Buffer Solutions

This lesson covers: 

1. What buffers are
2. The composition and mechanism of acidic buffers
3. The composition and mechanism of basic buffers
4. The importance of buffer solutions in blood
5. How to calculate the pH of a buffer solution

Buffers resist changes in pH

A buffer is a solution that minimises alterations in pH when small quantities of acid or base are introduced.

• Buffers do not completely prevent pH changes, but they significantly reduce them.
• Buffers are effective only for limited amounts of added acid or base. When a buffer solution's capacity is exceeded, it loses its ability to resist pH changes, and the pH will change more dramatically with further additions of acid or base.
• There are two types of buffers: acidic buffers and basic buffers.

Acidic buffers contain a weak acid and its conjugate base

Acidic buffers have a pH below 7 and are created by establishing an equilibrium between a weak acid and its conjugate base.

This can be achieved in two ways:

1. Combining a weak acid with the salt of its conjugate base

• For example, a mixture of ethanoic acid (CH₃COOH) and sodium ethanoate (CH₃COONa).
• The salt completely dissociates into its constituent ions on dissolution:

CH₃COONa_(aq) ➔ CH₃COO⁻_(aq) + Na⁺_(aq)

• The weak acid undergoes only partial dissociation:

CH₃COOH_(aq) ⇌ H⁺_(aq) + CH₃COO⁻_(aq)

2. Mixing an excess of weak acid with a strong alkali

• For instance, combining excess ethanoic acid (CH₃COOH) with sodium hydroxide (NaOH).
• The base reacts completely with the acid:

CH₃COOH_(aq) + OH⁻_(aq) ➔ CH₃COO⁻_(aq) + H₂O_(l)

• Due to the excess of weak acid, some remains in the solution after the base is fully consumed. This remaining acid partially dissociates:

CH₃COOH_(aq) ⇌ H⁺_(aq) + CH₃COO⁻_(aq)

In both scenarios, an equilibrium is established between the weak acid and its conjugate base:

CH₃COOH_(aq) ⇌ H⁺_(aq) + CH₃COO⁻_(aq)

The equilibrium solution contains:

• A large amount of undissociated acid (CH₃COOH).
• A large amount of the acid's conjugate base (CH₃COO^-).
• Sufficient H⁺ ions to make the solution acidic.

How conjugate acid-base pairs stabilise pH

In a buffer system, the conjugate acid-base pair plays a crucial role in regulating the pH by neutralising excess H⁺ or OH^- ions. Let's examine how this works using the example of the CH₃COOH ⇌ H⁺_(aq) + CH₃COO^-_(aq) buffer system.

Neutralising additional H⁺ ions

When a small amount of acid is added to the buffer:

• The H⁺ concentration increases.
• The majority of these additional H⁺ ions react with CH₃COO^- to form CH₃COOH.
• This shifts the equilibrium to the left:

CH₃COOH_(aq) ⇌ H⁺_(aq) + CH₃COO^-_(aq)

• The shift in equilibrium reduces the H⁺ concentration back towards its initial value.
• As a result, the pH change is minimal.

Neutralising additional OH^- ions

Conversely, when a small amount of base (e.g., NaOH) is added to the buffer:

• The OH^- concentration rises.
• Most of these extra OH^- ions react with H⁺ to form water:

OH^-_(aq) + H⁺_(aq) ➔ H₂O_(l)

• This reaction lowers the H⁺ concentration.
• To compensate, more CH₃COOH dissociates to replenish the H⁺:

CH₃COOH_(aq) ⇌ H⁺_(aq) + CH₃COO^-_(aq)

• This shifts the equilibrium to the right.
• The H⁺ concentration rises back towards its starting value.
• Consequently, the pH change is small.

Basic buffers contain a weak base and its conjugate acid

Basic buffers, characterised by a pH greater than 7, are created by mixing a weak base with the salt of its conjugate acid. A common example is a solution of ammonia (NH₃, a weak base) and ammonium chloride (NH₄Cl, a salt of ammonia).

