## Relative Amounts of Acid and Base

The pH of a buffer depends on the ratio [base]/[acid] rather than on the particular concentration of a specific solution.

### Learning Objectives

Calculate the relative amounts of a weak acid and its conjugate base that must be used to generate a buffer solution of desired pH.

### Key Takeaways

#### Key Points

• Buffers should be made using an acid and its conjugate base (or a base and its conjugate acid ); the pair should have a Ka very similar to the desired pH.
• The exact ratio of the conjugate base to the acid for a desired pH can be determined from the Ka value and the Henderson-Hasselbalch equation.
• A buffer is most effective when the amounts of acid and conjugate base are approximately equal.
• As a general rule of thumb, the relative amounts of acid and base should not differ by more than tenfold.

#### Key Terms

• conjugate base: The species that is created after the donation of a proton.
• conjugate acid: The species created when a base accepts a proton.
• conjugate acid-base pair: Two molecular entities differing only by a single proton.

A buffer is an aqueous solution consisting of a mixture of a weak acid and its conjugate base or a weak base and its conjugate acid. A buffer’s pH changes very little when a small amount of strong acid or base is added to it. It is therefore used to prevent change in the pH of a solution upon addition of another acid or base.

The pH of a buffer depends on the ratio [base]/[acid] rather than on the particular concentration of a specific solution. The exact ratio of the base to the acid for a desired pH can be determined from the Ka value and the Henderson-Hasselbalch equation.

For example:

Suppose you wish to prepare a buffer solution to keep the pH at 4.30. You can use one of these acid/conjugate base pairs:

• HSO4/SO42- (Ka = 1.2×10-2)
• HC2H3O2/C2H3O2 (Ka = 1.8×10-5)
• HCN/CN (Ka = 4.0×10-10)

Which pair should be used? What amount of acid and base should you use to create the buffer?

Solution:

The desired pH = 4.30, so:

[H+] = 10-pH = 10-4.30 = 5.0 x 10-5 M

Of the acids listed, the Ka value for acetic acid is closest to the desired hydrogen ion concentration. Therefore, you need only to adjust the ratio of [C2H3O2]/[HC2H3O2] to get the desired final hydrogen ion concentration. The pKa of acetic acid is

$\text{pK}_\text{a}=-\text{log}_{10}(1.8\cdot10^{-5})=4.74$

You can then use the Henderson-Hasselbalch equation:

$\text{pH} = \text{pK}_{\text{a}} + \text{log}_{10} \left (\frac{[\text{base}]}{[\text{acid}]} \right )$ Acetic acid: Pure, laboratory-grade acetic acid.

$4.30 = 4.74 + \text{log}_{10} \left (\frac{[{\text{C}}_2{\text{H}}_{3}{\text{O}}_{2}^-]}{[\text{HC}_2{\text{H}}_{3}{O}_{2}]} \right )$

$-0.44 = \text{log}_{10} \left (\frac{[{\text{C}}_2{\text{H}}_{3}{\text{O}}_{2}^-]}{[\text{HC}_2{\text{H}}_{3}{\text{O}}_{2}]} \right )$

$\frac {0.36}{1} =\frac{[{\text{C}}_2{\text{H}}_{3}{\text{O}}_{2}^-]}{[\text{HC}_2{\text{H}}_{3}{\text{O}}_{2}]}$

To satisfy the expression, the ratio of [C2H3O2]/[HC2H3O2] must be 0.36 to 1. Therefore, if you add 0.36 mol of sodium acetate and 1.00 mol acetic acid (or any other pair of amounts such that the ratio is still 0.36 to 1) to enough water to make 1.0 L of solution, the solution will be a buffer with a pH of 4.30.

