Lab 24: Determining Kby Half-Titration of a Weak Acid

Lab 24: Determining

K

by Half-Titration of a Weak Acid

Driving Question (#2)

How can the identity of an unknown weak acid be determined using titration?

Background (#2)

Ka is the symbol for the equilibrium constant for the ionization of an acid. The following equation describes the ionization of an acid:

HA + H2O ⇄ H3O+ + A–

An equilibrium exists, and an acid dissociation constant can be written:

Equation (1)

The value of Ka is an indication of the extent to which an acid dissociates. Strong acids dissociate nearly

completely. Weak acids reach equilibrium, where the fraction that has dissociated becomes a constant at a given temperature. For this reason, titrations are only used to find the equilibrium constants of weak acids. The numerical value of the equilibrium constant is unique to the acid and can be used to identify an unknown acid. Before the titration is begun, the initial pH of the solution is controlled by the auto-dissociation of the acid. At this point, the concentration of H3O+ and A– are very small compared to the concentration of HA. When the basic titrant solution is added, it is assumed that the OH– _{ions react completely with the weak acid, HA, to form water} and the conjugate base, A–_:

The resulting solution now has a smaller amount of HA and a larger amount of A–_{. Due to stoichiometry, the} increase in A– _{is the same magnitude as the decrease in HA. Solutions that contain a weak acid and also contain} the corresponding conjugate base are called buffers.

When the number of moles of added base is equal to the original number of moles of HA, the equivalence point has been reached. A titration curve, in which pH is plotted versus volume of titrant added, can be used to quickly determine the Ka of the acid.

The acid dissociation constant equation (Equation 1) can be revised to form an expression used to calculate the pH of mixtures of weak acids and their salts:

Taking logarithms,

Multiplying by –1,

Substituting pKa for –log Ka and pH for –log[H3O+],

Reordering,

Equation 2 is known as the Henderson-Hasselback equation which gives the pH of buffer solutions. Notice that when enough base has been added to reach the point that is halfway between the starting point and the

equivalence point, the molarity of A– _{and HA will be equal. Their ratio will be 1 and since log 1 = 0, the pH will} be equal to the pKa. The resulting Ka can be used to determine the identity of the acid.

The acid dissociation constants for several weak acids are shown in Table 1.

Table 1: Acid dissociation constants for 5 weak acids

Name

Formula

K

pK

Acetic acid

HC

H

O

1.8



10

4.7

Benzoic acid

HC

H

O

6.4



10

5

4.2

Formic acid

HCHO

1.8



10

3.7

Nitrous acid

HNO

4.6



10

3.4

Hypochlorous acid

HOCl

3.5



10

7.5

Pre-Lab Activity

In this lab you will use a method of titration that will bring the analyte halfway to the equivalence point. Halfway to the equivalence point, half of the acid molecules are converted to A–_{, therefore, for a monoprotic acid}

In the expression of Ka (Equation 2), [A–_{] and [HA] cancel out, giving}

The pH of the analyte at this point is equal to the pKa. You will convert this value to Ka and compare this Ka value to a table of known Ka values in order to identify the unknown acid.

You will perform the titration and determine the equivalence point; that is, how much of the titrant is necessary to react with all of the acid in the solution. The pH of the half-titration point is the pH of the solution after adding half the amount of titrant needed to reach the equivalence point.

Example calculation for students to try

A sample of 10.00 mL of dilute HNO2 solution was titrated with 0.1 M NaOH solution. The equivalence point was reached after 10.10 mL. The half-titration point, therefore, was at 5.05 mL. The pH that corresponded to that volume of titrant was 3.34, so the value of Ka is

Pre-Lab Questions – Conceptual and Procedural (#3)

1. Would adding NaOH solution to the HA solution increase or decrease the pH of the solution?

2. Use the Henderson-Hasselbach equation to show that the pH of the solution at the half-titration point is equivalent to the pKa value of the weak acid.

Before answering the rest of the questions, read the procedure and watch the videos on-line. 3. Why is necessary to rinse the buret with the NaOH solution?

4. Why is it important to remove air from the tip of the buret?

5. Why will it be necessary to start your titration over again if you accidentally allow the titrant to stream out of the stopcock instead of emerging by drops?

6. Why is it important to go past the equivalence point?

7. Do you expect a pH drop or a pH rise at the equivalence point? Explain your answer.

8. Do you expect the pH to be alkaline, neutral, or acidic at the equivalence point? Explain!

Materials and Equipment

Data collection system Graduated cylinder, 100-mL

pH sensor Funnel

Drop counter 0.20 M Sodium hydroxide (NaOH), 75 mL

Ring stand Unknown weak acid solution, 50 mL

Clamp, right-angle Buffer solutions, pH 4 and pH 10, 10 mL

Clamp, buret Cotton swab or tissue

Beaker (2), 100-mL Buret, 50-mL

Sequencing Challenge (#2)

The steps below are part of the Procedure for this lab activity. They are not in the right order. Determine the proper order and write numbers in the circles that put the steps in the correct sequence.

Then put an accurately measured quantity

(50.00 mL) of the unknown solution into a beaker.

Set up the titration

apparatus with a pH sensor and drop counter. Calibrate the pH sensor.

Fill a 50-mL buret with the titrant: 0.20 M NaOH, and set the meniscus to the zero mark or right below and record the initial volume. Perform the

titration and record the half-titration volume.

Procedure

After you complete a step (or answer a question), place a check mark in the box () next to that step.

