Buffers and the Uses of Buffer Solutions Chemistry Tutorial

Key Concepts

A buffer, or a buffer solution, undergoes only a slight change in pH when H⁺ or OH^- ions are added to it.

A buffer, or a buffer solution, is a solution which contains either:
- equal concentrations of a weak acid and its conjugate base
  or
- equal concentrations of a weak base and its conjugate acid

Because enzymes work best over very narrow ranges of pH, buffers are commonly found in biological processes.
In the human body:
- Blood is buffered to maintain a pH of between 7.0 and 7.9
- Saliva is buffered to maintain a pH of about 6.8
- Gastric juices in the stomach are buffered to maintain a pH of between 1.6 and 1.8

Common buffer solutions include:

Buffer solution			effective pH
weak acid	and	conjugate base (added as a salt)	effective pH
acetic acid (CH₃COOH)	and	sodium acetate (CH₃COONa)	4.7
carbonic acid ( H₂CO₃)	and	sodium hydrogen carbonate (NaHCO₃)	6.4
dihydrogen phosphate (H₂PO₄^-)	and	sodium hydrogen phosphate (Na₂HPO₄)	7.2
hydrogen carbonate ( HCO₃^-)	and	sodium carbonate (Na₂CO₃)	10.3
weak base	and	conjugate acid (added as a salt)	effective pH
ammonia (NH₃)	and	ammonium chloride (NH₄Cl)	9.3

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Effect of a Buffer

In a typical experiment to determine the effectiveness of buffer solutions, a student adds 0.10 mol of H⁺ (HCl_(aq)) to 1.0 L of each of the following:

water

1.00 mol L^-1 acetic acid (ethanoic acid)

1.00 mol L^-1 acetic acid - acetate ion buffer

The pH of the solutions are measured before and after the addition of H⁺.
The results of the experiment are shown below:

at 25^oC	water	acetic acid	acetic acid- acetate buffer
pH before addition of 0.10 mol L^-1 H⁺	7.0	2.37	4.74

pH after addition of 0.10 mol L^-1 H⁺	1.0	1.00	4.66

change in pH as a result of adding 0.10 mol L^-1 H⁺	6.0	1.37	0.08

Adding acid, H⁺, decreases the pH in all the sample solutions, but by different amounts:

Adding acid to water has a huge impact on the pH

Adding acid to acetic acid has a large impact on pH

Adding acid to the acetic acid-acetate buffer has almost no impact on the pH

WHY?

First, let's look at what is happening in the unbuffered acetic acid solution.
(we've included the mathematics behind the logic in the boxes on the right hand side of the page, ignore them if you find the maths distracting)

In 1 L of 1.0 mol L^-1 acetic acid, the acetic acid molecules, CH₃COOH, are in equilibrium with acetate ions, CH₃COO^-, and hydrogen ions, H⁺:

CH₃COOH

CH₃COO^- + H⁺
but because acetic acid is a weak acid (K_a is small) it dissociates only to a very small extent so that in the 1 mol L^-1 solution there are:

≈ 1.0 mol L^-1 CH₃COOH (undissociated acid molecules)

very small amounts of CH₃COO^- and H⁺ ions
[CH₃COO^-] = [H⁺] = 4.24 × 10^-3 mol L^-1
(acetate and hydrogen ion concentration calculations are shown in the box on the right)

CH₃COOH CH₃COO^- + H⁺ K_a = 1.8 x 10^-5 [CH₃COOH] = 1.0 mol L^-1
K_a	=	[CH₃COO^-][H⁺] [CH₃COOH]
Since [H⁺] = [CH₃COO^-]
K_a	=	[H⁺][H⁺] [CH₃COOH]
1.8 × 10^-5	=	[H⁺][H⁺] [1.0]
1.8 × 10^-5	=	[H⁺]²
√1.8 × 10^-5	=	√[H⁺]²
[H⁺]	=	4.2 × 10^-3 mol L^-1

When acid, H⁺, is added to the acetic acid, the equilibrium position should shift to the left by Le Chatelier's Principle in order to consume the additional H⁺.

BUT, we added 0.10 mol of H⁺, and there are only 4.2 × 10^-3 moles of CH₃COO^- that are available to react!

That means there is going to be a lot of H⁺ in excess !

There will be a significant increase in the concentration of H⁺, [H⁺], in solution.

Which means that the pH of the acetic acid will fall
(since pH = -log₁₀[H⁺])
(pH calcuations are shown in the box on the right)

In the unbuffered acetic acid, the pH falls when acid is added to it because there is an excess of H⁺, or, in other words, because the acetate ion, CH₃COO^-, is the limiting reagent.