In this solution, the salt fully dissociates:

NH₄Cl_(aq) ➔ NH₄⁺_(aq) + Cl^-_(aq)

Additionally, some of the ammonia molecules react with water:

NH_3(aq) + H₂O_(l) ⇌ NH₄⁺_(aq) + OH^-_(aq)

As a result, the solution contains a large amount of ammonium ions (NH₄⁺) and ammonia molecules (NH₃).

The equilibrium position of this reaction shifts in response to changes in pH:

1. When a small amount of base is added, the OH^- concentration increases. Most of the extra OH^- ions react with NH₄⁺ ions to form NH₃ and H₂O, shifting the equilibrium to the left and removing OH^- ions from the solution. This minimises the change in pH.
2. When a small amount of acid is added, the H⁺ concentration increases. Some of the H⁺ ions react with OH^- ions to form H₂O, causing the equilibrium to shift to the right to replace the consumed OH^- ions. Additionally, some H⁺ ions react with NH₃ molecules to form NH₄⁺. These reactions remove most of the added H⁺ ions, minimising the change in pH.

The importance of buffer solutions in blood

Buffer solutions, particularly the carbonic acid-hydrogen carbonate buffer system, play a crucial role in regulating blood pH within the narrow range of 7.35 to 7.45, which is essential for optimal health.

The main equilibrium reaction in this system is:

H₂CO_3(aq) ⇌ H⁺_(aq) + HCO₃^-_(aq)

The body maintains this equilibrium and stabilises blood pH through two primary mechanisms: regulation of carbonic acid (H₂CO₃) levels through respiration and regulation of hydrogen carbonate ions (HCO₃^-) levels by the kidneys.

Regulation of carbonic acid levels through respiration

The levels of carbonic acid (H₂CO₃) in the blood are primarily controlled by respiration.

When the body produces excess carbon dioxide (CO₂), it reacts with water to form carbonic acid:

CO_2(aq) + H₂O_(l) ⇌ H₂CO_3(aq)

To reduce the concentration of carbonic acid, the body can exhale CO₂ through the lungs. As CO₂ is removed from the system, the equilibrium shifts to the left, favouring the decomposition of carbonic acid into carbon dioxide and water. This process helps to lower the overall carbonic acid levels in the blood.

Regulation of hydrogen carbonate levels by the kidneys

The levels of hydrogen carbonate ions (HCO₃^-) in the blood are regulated by the kidneys. When there is an excess of hydrogen carbonate ions, the kidneys filter them out of the blood and excrete them in the urine.

This removal of hydrogen carbonate ions helps to maintain the equilibrium of the buffer system and prevent the blood pH from becoming too basic.

Calculating the pH of a buffer solution

To calculate the pH of an acidic buffer, you need to know the K_a of the weak acid and the concentrations of the weak acid and its salt.

The calculation requires the following assumptions:

• The salt of the conjugate base is fully dissociated, so assume that the equilibrium concentration of A^- is equal to the initial concentration of the salt.
• HA is only slightly dissociated, so assume that its equilibrium concentration is equal to its initial concentration.

Here's an example of how to calculate the pH of a buffer solution.

Worked example 1 - Calculating the pH of a buffer solution

A buffer solution is made by adding 0.50 mol of ethanoic acid (CH₃COOH) and 0.50 mol of sodium ethanoate (CH₃COONa) to enough water to make 1.0 dm³ of solution. The K_a for ethanoic acid is 1.8 × 10^-5 mol dm^-3.

Calculate the pH of this buffer.

Step 1: K_a equation

Ka ​=[CH3​COOH][H+][CH3​COO−]​

Step 2: Rearrange K_a equation

[H+]= Ka ​× ([CH3​COO−] [CH3​COOH]​)

Step 3: Calculate [H⁺]

Since [CH₃COOH] = [CH₃COO^-], the K_a equation simplifies to:

[H⁺] = K_a = 1.8 x 10^-5 mol dm^-3

Step 4: Calculate pH

pH =−log10​[H+]=−log10​(1.8×10−5)=4.74

Therefore, the pH of the buffer solution is 4.74.

