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Preparation and Properties of Buffers

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OBJECTIVES:

• Design and prepare buffer solutions at a given pH and molarity • Investigate the effect of adding water, strong acid, and a strong base to buffered and non-

buffered systems

INTRODUCTION:

Buffers are solutions whose pH values stay fairly constant even when a small amount of strong acid or base is added to it. In order to maintain its pH, the buffer solution needs to remove the added H+ or OH- via a chemical reaction so that the concentration of these ions in solution remains nearly constant. Therefore, the buffer system needs a weak acid, HA, (to react with any added base) and its conjugate base, A-, (to react with any added acid) as shown in equations 1 and 2 below. Figure 2 shows the change in the relative amounts of HA and A-, when small amounts of H+ or OH- are added. Notice that the amounts of HA and A- vary slightly but not by much from the initial amounts.

Figure 1: Buffer Solution

Figure 2: Buffering Action

H+ added OH-‐ added

A-‐

A-‐ A-‐

A-‐ HA

When acid is added: H+added + A-‐buffer HA (1) When base is added: OH-‐added + HAbuffer H2O + A-‐ (2)

HA A-‐

OH-‐ added

HA A-‐ HA A-‐

H+ added

Preparation and Properties of Buffers

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Calculating the concentrations of weak acids and bases in solution and the resulting solution’s pH requires the equilibrium constant expression. Although either expression can be used, it is customary to use the expression for the weak acid.

𝐾" = %& [()] [%(]

(3)

Rearrangement of equation 3 yields the Henderson-Hasselbalch equation:

𝑝𝐻 = 𝑝𝐾" + 𝑙𝑜𝑔 [𝐴2] [𝐻𝐴] (4)

The Henderson-Hasselbalch equation is useful for calculations involving buffers because buffers contain large concentrations of both HA and A- (unlike solutions made from just one or the other). The equilibrium concentrations of both HA and A- are nearly the same as their initial concentrations (because Ka values are small, we “neglect the x’s”), so knowing the composition of the buffer and the pKa of the acid is enough to calculate the pH of the buffer solution.

The pH of a buffer solution depends on two things: the pKa of the weak acid and the ratio of base to conjugate acid concentrations. If a buffer at a specific pH were to be prepared, one would select a weak acid, whose pKa most closely matches the desired pH of the buffer (the most effective buffers have an [𝐴2] [𝐻𝐴] ratio of 1). If the desired pH does not exactly match the pKa of an acid, then the required ratio of the [𝐴2] [𝐻𝐴] must be calculated to determine how much of the weak acid and its conjugate base must be used.

Making a Buffer Solution from Two Solutes with a Combined Molarity – Method 1

Suppose that a student desires to make a buffer solution with a pH = 4.50. By examining the available choices, he would select a pair of compounds in which the weak acid has a pKa close to 4.50. Let us assume that the closest pKa of a weak acid was 5.00. He would use the Henderson- Hasselbalch to calculate the ratio of [𝐴2] [𝐻𝐴] needed to prepare the buffer. Since both A- and HA are in the same solution and therefore, have the same volume, the concentration ratio is equal to the mole ratio. In this example, he would need 0.32 mole of A- for every one mole of HA (or 0.64 mole of A- for every 2 mole of HA, etc.). Conversion from moles to grams (for solids) or volume (for solutions) will give him the quantities of chemicals needed to make the solution.

𝑝𝐻 = 𝑝𝐾" + log [𝐴2] [𝐻𝐴] (5)

Preparation and Properties of Buffers

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4.50 = 5.00 + log [𝐴2] [𝐻𝐴] (6)

log [𝐴2] [𝐻𝐴] = −50 (7)

[()] [%(]

= 0.32 ≫ BCD ( )

BCD %( = 0.32 (8)

If he desires to make a buffer solution not only at a specific pH but also a specific volume and combined (or total) molarity, then he would continue with the calculations to determine the specific number of moles of each component. Let’s assume that the desired buffer volume is 1.00L and the desired combined molarity (includes both components) is 1.00 M.