Unbuffered Acetic Acid
	concentration (mol L^-1)
	before 0.1 mol H⁺ added	after 0.1 mol H⁺ added
H⁺	4.2 × 10^-3	≈ 0.1
CH₃COO^-	4.2 × 10^-3	≈ 0
CH₃COOH	1.0	≈ 1.0
pH before H⁺ added = 2.4 and pH after H⁺ added = 1

What would happen if you could make an acetic acid solution in which the acetate ion was no longer the limiting reagent, that is, an acetic acid solution in which the acetate ions are in excess?

Wouldn't that mean that if you added acid, H⁺, to the solution then the extra H⁺ would react with the CH₃COO^- in excess to produce CH₃COOH ?

Wouldn't the concentration of hydrogen ions in solution then remain about the same ?

So wouldn't the pH of the solution stay about the same ?

Yes! And this solution would be called an acetic acid-acetate buffer solution !

The acetic acid-acetate buffer used in the experiment described above is a mixture that contains:

≈ 1.0 mol L^-1 CH₃COOH (undissociated acetic acid molecules)

≈ 1.0 mol L^-1 CH₃COO^- (which was added in the form of soluble sodium acetate)

and a small amount of H⁺ (from the partial dissociation of CH₃COOH)

When acid, H⁺, is added to this acetic acid-acetate buffer, the additional H⁺ can react with the CH₃COO^- which is now in excess:

H⁺ + CH₃COO^- → CH₃COOH

The concentration of undissociated CH₃COOH molecules increases.

Because acetic acid is a weak acid, it dissociates to a small extent to produce hydrogen ions:

CH₃COOH H⁺ + CH₃COO^-

So the concentration of hydrogen ions in solution, H⁺_(aq), will increase slightly.

Since pH = -log₁₀[H⁺] the pH will decrease slightly.
The pH actually falls from 4.74 ( ≈ 4.7) to 4.66 ( ≈ 4.7)
([H⁺] and pH calculations are shown in the box on the right)

Buffered Acetic Acid
K_a	=	[H⁺][CH₃COO^-] [CH₃COOH]
rearrange equation to find [H⁺]:
[H⁺]	=	K_a[CH₃COOH] [CH₃COO^-]
K_a = 1.8 × 10^-5 at 25°C :
[H⁺]	=	1.8 × 10^-5[CH₃COOH] [CH₃COO^-]
Initially, [CH₃COOH] = 1.0 mol L^-1 and [CH₃COO^-] = 1.0 mol L^-1
[H⁺]	=	1.8 × 10^-5[1.0] [1.0]
[H⁺]	=	1.8 × 10^-5 mol L^-1
and pH	=	4.74
Add 0.1 mol L^-1 H⁺ new [CH₃COO^-]=1.0-0.1=0.9 M new [CH₃COOH]=1.0+0.1=1.1 M
new [H⁺]	=	1.8 × 10^-5[1.1] [0.9]
new [H⁺]	=	2.2 × 10^-5 mol L^-1
and pH	=	4.66
Adding 0.1 M H⁺ to 1 M acetic acid-acetate buffer has little effect on the pH of the solution.

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Composition of a Buffer

We have seen above that adding acetate ions, CH₃COO^-, to acetic acid, CH₃COOH, produces a buffer solution, that is, a solution that resists changes to pH because:

Excess acetate ions consume the added H⁺ to produce more acetic acid molecules:
CH₃COO^- + H⁺ → CH₃COOH
and

acetic acid dissociates only to a very small extent, so very few H⁺ ions are produced:
CH₃COOH H⁺ + CH₃COO^-

The buffer solution resists changes to pH because the both the undissociated acid molecules (CH₃COOH) and its conjugate base (CH₃COO^-) are present in appreciable amounts in the solution.

Can we produce other buffer solutions by adding the conjugate base to the acid?

Acid-Conjugate Base Buffer

Compare the effect of adding the salt of the conjugate base (A^-) of acids of different strengths to solutions of the acid (HA):

[HA] = 0.1 mol L^-1	Strength of Acid
[HA] = 0.1 mol L^-1	strong acid	weak acid
acid dissociation equation:	fully dissociated HA → H⁺ + A^-	partially dissociated HA H⁺ + A^-
before addition of A^-	[HA] = 0	[HA] bit less than 0.1
after addition of A^-	[HA] = 0	[HA] increases a bit Le Chatelier's principle

A strong acid cannot be used to make a buffer because the strong acid completely dissociates, there are no undissociated acid molecules in solution.
Adding H⁺ to a strong acid results in an increase in H⁺ concentration and therefore a fall in pH because the H⁺ ions will not be consumed by the conjugate base to produce undissociated acid molecules.

Strong acids unsuitable for use in buffers include:
HCl, HNO₃, HBr, HI, HClO₄

A weak acid can be used to make a buffer solution because it is only partially dissociated, that is, undissociated acid molecules exist in the solution.

