pHun with Buffers 

By K. Stone and M. Perona
CSU, Stanislaus

Introduction

Weak acids:  The dissociation of a weak acid HA, occurs according to the reaction

HA H+ + A-

(1)

The equilibrium constant, Ka is the dissociation constant of the weak acid and is given by

(2)

Ka can be used to determine the pH of a solution.    The pH of a  solution that is  0.1 M acetic acid can be calculated and then measured with a pH electrode.  Since some of the acid dissociates, the equilibrium concentration of the acid is 0.10-x, where x is the moles per liter of acid dissociated, and x = [H3O+] = [A-].  From the pH, the value of [H+], and hence of x can be determined.  

 

HA    

 A

   H3O+

Initial Concentration

0.1M

 0

      0

Equilibrium concentration

0.1-x

  x

      x

The Ka value for acetic acid is 1.8 x 10-5,  use that value to calculate the pH for a 0.1M solution

n of acetic acid by solving for x in equation 3.  Does the volume of the solution matter?  Why or why not?

 

(3)

Determination of the pKa: Titrating the acid with a strong base, and plotting the pH versus the volume of base added can be used to determine the pKa of a weak acid.  A typical graph is shown below.


Figure 1

At the end point the moles of base added equals the moles of acid initially present.  In the graph, the end point occurs after the addition of 20 mL of base.  At the end point essentially all of the acid is converted to A-.  If Ve is the volume of base at the end point, then Ve/2 is the volume half-way to the end point, 10 mL, in this case. After the addition of Ve/2 mL of base, one-half of the acid has been neutralized and [HA] = [A-].  From equation (2) we have:

 

(4)

and at the half-way point , 

[H+] = Ka

(5)

or 

 pH1/2 = pKa

(6)

where pH1/2 is the pH at the half-way point.  From Figure 1, we see that the accurate determination of pH1/2 requires an accurate determination of the end point.  The end point is that point on the titration curve where the slope is the steepest, that is, the greatest.  In this experiment the pH values in the titration will be collected and stored by a computer.  Using the Analyze option in the Labworks program we can plot  the pH  versus the mL of base added. We can also plot the slope of the pH curve versus the mL of base.  The two graphs can be superimposed, as shown in Figure 2.  The endpoint, Ve is now   accurately located by the slope versus mL graph.

Figure 2

Before the end point, the pH of the solution can be calculated using the Ka expression.  The base will decrease the amount of HA and add to the amount of A- by exactly the same amount.  The base is reacting with the H3O+ ions and in order to maintain equilibrium, the amount of A- will increase and the amount of HA will decrease.

 

HA    

 A-

   H3O+

Initial Concentration

0.1

 0

      0

Equilibrium concentration after added base

moles of HA-moles of base added

moles of base added

      x

How do you convert molarity into moles?  

After enough base has been added to reach the end point, there is no HA left in solution.  Only the A- species is present.  A- is the conjugate base of the weak acid.  It has its own equilibrium expression: 

(7)

 

[H3O+] x [OH-] = 1 x 10-14

(8)

 

Kb x Ka = 1 x 10-14  

(9)

Buffers:  Acid-base chemistry is very important in living systems. Biochemical reactions are catalyzed by enzymes that have very narrow ranges of optimum pH values. The pH of a living system is maintained with buffers. In humans, the pH of blood is maintained between 7.35 and 7.45. Typically 5 liters of blood contains enough buffering capacity to absorb 150 mL of 1M acid. The principal buffers in blood are bicarbonate, proteins (including hemoglobin and oxyhemoglobin), and phosphates.

A buffer is a mixture of a weak acid and its conjugate base. Because the solute can either absorb protons or release protons, the buffer solution can maintain the pH at a constant value.

For example, when 10 mL of a 0.1M solution of HCl is added to 1.0 L of a 0.1M Acetic acid solution at pH 4.8, the equilibrium shifts to the left and more acetic acid is made. The added protons are now part of acetic acid. The amount of free hydrogen ions does not change, despite the fact that acid has been added. The new pH is 4.79.

acetica.gif (1638 bytes)

Scheme 1. Acetic acid equilibrium

A useful equation for the understanding of buffer solutions can be obtained by writing equation (4) in logarithmic form:

                                               (10)

Since pH = -log [H+], we can rewrite the above equation to obtain

(11)

Equation (11) is the Henderson-Hasselbach equation.
    A buffer solution is at its maximum buffering capacity when the ratio of conjugate  base to conjugate acid is 1. What happens to equation (11) when the concentration of weak acid equals the concentration of its conjugate base? (When [A-] = [HA]?) What is the log of 1? At this point we see that pH = pKa. In order for a buffer to have maximum buffering capacity, the ratio of the concentrations of conjugate acid to conjugate base should be close to 1.0 and the pH of the solution will be close to the pKa of the weak acid.