BCD ()

BCD %( = 0.32 ≫ mol A- = 0.32 mol HA (9)

𝑇𝑜𝑡𝑎𝑙 𝑚𝑜𝑙𝑒𝑠 = 𝑀 × 𝑉 = 1.00 𝑀 ×1.00 𝐿 = 1.00 𝑚𝑜𝑙𝑒 (10)

Total moles = moles of A- + mole HA = 1.00 mole (11)

(0.32 x mol HA) + mole HA = 1.00 mol

mole HA = 0.76 mol

mole A- = 0.32 x mol HA = 0.24 mol

Making a Buffer Solution from One Solute Reacting with a Second Solute-Method 2

Instead of mixing two components required to make a buffer, another way of making the buffer is to select one of the components and then create the other component in the container (in situ) through a chemical reaction. This can be accomplished by adding a strong acid (if the base component is selected) or a strong base (if the acid component is selected) since reactions of the strong acid/base with the component will essentially go to completion.

Preparation and Properties of Buffers

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Let’s continue with the combined molarity values from the example above. Suppose the student realized that although he required 0.76 mole of HA and 0.24 mole of A- to make the buffer, only HA was available. How can he still make the buffer from only one component? He can create the second component by reacting HA (weak acid) with a strong base according to the equation below. Since he wants to end up with the 0.76 mol HA and 0.24 mol A-, he can back-calculate and determine the initial moles of HA (1.00 mol) and OH- (0.24 mol) needed to accomplish the task. Notice that all OH- are consumed (reaction going to completion) so none of it is left in the buffer solution.

HA + OH- à H2O + A- (12)

Initial Mole 1.00 0.24 --- 0 Change in Mole -0.24 -0.24 --- +0.24 Final Mole 0.76 0 --- 0.24

A similar kind of equation and calculation are used when a strong acid or base is added to a buffer resulting in the conversion of one buffer component into another. For example, adding a strong acid will convert some of the A- in the buffer to HA. Conversely, adding a strong base will convert some of the HA to A- (see equations 1 and 2). The only difference is that in a buffer solution there will be both HA and A- initially present in solution (unlike in the above example where there is no initial A- present).

Since the moles of HA and A are both changed, this changes the ratio of [𝐴2] [𝐻𝐴] in the Henderson-Hasselbalch equation and therefore the pH of the solution (although not by much). Reactions with strong acids and bases go essentially to completion, so use stoichiometry first to determine the change in moles for both HA and A- (see equation 12) before using the Henderson- Hasselbalch equation. Either the mole ratio or the concentration ratio can be used in the

HA A-‐

Initial moles of each component

OH-‐ added

HA A-‐ HA A-‐

H+ added

Preparation and Properties of Buffers

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Henderson-Hasselbalch equation. If using concentration ratio, be sure to account for volume change when adding solutions.

In Part 1 of the lab, you will design and quantitatively prepare a buffer solution at a specific pH, molarity, and volume. You will choose a weak acid and its conjugate base from a list to make the buffer and using Method 1 as explained above, determine the amount of the weak acid and the conjugate base needed. The pH of the prepared buffer will be measured and compared to the theoretical value.

In Part 2 of the lab, you will add a quantity of strong acid and strong base to buffered and non- buffered systems and determine their effect by measuring and comparing their pH values before and after the addition.

In Part 3 of the lab (check with your professor to see whether you will do this part), you will design and prepare a buffer solution using only one of the components from the chosen pair from Part 1 and create its conjugate component in solution by adding either a strong acid or strong base. You will then be asked to determine the volume of acid or base needed to increase or decrease the pH of the buffer by a specific amount.

PRE-LAB QUESTIONS:

1. What are buffers? What are the two components of a buffer?

2. Derive the Henderson-Hasselbalch equation from the Ka expression.

3. Which of the following pairs of chemicals will produce a buffer? a. HCl and HC2H3O2 c. H2CO3/Na2CO3

b. NaF and HF d. NH3 and NaOH

4. Write balanced net ionic equations that show how a buffer containing NaHCO3 and

Na2CO3 maintains its pH when a small amount of HCl or NaOH is added.

5. Calculate the pH of a buffer made from mixing 10.0 mL of 0.100 M NaC2H3O2 and 10.0 mL of 0.100 M HC2H3O2.

a. Calculate the pH of the buffer when 5.00 mL of a 0.0100 M NaOH is added.

b. Calculate the pH of the buffer when 5.00 mL of a 0.0100 M HCl is added.