In addition to calculating the initial pH of a buffer solution, it is also important to understand how the pH changes when small amounts of acid or alkali are added. The following worked examples illustrate how to calculate the new pH of a buffer solution after such additions.

Worked example 2 - Calculating the pH of a buffer solution after adding acid

A buffer solution initially contains 0.50 mol of ethanoic acid (CH₃COOH) and 0.50 mol of sodium ethanoate (CH₃COONa) in 1.0 dm³ of solution. The K_a for ethanoic acid is 1.8×10−5 mol dm^-3. 

Calculate the new pH of this buffer after adding 10 cm³ of 2.0 mol dm^-3 hydrochloric acid (HCl).

Step 1: Conversion of cm³ into dm³

To convert from cm³ into dm³, divide by 1,000

10 cm³ = 0.010 dm³

Step 2: Calculate number of moles of HCl added

n = c × V =2.0×0.010=0.020 mol

Step 3: Calculate number of CH₃COOH and CH₃COO^- moles after addition

The added H⁺ ions from HCl will react with CH₃COO^- to form CH₃COOH:

 H⁺ + CH₃COO^- ➔ CH₃COOH



Step 4: Calculate [CH₃COOH] and [CH₃COO^-] after addition

Total volume after HCl addition = 1.010 dm³

[CH3​COOH]=Vn​=1.0100.52​=0.51 mol dm−3

[CH3​COO−]=Vn​=1.0100.48​=0.48 mol dm−3

Step 5: Rearrange K_a equation

[H+]= Ka ​× ([CH3​COO−][CH3​COOH]​)

Step 6: Substitution and correct evaluation

[H+]=(1.8×10−5)×(0.480.51​)=1.95×10−5 mol dm−3

Step 7: Calculate pH

pH =−log10​[H+]=−log10​(1.95×10−5)=4.7

Therefore, the pH of the buffer solution after addition of HCl is 4.7.

Worked example 3 - Calculating the new pH of a buffer solution after adding alkali

Consider a buffer solution containing 0.40 mol dm^-3 methanoic acid (HCOOH) and 0.60 mol dm^-3 sodium methanoate (HCOONa) in 500 cm³ of solution. The K_a for methanoic acid is 1.6×10−4 mol dm^-3.

Calculate the new pH of this buffer after adding 25 cm³ of 0.30 mol dm^-3 sodium hydroxide (NaOH).

Step 1: Conversion of cm³ into dm³

To convert from cm³ into dm³, divide by 1,000

500 cm³ = 0.500 dm³

25 cm³ = 0.025 dm³

Step 2: Calculate number of HCOOH and HCOO^- moles before addition

HCOOH:  n = c × V =0.40×0.500=0.20 mol

HCOO^-:  n = c × V =0.60×0.500=0.30 mol$

Step 3: Calculate number of moles of NaOH added

n = c × V =0.30×0.025=7.5×10−3 mol

Step 4: Calculate number of HCOOH and HCOO^- moles after addition

The added OH^- ions from NaOH will react with HCOOH to form HCOO^-:

OH^- + HCOOH ➔ HCOO^- + H₂O

Step 5: Calculate [HCOOH] and [HCOO^-] after addition

Total volume after NaOH addition = 0.525 dm³

[HCOOH]=Vn​=0.5250.1925​=0.37 mol dm−3

[HCOO−]=Vn​=0.5250.3075​=0.59 mol dm−3

Step 6: Rearrange K_a equation

[H+]= Ka ​× ([HCOO−][HCOOH]​)

Step 7: Substitution and correct evaluation

[H+]=(1.6×10−4)×(0.590.37​)=1.00×10−4 mol dm−3

Step 8: Calculate pH

pH =−log10​[H+]=−log10​(1.00×10−4)=4.0

Therefore, the pH of the buffer solution after addition of NaOH is 4.0.