Overview of the experiment:  Each student must prepare their own buffer.  You will add acid to your buffer and compare that to adding acid to pure water.  You will also titrate a solution of glycine to determine its pKa values.

Buffer: Make a buffer and then compare it to pure water. What happens to the pH of a buffer when acid is added? What happens to the pH of pure water? Why do they behave differently? Does it matter how much acid you add?

Glycine: Titrate a 0.1M solution of glycine with 0.1M NaOH. What is the structure of glycine? What is the predominate species at the first end point? What is the predominate species at the second end point? Why are there two end points? Plot out your titration curve and label it with the species that exist at these points: endpoints, midpoints. From your graph, determine the pKa values for glycine. Compare these values to the literature values in your conclusion.

Special Equipment: Things to use and return on the same day.

  • You will be using a buret (~$75), buret brush, 25 ml pipet (~$20) and a red pipet pump. It will all be in the lab.
  • Be sure to rinse all the glassware with water and then return it to the box when you are done using it.

Procedure

1.      Wastes and Spills: all of the chemicals in this experiment can be put in the trash or down the drain. Be sure the water is running. Use wet paper towels to wipe up small spills. Thoroughly rinse the pipet, buret and other glassware with water before returning them to the stockroom.  You will want to clean all of your glassware before beginning this experiment. Be sure to triple rinse with distilled water and then triple rinse with the solution you are using before filling burets, beakers or pipets.

  1. Calibration of pH electrode: Open MicroLab, select new experiment, add sensor.
    1. Add pH/DO sensor, select input (click on red square on picture)
    2. Click on “pH”, even though it looks “selected” you  have to click on it.
    3. Units= pH
    4. New Calibration
    5. Add Calibration point
    6. Actual value = 7 (put electrode in pH 7) solution
    7. Save and continue
  2. Add sensor, select keyboard, input = NaOH
    1. Type in “Enter total volume of NaOH added”
    2. Units = mL
  3. Drag the mL NaOH to the x axis, the first column and the Digital display
  4. Drag the pH to the y axis, the second column and the Digital display

Part A  Titration of glycine with sodium hydroxide

Show all of your calculations in your lab notebook under results. 

1.      Place 25 mL of the 0.1 M glycine solution into a clean 100 mL beaker.  Place a stir bar in the beaker, and place the beaker on the stirrer.  Carefully place the calibrated pH electrode in the acid solution.  Position it so that it does not touch the rotating stir bar.  Fill your buret with 0.100 M NaOH solution.  Be sure to expel any air bubbles from the tip, and adjust the volume of base so that the meniscus is at zero on the buret scale.  Use a buret clamp to position the buret above the beaker of acid.  The buret tip should be below the top of the beaker.  

2.      On the computer screen, click on  start.  A pH value is displayed on the screen.  This is the pH of the solution before any base is added.  The next step is to obtain data for the pH versus mL plot needed to determine the Ka.  a) In response to the prompt "Enter the total amount of NaOH added",  enter the amount of NaOH that has left the buret.  Wait a few moments and then hit “enter and continue”.    Now, add more NaOH, the new pH and volume of base will appear on the screen. Repeat this process for each addition of base.  After each addition of base, enter the total volume of base added at that point.  Initially you should add the base in 1.00 mL increments, so that the second entry after the prompt "enter total volume added" will be "2.00".  Once the pH has increased to about 5 reduce the volume increment of base to 0.5 mL or less.  Near the endpoint, a pH of about 6, reduce the volume increment to a single drop.  Continue the titration to a pH of 11 to 12.

3.      End the experiment  by clicking on Stop.  Save your data in a file on the "Desktop".

4.      Under the graph, select “Analysis”

1.      Select Plot 1st derivative (change in slope),  the high point of this graph is the titration end point volume.

2.      Drag the “fx” to the third column on the sheet.

5.      Export (file, export, comma separated list)  to the desktop.  Open the file in Excel, you will need to select “all files” under file type.  Make sure the columns in Excel are in this order: volume, pH, change in slope.  Use the insert graph button to make a graph of pH vs volume and 1st derivative vs volume on the same graph.  Then you can highlight everything and select the graph tool.)