Extrapolating further from this, a buffer is most effective when the concentrations of acid and conjugate base (or base and conjugate acid) are approximately equal—in other words, when the log [base]/[acid] equals 0 and the pH equals the pKa. This is due to the change that occurs when another acid or base is added to the buffer. The change is minimized if the concentrations of acid and conjugate base are equal. The more the ratio needs to differ to achieve the desired pH, the less effective the buffer. As a general rule of thumb, the relative amounts of acid and base in a buffer should not differ by more than tenfold.

## Absolute Concentrations of the Acid and Conjugate Base

For an effective buffer, there must be enough acid/conjugate base to consume all newly added ions so that the pH is maintained.

### Learning Objectives

Calculate the final pH of a solution when a strong acid or base is added to a buffer solution.

### Key Takeaways

#### Key Points

• The pH of an effective buffer changes very little when a small amount of strong acid or base is added to it.
• The change in the pH of a buffer upon the addition of an acid or base can be calculated using the balanced equation and the formula for the equilibrium acid dissociation constant.
• Any buffer will lose its effectiveness if too much strong acid or base is added.

#### Key Terms

• conjugate acid: The species created when a base accepts a proton.
• conjugate base: The species that is created after the donation of a proton.
• acid dissociation constant: Quantitative measure of the strength of an acid in solution; typically written as a ratio of the equilibrium concentrations.

### Identifying Acid and Conjugate Base Pairs

A buffer is an aqueous solution consisting of a mixture of a weak acid and its conjugate base or a weak base and its conjugate acid. Therefore, it is very important to be able to identify acid and conjugate base pairs. The conjugate acid is created by accepting (adding) a proton (H+) donated by the conjugate base.

8.1.3 Deduce the formula of the conjugate acid/base of any Brønsted-Lowry base/acid IB Chemistry SL – YouTube: Remember: A conjugate ACID is made by ADDING a proton (H+). So check the equation and see what product has had a proton added—it’s the conjugate acid. The conjugate base is the other product, which has had a proton removed.

A buffer’s pH changes very little when a small amount of strong acid or base is added to it. Therefore, it can be used to prevent change in the pH of a solution. Buffer solutions are used as a means of keeping pH at a nearly constant value in a wide variety of situations.

One of the main requirements of a buffer is that it have the capacity to control pH after the addition of a reasonable amount of acid or base. In other words, there must be a large-enough concentration of acetic acid in an acetic acid/acetate ion buffer, for example, to consume all of the hydroxide ions that may be added. Hydrochloric acid: A container of concentrated hydrochloric acid (HCl).

### Calculating the Final pH

A concentrated buffer can neutralize more added acid or base than a dilute buffer, because it contains more acid/conjugate base. However, any buffer will lose its effectiveness if too much strong acid or base is added.

### Example:

Calculate the pH change when you add 1.0 mL of 1.0 M HCl to 1.0 L of acetic acid/sodium acetate buffer with [HC2H3O2] = 0.70 M and [C2H3O2] = 0.60 M.

Next, calculate the pH change for a buffer with [HC2H3O2] = 7 mM (7 x 10-3 molar) and [C2H3O2] = 6 mM (6 x 10-3 molar). The Ka for acetic acid is 1.8 x 10-5.

#### Solution:

The balanced equation for the buffer is:

$\text{HC}_2\text{H}_3\text{O}_2 \rightleftharpoons \text{H}^+ + \text{C}_2\text{H}_3\text{O}_2^-$

The ICE table for the reaction is: ICE table for the reaction of acetic acid in water: ICE table showing the concentrations of acetic acid, a hydrogen ion, and the acetate ion.

The acid dissociation constant is:

$\text{K}_\text{a}=\frac{[\text{H}^+][\text{CH}_3\text{CO}^-_2]}{\text{CH}_3\text{CO}_2\text{H}]}=\frac{(\text{x})(0.60+\text{x})}{0.70-\text{x}}=1.8\times 10^{-5}$

Solving for x using the quadratic equation, we get [H+] = 2.1 x 10-5 M. Therefore, the pH for the buffer with an acid/base concentration of 0.7/0.6M is 4.68.