Weak acids are suitable for use in buffers when enough of the salt of the
conjugate base can be dissolved in solution so that the concentration
of the undissociated acid is the same as the concentration its conjugate base.

Buffer solutions can be produced using the following weak acids and the salts of their conjugate bases:

Example of a Buffer	Buffer Composition
Example of a Buffer	Weak Acid	Salt of Conjugate Base
acetic acid-acetate buffer	CH₃COOH	CH₃COONa
carbonic acid-bicarbonate buffer	H₂CO₃	NaHCO₃
dihydrogen phosphate-hydrogen phospahte buffer	NaH₂PO₄	Na₂HPO₄
bicarbonate-carbonate buffer	NaHCO₃	Na₂CO₃

Note that sodium or potassium salts are often used because the salts of Group 1 metals tend to be soluble at 25^oC in aqueous solutions.^*

Base - Conjugate Acid Buffer

Buffer solutions can also be produced using a weak base and the salt of its conjugate acid.

A base, B^-, accepts a proton from water to produce hydroxide ions, OH^- :

B^- + H₂O_(l) HB_(aq) + OH^-_(aq)

The other species produced, HB, is called the conjugate acid.

Hydroxides of Group 1 or Group 2 metals are strong bases, that is, the only species in the aqueous solution are metal cations and hydroxide ions, there are no "metal hydroxide molecules" in solution. Hydroxides of Group 1 and Group 2 metals can not be used to make a buffer.

Weak bases, such as ammonia, can be used to make a buffer solution since a solution of weak base will contain molecules of the unreacted base molecules as well as molecules of its conjugate acid.

K_b for ammonia is 1.8 × 10^-5 which is very small, so ammonia is a weak base.
The ammonium ion, NH₄⁺, is the conjugate acid of ammonia, NH₃.
The ammonia-ammonium ion buffer solution contains about equal concentrations of unreacted ammonia (NH₃) and a soluble salt of its conjugate acid (NH₄⁺).

When a base, OH^-, is added to the ammonia-ammonium ion buffer:

ammonium ion which is in excess reacts with hydroxide ions to produce ammonia:
NH₄⁺ + OH^- → NH₃ + H₂O

ammonia molecules react with water to a very small extent to produce a small amount of hydroxide ions:
NH₃ + H₂O NH₄⁺ + OH^-

The increased NH₃ concentration produces a very small increase in OH^- concentration.
Remember that pOH = -log₁₀[OH^-] and for aqueous solutions at 25° pH = 14 - pOH
so, since the [OH^-] increases slightly, pOH decreases slightly, therefore, pH increases, but only very slightly.

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Buffer Example: Carbonic Acid - Hydrogen Carbonate Ion Buffer

A buffer solution can be made using carbonic acid and hydrogen carbonate ions (also known as bicarbonate ions) because:

carbonic acid, H₂CO₃, is a weak acid, and,

hydrogen carbonate ion (or bicarbonate ion), HCO₃^-, is the conjugate base of carbonic acid

The carbonic acid - hydrogen carbonate ion buffer system is used to regulate pH in chemical systems exposed to carbon dioxide gas.

Cell respiration in your body produces carbon dioxide gas, CO_2(g).
CO_2(g) dissolves in water to form carbonic acid, H₂CO₃.
Carbonic acid dissociates to form hydrogen ions, H⁺.
If your blood wasn't buffered, the pH of your blood would steadily decrease as it became more and more acidic!

Similarly, the water in swimming pools is exposed to carbon dioxide gas in the atmosphere.
Carbon dioxide gas dissolves in the water to form carbonic acid.
The carbonic acid dissociates to form hydrogen ions.
So without buffering the pH of the pool water would decrease as it became more acidic.

In an aqueous system that is not buffered and exposed to carbon dioxide gas:

carbon dioxide, CO_2(g) dissolves to produce carbonic acid, H₂CO₃:
CO_2(g) + H₂O_(l) H₂CO_3(aq)

carbonic acid, H₂CO₃, dissociates to produce hydrogen ions, H⁺ (or oxonium, oxidanium or hydronium ions, H₃O⁺):
H₂CO_3(aq) + H₂O_(l) HCO₃^-_(aq) + H₃O⁺_(aq)

As more CO_2(g) dissolves in the water, more H₂CO_3(aq) is produced which then dissociates to produce more H₃O⁺ (or H⁺_(aq)) so the pH of the solution decreases.

