Acids and Bases
Arrhenius Model of Acids and Bases
The classical, or Arrhenius, model defined an acid as any substance
that liberates or yields hydrogen ions (H+) or protons in water. An
example would be hydrogen chloride, HCl, gas, which when put in
water ionizes to yield hydrogen ions, H+, and chloride ions. The
resulting water solution of ionized H+ and Cl- is known as
hydrochloric acid.
This process involving the breakdown of a substance into ions is
known as ionization.
An Arrhenius base is a substance that dissociates in water to
produce hydroxide ions, OH-. Two examples of strong, or almost
completely dissociated bases are potassium hydroxide, KOH, and
sodium hydroxide, NaOH or lye.
Brønsted-Lowry Acid-Base Model
The Arrhenius theory applies only when water is used as the solvent.
It restricts the term acid to substances yielding hydronium ions and
the term base to those yielding hydroxide ions.
Brønsted and Lowry independently proposed a much broader and
more useful concept of acids and bases. According to their model, a
Brønsted-Lowry acid is any substance capable of donating a
hydrogen ion or proton to another substance, and a Brønsted-
Lowry base is any substance capable of accepting a proton or
hydrogen from another substance. In other words, acids are proton
donors, and bases are proton acceptors.
According to this concept, any reaction involving the transfer of a
proton or H+ from one substance to another is an acid-base
reaction. Therefore, base is a proton acceptor and an acid is a
proton donor.
For example:
Notice that water can act as either an acid or as a base. For this
reason it is called amphoteric.
Some examples of acids and bases
Acid
HCl
=
H+
CH3COOH
=
H+
+ CH3COO_
NH4+
=
H+
+
NH3
H2CO3
=
H+
+
HCO3-
HCO3-
=
H+
+
CO3--
H2O
=
H+
+
OH-
H3O+
=
H+
+
H2O
Hydronium ions
Conjugate base
+
Cl-
Consider HCl, a gas composed of polar covalent molecules. When
HCl gas is passed through water we achieve the classic substance,
hydrochloric acid, HCl(aq). The original gas does not have any of the
properties of the resulting solution. It is reasonable to assume that
molecules of HCl react with the water to produce ions. It is these
ions that ultimately give the water and HCl solution it's acidic
properties.
The reaction above consists of a breaking away of a proton, H+, from
the HCl molecules. A stable co-ordinate bond is formed when a
proton, H+, shares a pair of electrons with an oxygen atom of the
highly polar water molecule. A hydrated proton, called the
hydronium ion, H3O+, is formed.
Concentrated vs. Dilute; Strong vs. Weak:
These terms are often the most misused in chemistry. Concentrated
and dilute refer to the concentration of an acidic or basic substance
in a solvent. eg. 16 M HCl is more concentrated than a 0.5 M
solution of the same acid.
Strong and weak refer to the ability of an acid or base to dissociate.
A strong acid will dissociate completely in water to form hydronium
ions. i.e. 100% of it will form H3O+. A weak acid or base will only
dissociate to a certain percentage. Often a very small percentage
only.
Strong and Weak Bases
NH3(aq) is a poor conductor of electricity when compared with
NaOH(aq). This means that the degree of dissociation of NH3 in
water is relatively small when compared with that of the NaOH.
A base which is only slightly dissociated in aqueous solution is called
a weak base; one which is highly dissociated is called a strong base.
All the strong bases happen to be inorganic, that is, the NaOH, KOH,
RbOH group. Even Ca(OH)2 and Ba(OH)2 are considered to be strong
bases. All of the rest are too insoluble to provide a significant [OH-]
in water.
The double arrow convention should be used when
dealing with a weak base. A single arrow is to be used when
showing the dissociation of a strong base since for all practical
purposes, dissociation is 100% complete. i.e., a water solution made
from NaOH(s) will have no molecules of NaOH in it. The NaOH will
be completely ionized into Na+ and OH-.
The pH Scale
Every aqueous solution is either acidic, basic or neutral. There is a
quantitative relationship between the concentration of hydronium
and hydroxide ions in the solution.
The pH scale is a numerical scale which, for most applications
extends from 0 through to 14. The numbers on the scale represent
the relative acidity of solutions and can be converted into actual
hydronium ion concentrations. The brackets as usual denote molar
concentrations.
The pH scale is based on the self-ionization of pure water. Two
water molecules will sometimes combine into hydronium and
hydroxide ions.
