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. Applications of buffers
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.

Composition and mechanism of acidic buffers

Acidic buffers, characterised by a pH below 7, are created by mixing a weak acid with one of its salts. A common example is a solution of ethanoic acid (CH₃COOH) and sodium ethanoate (CH₃COONa).

In this solution, the weak acid (ethanoic acid) only slightly dissociates:

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

On the other hand, the salt (sodium ethanoate) fully dissociates into its ions when dissolved:

CH₃COONa_(aq) ➔ CH₃COO^-_(aq) + Na⁺_(aq)

As a result, the solution contains a large amount of undissociated ethanoic acid molecules and ethanoate ions from the salt.

The equilibrium position of this reaction shifts in response to changes in the concentration of H⁺ or OH^- ions, following Le Chatelier's principle:

1. When a small amount of acid is added, the H⁺ concentration increases. Most of the extra H⁺ ions combine with CH₃COO^- ions to form CH₃COOH, shifting the equilibrium to the left and reducing the H⁺ concentration to a value close to its original level. Consequently, the pH remains relatively stable.
2. When a small amount of base (e.g., NaOH) is added, the OH^- concentration increases. Most of the extra OH^- ions react with H⁺ ions to form water, removing H⁺ ions from the solution. This causes more CH₃COOH to dissociate, forming H⁺ ions and shifting the equilibrium to the right. The H⁺ concentration increases until it is close to its original value, maintaining a stable pH.

Composition and mechanism of basic buffers

Basic buffers, characterized by a pH greater than 7, are created by mixing a weak base with one of its salts. 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.

Practical applications of buffers

Buffers have numerous practical applications in everyday life and various industries.

Some examples include:

1. Shampoos - Most shampoos contain a pH 5.5 buffer to prevent hair from becoming rough when exposed to alkaline conditions, keeping it smooth and shiny.
2. Biological washing powders - These products contain buffers to maintain the optimal pH for enzymes to function efficiently.
3. Biological systems - Many biological buffer systems exist in the human body to ensure that tissues are maintained at the proper pH. For example, blood must remain at a pH close to 7.4, and it contains a buffer system to maintain this narrow range.

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.