The carbonic acid - hydrogen carbonate ion buffer can act to reduce the effect of dissolving CO_2(g) on the pH of the solution.
The carbonic acid - hydrogen carbonate ion buffer is produced by mixing together the weak acid, carbonic acid (H₂CO₃), and a salt of its conjugate base such as sodium hydrogen carbonate (NaHCO₃).
Enough sodium hydrogen carbonate (NaHCO₃) is added so that the concentration of hydrogen carbonate ions (HCO₃^-) in solution is about the same as the concentration of the undissociated carbonic acid molecules in solution (H₂CO₃):
In the buffer solution: [HCO₃^-] = [H₂CO₃]
By adding the conjugate base (HCO₃^-) in appreciable quantities, we introduce a way in which the addition of significant amounts of H⁺ can be consumed so that the pH of the solution can remain about the same.

In an aqueous system that is buffered by carbonic acid and hydrogen carbonate ions and exposed to carbon dioxide gas:

carbon dioxide dissolves in water to produce carbonic acid:
CO_2(g) + H₂O_(l) H₂CO_3(aq)

carbonic acid dissociates to produce hydrogen ions (or oxidanium, oxonium or hydronium ions):
H₂CO_3(aq) + H₂O_(l) HCO₃^-_(aq) + H₃O⁺_(aq)

but, instead of this resulting in a significant increase in hydrogen ion concentration as in the unbuffered solution, the substantial amount of HCO₃^- present in the buffered solution can use the increased amount of H⁺_(aq) (or H₃O⁺) to produce carbonic acid molecules:
H₃O⁺_(aq) + HCO₃^-_(aq) → H₂CO_3(aq) + H₂O_(l)
or
H⁺_(aq) + HCO₃^-_(aq) → H₂CO_3(aq)

The carbonic acid produced, H₂CO₃, then dissociates to a small extent to produce small amounts of H⁺ (or H₃O⁺):
H₂CO_3(aq) + H₂O_(l) HCO₃^-_(aq) + H₃O⁺
or
H₂CO_3(aq) HCO₃^-_(aq) + H⁺_(aq)

The increase in undissociated carbonic acid molecule concentration produces only a very small increase in the hydrogen ion concentration.
Since pH = -log₁₀[H⁺] a slight increase in [H⁺] results in a slight decrease in pH
In the buffered solution, an increase in the amount of CO_2(g) does NOT result in any significant change in the pH of the solution!

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Effective pH of a Buffer

A buffer is most effective when the concentration of the weak acid is the same as the concentration of its conjugate base, or, when the concentration of the weak base is the same as the concentration of its conjugate acid.

Consider a weak acid, HA, dissolving in water. The following equilibrium is established:

HA H⁺ + A^-

and the equilibrium expression, K_a, for this system is:

K_a

[H⁺][A^-]
[HA]

the expression can be rearranged to find the concentration of H⁺ as shown below:

K_a × [HA]
[A^-]

[H⁺]

Remember that pH = -log₁₀[H⁺]
Therefore the pH of the solution can be calculated:

-log₁₀[H⁺]

= -log₁₀(

K_a × [HA]
[A^-]

)

= -log₁₀(

K_a × [HA]
[A^-]

)

Remember that K_a is a constant for a particular acid at a particular temperature
Rearrange the equation to separate out the constant, K_a:

-log₁₀K_a -log₁₀(

[HA]
[A^-]

)

A buffer is most effective when enough of the salt of the conjugate base has been added to the solution of the weak acid so that [HA] = [A^-], so let y = [HA] = [A^-]

pH	=	-log₁₀K_a -log₁₀(	y y	)
pH	=	-log₁₀K_a -log₁₀	(1)
pH	=	-log₁₀K_a

This equation can then be used to determine the pH at which a buffer system will be most effective:

buffer				K_a (25°C)	-log₁₀K_a	= effective pH
	[weak acid]	=	[conjugate base]	K_a (25°C)	-log₁₀K_a	= effective pH
acetic acid (ethanoic acid) and acetate ion (ethanoate ion)	[ CH₃COOH ]	=	[ CH₃COO^- ]	1.8 × 10^-5	-log₁₀1.8 × 10^-5	= 4.7
carbonic acid and hydrogen carbonate ion (bicarbonate ion)	[ H₂CO₃ ]	=	[ HCO₃^- ]	4.2 × 10^-7	-log₁₀4.2 × 10^-7	= 6.4
dihydrogen phosphate ion and hydrogen phosphate ion	[ H₂PO₄^- ]	=	[ HPO₄^2- ]	6.3 × 10^-8	-log₁₀6.3 × 10^-8	= 7.2
hydrogen carbonate ion and carbonate ion	[ HCO₃^- ]	=	[ CO₃^2- ]	5.6 × 10^-11	-log₁₀5.6 × 10^-11	= 10.3

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^* Also, the ions of Group 1 metals (alkali metal ions) do not hydrolyse, that is, do not react with water.