Preparation and Properties of Buffers

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CHEMICALS AND MATERIALS:

Solutions: Solids: 0.0100 M NaOH NaC2H3O2·3H2O 0.0100 M HCl NaHCO3 0.100 M NaOH Na2CO3 0.100 M HCl NaH2PO4 1.00 M NaOH Na2HPO4 1.00 M HCl Na3PO4·12H2O 1.00 M HC2H3O2 NH4Cl 1.00 M NH3 0.1 M NaCl pH 4, 7, and 10 buffers EQUIPMENT TO BE CHECKED OUT:

50 mL volumetric flask + stopper 10 mL graduated pipet pH electrode Vernier LabPro Kit

WASTE DISPOSAL: Dispose of all chemical solutions in the aqueous waste container. Dispose of any solid salts into the solid waste container.

EXPERIMENTAL PROCEDURE:

Part 1: Preparation of a Buffer from a Weak Acid/Base and Its Conjugate

1. Obtain your buffer assignment (pH and total molarity) from your professor. 2. Select an appropriate pair from the list below to prepare 50.00 mL of your assigned

buffer. Consult your text for Ka or Kb values. a. NaC2H3O2·3H2O and HC2H3O2 (aq., 1.00 M) b. NaHCO3 (s) and Na2CO3 (s) c. Na2HPO4(s) and Na3PO4·12 H2O (s) d. NaH2PO4(s) and Na2HPO4(s) e. NH4Cl(s) and NH3 (aq, 1.00 M)

3. Calculate the mass or volume of acid and base components needed to obtain the pH and molarity assigned (see example calculation for Method 1 in the Introduction). Note: Some salts contain waters of hydration in the formula so be sure to include them in the calculation for molar mass.) Check your answers with your professor.

4. Write a detailed procedure on how you would prepare 50.00 mL of the desired buffer using the chemicals above. Obtain instructor’s approval.

Preparation and Properties of Buffers

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5. Check out a 50 mL volumetric flask and prepare the buffer according to your procedure. 6. Calibrate the pH electrode using the pH 4/7 or pH 7/10 buffer solutions, depending on

whether your buffer falls in the acidic or basic range. Follow proper calibration procedure as directed by your professor; guidelines for calibration are provided with the pH meters.

7. Pour the prepared buffer into a clean, dry 150 mL beaker and measure and record the pH of the buffer. The measured pH value of your buffer should be identical (or very close) to the assigned value. Save the prepared buffer for Part 2.

8. Rinse the volumetric flask with tap water and do a final rinse with DI water.

Part 2: Properties of Buffered and Non-Buffered Systems

1. Check out a 10 mL graduated pipet and pipet pump from your professor. 2. Obtain and label (#1-4) 4 clean and dry beakers (50 or 100 mL). 3. Add the following liquids/solutions into beakers using a 50-mL graduated cylinder.

a. Beaker 1-20.0 mL of 0.1M NaCl b. Beaker 2-20.0 mL of 0.1 M NaCl c. Beaker 3-20.0 mL of your prepared buffer from Part I. d. Beaker 4-20.0 mL of your prepared buffer from Part I.

4. Measure and record the pH of the contents in each beaker. Be sure to rinse the electrode with deionized water in between uses to avoid contamination. DO NOT blot the electrode with paper towels or Kimwipes.

5. Effect of acid: Add 5.00 mL of 0.0100 M HCl solution (be sure to condition the pipet first) into beakers 1 and 3. Mix the contents well and measure and record the pH.

6. Effect of base: Add 5.00 mL of 0.0100 M NaOH solution (be sure to condition the pipet first) into beakers 2 and 4. Mix the contents well and measure and record the pH.

7. Dispose of all solutions into the chemical waste container.

Part 3: Preparation of a Buffer Using One Component (Optional)

1. Write a detailed procedure (using Method 2) for the preparation of 50.00 mL of the same assigned buffer (same pH and molarity) using just ONE of the chemicals from the pair you selected in step 2 and either 1.00 M NaOH OR 1.00 M HCl to generate the conjugate species in situ. Once your calculations and procedure are approved by your professor, check out the 50-mL volumetric flask and prepare the buffer accordingly.