Pure water is considered to neutral and the hydronium ion
concentration is 1.0 x 10-7 mol/L which is equal to the hydroxide ion
concentration.
The equilibrium law for this reaction at 25oC should be:
You will please note that at neutrality the molarity of the hydronium
ion is 10-7. The 7 plays a part in the pH scale by indicating neutrality.
The scale reaches a maximum at 14. Please note again that the
hydronium and hydroxide concentrations multiply out to 10-14 M.
The pH scale was derived around this relationship:
So the pH is the -log of the [hydronium ion].
pH
[H3O+]
[OH-]
pOH
1
10-1
10-13
13
2
10-2
10-12
12
3
10-3
10-11
11
4
10-4
10-10
10
5
10-5
10-9
9
6
10-6
10-8
8
7
10-7
10-7
7
8
10-8
10-6
6
9
10-9
10-5
5
10
10-10
10-4
4
11
10-11
10-3
3
12
10-12
10-2
2
13
10-13
10-1
1
The pH of a solution may be determined by the use of an electronic
instrument known as a pH meter, or through the use of chemical
indicators. Acid-base indicators are dyes which undergo slight
changes in molecular structure and color when the pH value of the
solution changes.
Specific colors correspond to specific pH values. Some examples are:
litmus, phenolphthalein, bromothymol blue, etc. There is a list of
acid-base indicators in the databook.
Sample Problems
What is the pH of an HCl solution which has a [H3O+] = 1.0 x 10-3?
pH = -log[H3O+] = -log[1.0 x 10-3] = -(-3) = 3
What is the pH of an acetic acid solution whose [H3O+]=2.5 x 10-4?
What is the hydronium concentration of nitric acid if the pH=4.0?
[H3O+] = 10-pH = 10-(4) = 1.0 x 10-4 mol/L
What is the [H3O+] of HCl if the pH = 2.57?
What is the pH of 0.010 mol/L hydrochloric acid?
The pOH Scale
The pOH scale is the corollary of the pH scale
ie. pH + pOH = 14 You'll remember from math class that when you
multiply two numbers you only add their logs.
[H3O+]*[OH-] = (1.0 x 10-7 )*(1.0 x 10-7) = 1.0 x 10-14
or
-log[H3O+] + -log[OH-] = 7 + 7 = 14
Thus a solution that has a pH = 7 must also have a pOH = 7.
Problems
What is the pOH of a 0.010 mol/L NaOH solution?
What is it's pH?
2- What are the hydronium ion and hydroxide ion concentration of a
solution prepared by adding 1 mL of 1.0 mol/L HCl to 9 mL of water?
Assume that volumes are additive and that the 1 mol/L HCl
dissociates completely.
3- What are the hydronium ion and hydroxide ion concentrations of
a solution made by adding 1 mL of 0.1 mol/L NaOH to 9 mL of
water?
4- Find the pH, pOH, [OH-] of a 0.00010 mol/L HCl solution.
5- Find the pH of a 0.00325 mol/L NaOH solution.
6- What is the hydronium ion concentration of a solution that has a
pH = 2.6?
Dissociation of water:
From conductivity measurements, water has been shown to be very
weakly ionized and at 25°C the concentration of hydrogen ions is
only 10-7 gram equivalents per liter.
The equilibrium constant for the dissociation of water is given by:
or
Now the concentration of water to all intents and purposes is
constant, so we can write:
The ionic product of water at 25°C is, therefore,
At neutrality the pH of pure water at 25°C is 7
At other temperatures, the pH at neutrality is not 7 since K w varies
with temperature. Even a small change in temp from 37 to 40°C
causes an 8% increase in hydrogen and hydroxyl ions so that a
slight rise or fall in temp may produce a profound biological change
in a living system sensitive to hydrogen ion concentration.
Temperature [°C]
pH of neutrality
0
7.97
25
7.00
37
6.80
40
6.77
75
6.39
100
6.16
Measurement of pH:
The most convenient and reliable method for measuring pH is by the
use of a pH meter. This instrument measures the EMF of a
concentration cell using a reference electrode (Calomel reference
electrode) and a glass electrode reverseble to hydrogen ions.
The usual type of cell employed is shown below:
Glass electrode is very sensitive to pH change. The glass electrode
rapidly responds to hydrogen ion concentration and can be used in a
wide variety of media.