HCl is a strong acid that is fully ionized in water. We only need to account for the fact that it supplies [H+] and reacts completely with the base in solution. The change in the concentrations after the reaction is:

$\text{H}^+(\text{from HCl})+\text{C}_2\text{H}_3\text{O}^-_2\leftrightarrow \text{HC}_2\text{H}_3\text{O}_2$ ICE table for the addition of HCl to a solution of acetic acid: Acetic acid after the HCl is added.

Once again, using the acid dissociation constant, we can solve for x to get [H+] = 2.11 x 10-5 M. Therefore, the pH for the buffer with an acid/base concentration of 0.7/0.6M after the addition of HCl is 4.68.

Finally, we repeat the calculation for the buffer with 7/6 mM after the addition of HCl. We know from the Henderson-Hasselbalch equation that the ratio of the concentration of the buffer determines the pH rather than the concentration. Therefore, the pH of the weaker buffer before the addition of HCl is the same. ICE table for the addition of HCl to acetic acid using smaller initial concentrations.: ICE table for the buffer solution of acetic acid with 7/6 mM after the addition of HCl.

Using the same equations as above, we get [H+] = 2.80 x 10-5 M, which gives a pH of 4.54. In this case, the pH changes more dramatically.

### Buffer Range and Capacity

A buffer’s capacity is the pH range where it works as an effective buffer, preventing large changes in pH upon addition of an acid or base.

### Learning Objectives

Discuss correlation between the pKa of the conjugate acid of a buffer solution and the effective range of the corresponding buffer.

### Key Takeaways

#### Key Points

• When H+ is added to a buffer, the conjugate base will accept a proton (H+), thereby “absorbing” the H+. Similarly, when OH is added, the weak acid will donate a proton (H+).
• The buffering region is about 1 pH unit on either side of the pKaof the conjugate acid.
• A titration curve visually demonstrates buffer capacity, where the middle part of the curve is flat because the addition of base or acid does not affect the pH of the solution drastically.

#### Key Terms

• conjugate base: The species that is created after the donation of a proton.
• equivalence point: The point in a chemical reaction at which chemically equivalent quantities of acid and base have been mixed.
• conjugate acid: The species created when a base accepts a proton.
• conjugate acid-base pair: Two molecular entities differing by a single proton.

A buffer solution usually contains a weak acid and its conjugate base. When H+ is added to a buffer, the weak acid’s conjugate base will accept a proton (H+), thereby “absorbing” the H+ before the pH of the solution lowers significantly. Similarly, when OH is added, the weak acid will donate a proton (H+) to its conjugate base, thereby resisting any increase in pH before shifting to a new equilibrium point. In biological systems, buffers prevent the fluctuation of pH via processes that produce acid or base by-products to maintain an optimal pH.

Each conjugate acid-base pair has a characteristic pH range where it works as an effective buffer. The buffering region is about 1 pH unit on either side of the pKa of the conjugate acid. The midpoint of the buffering region is when one-half of the acid reacts to dissociation and where the concentration of the proton donor (acid) equals that of the proton acceptor (base). In other words, the pH of the equimolar solution of acid (e.g., when the ratio of the concentration of acid and conjugate base is 1:1) is equal to the pKa. This represents the point in the titration that is halfway to the equivalence point. This region is the most effective for resisting large changes in pH when either acid or base is added.

A titration curve visually demonstrates buffer capacity. The middle part of the curve is flat because the addition of base or acid does not affect the pH of the solution drastically. This is the buffer zone. However, once the curve extends out of the buffer region, it will increase tremendously when a small amount of acid or base added to the buffer system. If too much acid is added to the buffer, or if the concentration is too strong, extra protons remain free and the pH will fall sharply. This effect demonstrates the buffer capacity of the solution. Titration curve for the addition of NaOH to oxalic acid: Shows the equivalence point and maximized buffering region for the addition of NaOH to oxalic acid.