2. Pour the buffer into a 100 mL beaker. Measure and record the pH of the solution. 3. Obtain two clean and dry 50-mL beakers (beakers 1 and 2). Using a 50-mL graduated

cylinder, pour 20.0 mL of the buffer into each of the beakers. 4. Calculate the volume of 0.100 M HCl required to decrease the pH of the buffer solution

by 0.15 pH units in beaker 1. 5. Calculate the volume of 0.100 M NaOH required to increase the pH of the buffer solution

by 0.10 pH units in beaker 2.

Preparation and Properties of Buffers

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6. Once your calculations and procedure are approved b your professor, use a conditioned pipet and add the calculated volume of acid (or base) into the beakers. Measure and record the new pH.

7. Dispose of the solutions into the waste containers. Returned the clean volumetric flask to your professor.

DATA ANALYSIS:

Part 1: Preparation of a Buffer from a Weak Acid/Base and Its Conjugate

1. Complete the table below. If the actual amounts of the weak acid/base and its conjugate used during the preparation differ from the calculated amounts, compute the new target pH. Target pH Measured pH % error Buffer

2. What are some likely sources of error for the preparation of the buffer?

Part 2: Properties of Buffered and Non-buffered Systems

1. Using your measured pH values, calculate the concentration of H+ (M) in beakers 1 and 3, before and after the addition of HCl. Organize your answers in a table as shown below

Initial [H+] (M) [H+] (M) after addition of HCl

By what factor did the [H+] (M) increase?

Beaker 1 (0.1 M NaCl)

Beaker 3 (Buffer)

2. Using your measured pH values, calculate the concentration of H+ (M) in beakers 2 and 4, before and after the addition of NaOH. Organize your answers in a table as shown below.

Initial [H+] (M) [H+] (M) after addition of NaOH

By what factor did the [H+] (M) decrease?

Beaker 2 (0.1 M NaCl)

Beaker 4 (Buffer)

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3. Which system (buffered or non-buffered) shows a smaller increase/decrease in the concentration of H+? Explain.

4. For each beaker, calculate the expected (theoretical) pH when 5.00 mL of 0.0100 M HCl or 5.00 mL of 0.0100 M NaOH is added to 20.0 mL of buffered and non-buffered systems. Use the actual volume of acid/base added in the calculation. Organize your answer in a table as shown below.

Actual volume of

acid or base added (mL)

Measured pH

Calculated (Theoretical)

% Error

0.1 M NaCl + acid (beaker 1)

0.1 M NaCl + base (beaker 2)

Buffer + acid (beaker 3)

Buffer + base (beaker 4)

Part 3: Preparation of a Buffer Using One Component (Optional)

1. Complete the table below. Target pH Measured pH % error Buffer Buffer + acid (beaker 1) Buffer + base (beaker 2)

2. What are some likely sources of error for the preparation of the buffer and the addition of acid/base?

POST-LAB QUESTIONS:

1. What is the effect on the pH of the solutions in beaker 1 and 3 if the pipet was rinsed with DI H2O but not conditioned with the HCl solution?

2. Which of the following pairs of solutions will produce a buffer solution? Explain your reasoning.

a. 10.0 mL of 0.10 M HCl + 10.0 mL of 0.10 M NaOH

b. 10.0 mL of 0.10 M HCl + 5.0 mL of 0.10 M NaOH

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c. 10.0 mL of 0.10 M HF + 10.0 mL of 0.10 M NaOH

d. 10.0 mL of 0.10 M HF + 5.0 mL of 0.10 M NaOH

3. A student prepared 50.0 mL of “Buffer Q” using 0.50 moles of HA and 0.50 moles of A- while another student prepared 50.0 mL of “Buffer S” using 0.25 moles of HA and 0.25 moles of A-.

a. Do the two buffer solutions have the same or different pH? Explain.

b. If 1.00 mL of 0.010 M NaOH were added to the two buffer solutions, would the pH of the two solutions increase or decrease? Explain.

c. Which solution (Buffer Q or Buffer S) would show a smaller change in the pH for question (b)? Explain.

REFERENCES: Written by Jenny Leung and Janet Truttmann, April 2011