CHEM 1112: Buffers and the Vampire Slayers

By K. Stone and M. Perona
CSU, Stanislaus

Introduction

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

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

One purpose of this experiment is to measure the dissociation constant of  the  weak acid, acetic acid, CH₃CO₂H.  This will be done by two methods, Method 1 and Method 2.

Method 1: In this method the pH of a  solution initially 0.1 M in  the acid is 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 = [H⁺] = [A^-].  From the pH, the value of [H⁺], and hence of x can be determined.  The value of K_a is then given by

Method 2: This method involoves titrating the acid with a strong base, and plotting the pH versus the volume of base added.  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 V_e is the volume of base at the end point, then V_e/2 is the volume half-way to the end point, 10 mL, in this case. After the addition of V_e/2 mL of base, one-half of the acid has been neutralized and [HA] = [A^-].  From equation (2) we have:

and at the half-way point , 

or 

where pH_1/2 is the pH at the half-way point.  From Figure 1, we see that the accurate determination of pH_1/2 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, V_e is now   accurately located by the slope versus mL graph.

Figure 2

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.

Scheme 1. Acetic acid equilibrium

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

(7)

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

Equation (8) 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 (8) 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 = pK_a. 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 pK_a of the weak acid.

Overview of the experiment: There are two parts of this laboratory exercise. In Part A you will   determine the pK_a of a weak acid using Methods 1 and 2. In Part B, you will prepare a buffer solution. Each student will prepare his or her own  own buffer.

Stockroom: Things for each group to borrow and return on the same day.

• Buret and brush (~$75)
• 500 ml vol flask (~$25)
• 25 ml pipet (~$15)
• Pipet pump

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.

2. Calibration of pH electrode:  Turn on the computer and the labworks interface box.Click on   the Labworks icon on the desktop.  Click on Calibrate, followed by pH.  Follow the instructions on the screen.  A reference solution of known pH for the calibration will be provided by the Stockroom.  The pH electrode is very fragile.  It must be kept immersed in water at all times.  Rinse it with deionized water from your wash bottle when moving it from one solution to another.

    Part A  Measuring the K_a of Acetic Acid
      

1.  Place 25 mL of the 0.1 M acetic acid 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 Design, and under File options, click on open an existing file, followed by OK.  Double click  on the folder "shortcut to experiments" and select the experiment "titration3.exp", and open it.  Click on Aquire, and start.  The prompt "enter total volume added" will appear.  Click OK.   The next prompt asks you to "enter a number ". A zero should appear in the box to the right of the prompt.  Click OK. A pH value will now be displayed on the screen.  This is the pH of the acetic acid solution before any base is added, and is the pH value to be used in the Method 1 calculation. 

3. 
      The next step is to obtain data for the pH versus mL plot needed for Method 2.  a) In response to the prompt "add more base", click OK.  The prompt "enter total volume added" will reappear.  Click OK.  b) When the prompt "enter a number " appears, add 1.00 mL of base to the acid, and enter "1.00" in the box to the right of the prompt.  Click OK.  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.
   

4. Stop the data collection by selecting cancel in response to the prompt "add more base" and yes in response to "Do you want to stop the program now?
   

5. Save your data in a file in the "Personal" folder in the desktop.  
   

6. Click on Analyze in the main Labworks menu.  This will open a spreadsheet program which you can   use to prepare your graphs.  The pH and volume data will be in columns A and B, respectively.  To To calculate the slope of the pH curve versus mL, click in column C, click on column setup on the menu bar, and enter the function DERIV(A,B).  This will calculate D A/D B for each pair of data points.  To plot the pH and the slope versus mL, select Graph setup on the menu bar.  Choose B for the X axis, A for the Y1 axis and C for the Y2 axis.  Click OK, and the desired graphs will appear.
   

7. Save your spreadsheet and graph to a diskette.  To obtain a hard copy of your spreadsheet and graph it will necessary to import the file into Excel and use a computer with access to a printer.
   

  Part B. Preparation of a buffer

Choose an appropriate weak acid from the list below to make 0.5 liter of a 0.1M buffer solution that has a pH of 7.4. You are required to do your own calculations. There are several methods that can be used to make buffers, two of these methods are described below.

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.

Combining volumes method:
Since the total molarity of the solution must be 0.1 M, you can make up a 0.1 M solution of the weak acid and a 0.1M solution of the conjugate base, then combine the appropriate volumes of the two solutions to get the correct ratio of base/weak acid. (Use the Henderson-Hasselbalch equation to calculate the ratio, and remember that the total volume is 500 mL) A modification of this method that is used frequently, is to start with the appropriate volume of either solution (you must first calculate the appropriate volume) and add the other solution until the correct pH is obtained. For this you will need to monitor the pH of the solution as you are adding the second solution. You will need a pH meter, a stirring plate and a stir bar. You may end up with more or less than 500 mL, do not add water to make up the volume.

Mass method:
Calculate the mass of the weak acid and the mass of the conjugate base that are required to make a pH 7.4 solution that has a combined molarity of 0.1M.

1. Use the Henderson-Hasselbalch equation to determine the molar ratio of weak acid to conjugate base.
2. (moles of weak acid + moles weak base)/.5 L = 0.1M
3. moles x MW = grams

Weigh out each substance and add distilled water to make a 0.5L solution.  See sample calculation.

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. Use the same procedure as was used for Method 1 in Part A. 
   

2. How effective is your buffer in resisting pH change?  To each of two clean, dry 100 mL beakers add 50 mL of deionized water.  Measure and record the pH of each one.  To one beaker, add 20 drops of 1 M HCl and to the other add 20 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?
   
       Repeat the procedure in the above paragraph using your buffer solution instead of the deionized water.

Results, calculations:

Ka of Acetic acid

• Calculate the K_a for acetic acid using Method 1
• Include  the graph of pH vs mL NaOH added. 
• Show how you used this graph to determine the K_a according to Method 2.

Buffers

• Clearly show your calculations for making a buffer.
• Report the initial pH of your buffer.
• Report the pH changes caused by adding acid and base to water and to your buffer solution, respectively.

Conclusion:

•  Report the values of Ka obtained by Methods 1 and 2.

•   Look up the value of K_a of acetic acid in your Text book.  This is the "literature value".  What is it?   Using the formula below, calculate the relative percent error for each value that you determined. 
  
  

•  Which method is more accurate, 1 or 2 ?  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 K_a be higher or lower than the actual K_a value? This is only one example, there are several others.
  

• What weak acid did you choose to make your buffer, why did you select this one?
  
• 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 M. Perona   10/28/03.