Set Up

1.  Start a new experiment on the data collection system. 2.  Connect a pH sensor to the data collection system. 3.  Calibrate the pH sensor.

4.  Assemble the titration apparatus, using the steps below and the illustration as a guide.

a. Position the magnetic stirrer on the base of the ring stand.

b. Use the buret clamp to attach the buret to the ring stand.

c. Place a waste container below the buret.

d. Position the drop counter over the waste container and attach it to the ring stand using the right-angle clamp.

e. Place the pH sensor through one of the slots in the drop counter.

Note: Do not connect the drop counter to the data collection system yet.

5.  Rinse the buret with several milliliters of the 0.20 M NaOH solution:

a. Ensure that the stopcock is closed and rinse the

inside of the buret with several milliliters of the standardized NaOH solution. b. Open the stopcock on the buret and drain the rinse NaOH into the waste container. c. Repeat this process two more times.

6.  Make sure the stopcock on the buret is in the “off” position and then use a funnel to fill the buret with about 50 mL of the 0.20 M NaOH solution (titrant).

7.  Drain a small amount of the titrant through the drop counter into the waste beaker to remove any air in the tip of the buret.

8.  Practice adjusting the stopcock on the buret so that the titrant goes through the drop counter in distinguishable drops that fall at about 1 to 2 drops per second.

Note: Good control of the stopcock is important. If you accidentally open the stopcock too far and the NaOH streams out (as opposed to coming out in drops), you will have to start over.

9.  Remove the waste container.

10.  Add the micro stir bar to the end of the pH sensor.

11.  Add additional 0.20 M NaOH to the buret so the solution is above the zero mark. Allow some of the NaOH solution to drip into the waste container until the bottom of the meniscus is lined up with or just below the zero mark and record the initial reading in Table 2.

12.  Use the graduated cylinder to pour 50.0 mL of the unknown weak acid solution into a 100-mL beaker and set the beaker below the buret.

13.  Connect the drop counter to the data collection system. 14.  Display pH versus Drop Count (drops) on a graph.

pH sensor

Micro stir bar

Ring stand Buret

Buret clamp

Magnetic stirrer pH sensor

Collect Data (#4 & #5)

15.  Clean the lens of the drop counter with water and a cotton swab or tissue. 16.  Start recording data.

17.  Turn the buret stopcock carefully, allowing the titrant to drip slowly (1 to 2 drops per second) into the solution.

18.  Continue the titration past the equivalence point until the pH curve flattens. 19.  Stop recording data.

20.  Record the final drop count and the final reading of the titrant in the buret to a precision of 0.01 mL in Table 2.

21.  Calculate the volume of titrant (final reading minus initial reading) and record this value in Table 2.

T

Titration Information

Measurement or Calculation

Initial reading of NaOH in the buret (to 0.01 mL)

Final reading of NaOH in the buret (to 0.01 mL)

Volume of titrant (to 0.01 mL)

Final drop count

22.  Calibrate the drop counter.

23.  Set the horizontal axis to the calculated volume.

24.  In Table 3, record the volume of titrant used to reach the equivalence point. The equivalence point will be where the slope of the titration curve is the steepest. Find the steepest slope of the data plot to determine this point.

25.  Record the pH at the half-titration point (half the volume of titrant used to reach the equivalence point) in Table 3.

26.  Remove the beaker and dispose of its contents according to the teacher’s instructions.

Data Analysis (#6)

Table 3: Measurements and determination of the pK

Parameter

Measured or Calculated

Quantity

Volume of 0.20 M NaOH to reach the equivalence point (mL)

Volume of NaOH to the half-equivalence (or half-titration) point

(mL)

pH at the half-titration point

Experimental p

K

Possible solution

Post Lab Questions (#9)

1. What is the experimental pKa of the unknown solution?

2. How can you identify the unknown solution based on the experimental pKa?

3. What is the unknown solution?

4. What are sources of error from the titration? Calculate the percent error and record it in Table 3.

5. Is the pH of the solution neutral, alkaline, or acidic at the equivalence point?

6. At the half-titration point, the solution is considered to be a buffer. Explain why.

7. Would the half-titration volume (the volume of titrant used to reach the half-titration point) be different if propionic acid (which is also a monoprotic weak acid), with the same concentration, had been the unknown weak acid?

Synthesis Questions - Use available resources to help you answer the following questions.

1. The acidity constant of formic acid (HCOOH) is Ka = 1.8  10–4. Would you expect a higher or lower pH if

formic acid were used instead of your unknown at the half-titration point? Explain your answer!

2. If you had to determine the acidity constants of oxalic acid, which is a diprotic acid

(Ka1 = 6.5  10–2, Ka2 = 6.1  10–5), what differences would you expect to find in the titration curve?

Multiple Choice Questions

1. At the equivalence point the solution contains: A. Only water

B. Half of the untitrated acid and the same amount of salt C. The product of the titration (salt) and water

D. Some acid left untitrated

2. At the half-titration point:

A. Half of the acid molecules are still untitrated B. Half of the acid molecules are dissociated C. Half of the acid molecules are overtitrated D. There are no acid molecules left

3. The pH at the half-titration point:

A. Can be calculated from the volume of the titrant necessary to reach the equivalence point B. Is the same as the pH at the equivalence point

C. Is the same as the pKa of the weak acid D. Is half of the pKa of the weak acid

4. The solution is considered a buffer at:

A. The equivalence point

B. The beginning, before the titration