6.      You need a plot of pH vs volume  and change in slope vs vol.  Show how you determined pKa with notes on the graph.  (You can use hand writing.)

 

Part B.  Preparation of a buffer: Here is a list of weak acids and their pKa values.  We will be making a phosphate buffer.  We will make a 100 ml of a 0.1M buffer solution that has a pH of 7.4. 

Weak acid

Ka

acetic acid

1.8 x 10-5

phthalic acid

1.3 x 10-3

dihydrogen phosphate (monobasic)

6.2 x 10-8

monohydrogen phosphate (dibasic)

4.8 x 10-13

carbonic acid

4.6 x 10-7

citrate

8.4 x 10-4

dihydrogen citrate(monobasic)

1.8 x 10-5

monohydrogen citrate (dibasic)

4.0 x 10-6

In your notebook, be sure to show all calculations for determining the amounts of the weak acid and the conjugate base. Be sure to carefully describe the procedure that you used in the method section of your lab report.  Why did we choose the dihydrogen phosphate for the acid?  What phosphate species on the list is the acid for our buffer?  Which phosphate species is our conjugate base?


Calculate the volume of the 0.1M dihydrogen phosphate (monobasic)and the volume of the 0.1M monohydrogen phosphate (dibasic) that are required to make a pH 7.4.  

  1. Use the Henderson-Hasselbalch equation to determine the ratio of weak acid to conjugate base. 
  2. Both volumes must add up to 100 mL.  
  3. Solve the two equations for two unknowns.  
  4. Make the solution.

Testing your Buffer.

1.      Measure the pH of your buffer: Place 25.00 ml of your buffer in a clean 100 ml beaker. Determine the pH of the solution using the pH electrode. 

2.      How effective is your buffer in resisting pH change?  To each of two clean, dry 100 mL beakers add 25 mL of deionized water.  Measure and record the pH of each one.  To one beaker, add 10 drops of 1 M HCl and to the other add 10 drops of 1 M NaOH.  Measure the pH of each solution.  What is the pH change caused by the addition of the acid and base, respectively?

3.      Repeat the procedure in the above paragraph (#2) using your buffer solution instead of the deionized water.   To each of two clean, dry 100 mL beakers add 25 mL of your phosphate buffer.  Measure and record the pH of each one.  To one beaker, add 10 drops of 1 M HCl and to the other add 10 drops of 1 M NaOH.  Measure the pH of each solution.  What is the pH change caused by the addition of the acid and base, respectively?

Results, calculations:

Titration of Glycine

  • Show how you used the graph of pH vs volume of sodium hydroxide added, to determine the Ka for glycine.

Buffers

  • Clearly show your calculations for making a buffer.
  • Report the initial pH of your buffer.
  • What is the molarity of your buffer?

Conclusion:

  • Report the values of Ka for glycine using the titration graph.
  • What is the structure of glycine? What is the predominate species at the first end point? What is the predominate species at the second end point? Why are there two end points? Plot out your titration curve and label it with the species that exist at these points: endpoints, midpoints. From your graph, determine the pKa values for glycine. Compare these values to the literature values in your conclusion.

·         Look up the values of Ka of glycine.  These are the "literature values".  What are they?   Using the formula below, calculate the relative percent error for the value that you determined using the graph.

% error =  Measured value - Literature value     x 100%
                         Literature value

·         Be sure to discuss the sources of error and how each error would affect your experimental value. For example if the pH electrode was not calibrated correctly, and the actual pH was lower than the measured pH, would the calculated Ka be higher or lower than the actual Ka value? This is only one example, there are several others.

·         Why did we make a phosphate buffer?  What phosphate species on the list is the acid for our buffer?  Which phosphate species is our conjugate base?  Is there another weak acid on the list that could have worked for making a pH 7.4 buffer? 

  • What was the initial pH of your buffer? How does this compare with the solution that you were trying to make? 
  • Compare the pH changes resulting from the addition of 1 M HCl and 1 M NaOH, respectively, to pure water and to the buffer solution.   Is your buffer solution resistant to pH change?  Please explain. 

Last edited by K. Stone  04/07/08.