your titration curves.

Calculate the concentration of each of the acid samples and average the results. Show your work!

Complete the table below. (Recall that the pH pf the solution will equal the pKa of the weak acid at a point half

way to the equivalence point.)


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REPORT FORM Name _______________________________

Instructor ___________________________

Date _____________

Part I. NaOH Standardization

mass of Erlenmeyer flask _______g ________g ________g

flask + KHP _______g ________g ________g

mass of KHP final buret reading _______g ________g ________g

initial buret reading _______ml ________ml ________ml

volume NaOH _______ml ________ml ________ml

Molarity of NaOH _______M _______M ________M

Average molarity of NaOH _______M

Trial # mass KHP (g) volume NaOH (mL) molarity (M)

Calculation

Average Molarity (Normality): _______________ Standard Deviation: ________________


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Part II. Determination of ka of unknown acid

Calculate the concentration of each of the acid samples and average the results. Complete the table below.

(Recall that the pH pf the solution will equal the pKa of the weak acid at a point half way to the equivalence

point.) . Show your calculation for Ka, average Ka, and standard deviation of Ka.

Calculation:

Standard deviation of Ka (calculation)______________________

Part III. Determination of concentration of unknown acid

M (average of NaOH) from above (part I) _______ M

Volume of unknown acid _______ ml _______ ml _______ ml

Volume of NaOH at equilibrium point _______ ml _______ ml _______ ml

Molarity of unknown acid _______ M _______ M _______ M

Average Molarity of unknown acid _______ M

(show calculation)

Measurements Sample 1 Sample 2 Sample 3

Volume at the equivalence point

(from graph)

Volume at the half - equivalence

point (from graph)

pKa (from graph)

Ka values

Average Ka


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Pre Laboratory Review Questions and Exercises Due before lab begins. Answer on a separate sheet of paper.

Name ________________________________

Date________________________

1. Define acid and base in Arrhenius terms.

2. A weak acid with the general formula of HA will react with a base, such as NaOH. Write the neutralization

equation which describes the reaction and write Ka expression.

3. What is the pH of a solution that is 0.40 M in sodium acetate and 0.60 M on acetic acid?

(Ka for acetic acid is 1.85x10-5.)

4. Ka for benzoic acid, C6H5COOH, 6.5x10-5. Calculate the pH of solution after addition of 10.0, 20.0, 30.0,

and 40.0 mL of 0.10 M NaOH to 40.0 mL of 0.10 M Benzoic acid.


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Post- laboratory Questions and Exercises Name________________________ Due after completing lab. Answer in the space provided.

Date ________________________

1. Why are air bubbles in the buret tip a possible source of error in a titration experiment? How do you remove

air bubbles from the buret tip?

2. The following data was collected when a 25.0 mL sample of an unknown acid was titrated with a 0.100 M

NaOH solution.

Determine Ka for the unknown acid.

3. A student needed to standardize a solution of NaOH which was approximately 0.125 M. The student

carefully prepared the titration setup, but after 25 mL of NaOH was added, what is the pH of solution if

initially flask contains 25 mL of 0.250 M HCl solution?

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DETERMINATION OF THE EQUILIBRIUM CONSTANT, Ka, OF A WEAK ACID