The electrode must be always be thoroughly washed after use and
stored in distilled water.
Standard pH solutions:
The pH meter is calibrated before use by means of a standard
solution. In the United Kingdom, potassium hydrogen phthalate is
the recommended standard; at 15°C a 0.05 M solution has a pH of
4.000. The pH at other temperatures (0 – 60°C) can be obtained
from the equation:
pH = 4.000 + ½ ( t-15 / 100)2
The meter should be calibrated with a solution whose pH is close to
that under test and several convenient standards are given below.
Primary standards for the calibration of a pH meter
Dissociation of acids and bases
Strong acids: They are completely dissociated to hydrogen ions and
the conjugate base occurs, so that the hydrogen ion concentration is
the same as that of the acid. The pH can therefore, be very easily
calculated:
In a solution of 0.01 N HCl, H concentration = HCl concentration = 0.01 N
= 10-2 N
pH = -log [10-2] = 2
Strong basis:
They are also completely dissociated .
In a solution of 0.01 N NaOH, OH concentration =
0.01 N = 10-2 N
pOH = -log [OH-]
pOH = -log [10-2] = 2
pH = pKw – pOH
pH = 14 – pOH = 14- 2 = 12
NaOH concentration =
Weak acids: Weak acids are only slightly ionized in solution and a
true ewquilibrium is established between the acid and the conjugate
base.
If HA represents a weak acid,
HA = H+ + A-
According to the law of mass action, Ka the acid dissociation
constant is defined as:
Taking negative logarithms,
This formula is known as the Henderson-Hasselbalch equation and is
valid over the pH range 4-10 where the hydrogen and hydroxyl ions
do not contribute significantly to the total ionic concentration. In
addition, the ratio of conjugate base to acid should be less than 0.1.
pKa is the negative logarithm of the acid dissociation constant of a
waek acid
Another way of defining pKa is the pH at which the concentrations
of the acid and its conjugate base are equal.
Buffer Solutions
A buffer solution is one that resists pH change on the addition of
acid or alkali. Buffer consisted of weak acid + its salt (acetic acid +
sodium acetate) or weak base + its salt (ammonium hydroxide +
ammonium chlorid). Such solutions are used in many biochemical
experiments where the pH needs to be accurately controlled.
From the Henderson-Hasselbalch equation, the pH of a buffer
solution depends on two factors; one is the pKa value and the other
the ratio of salt to acid.
Let us take as an example acetate buffers consisting of a mixture of
acetic acid and sodium acetate:
Since acetic acid is only weakly dissociated, the concentration of
acetic acid is almost the same as the amount put in the mixture;
likewise the concentration of acetate ion can be considered to be
the same as the concentration of sodium acetate placed in the
mixture since the salt is completely dissociated.
Example:
What is the pH of a mixture of 5 ml of 0.1 M sodium acetate and 4 ml
of 0.1 M acetic acid. (pKa CH3COOH = 4.76)
Solution
Example:
How is the pH changed on adding 1 ml of 0.1 N HCl to the above
mixture.
Solution
Addition of HCl provides H+ which combines with the acetate ion to
give acetic acid. This reduces the amount of acetate ion present and
increases the quantity of undissociated acetic acid, leading to an
alteration in the salt/acid ratio and hence to a change in pH.
Concentration of CH3COO- = (5/10)
x 0.1 M
- (1/10) x 0.1 M
= 0.04 M
Concentration of CH3COOH = (4/10) x 0.1 M + (1/10) x 0.1 M =
0.05 M
pH = pKa + log10 [salt] / [acid]
pH = 4.76 + log10 [0.04] / [0.05]
pH = 4.76 + (- 0.097)
pH = 4.66
The pH of the solution has been reduced from 4.86 to 4.66, a change
of only 0.2 of a unit, whereas if the HCl had been added to distilled
water, the pH would be 2. The solution has, therefore, acted as a
buffer by resisting pH change on the addition of acid.
Titration curves
When a strong base is mixed with a solution of acid and the pH
recorded, a plot of the base added against pH recorded can be
obtained and this is known as a titration curve.
Strong acid and a strong base:
There is little change in pH value on adding base until complete
neutralization when only a slight excess of base causes a large
increase in pH.
In effect, the strong acid is acting as a buffer
solution in resisting change in pH.
Example: Suppose 10 ml o.1 N HCl is titrated with 0.1N NaOH
1. Initial pH value:
[H+] = 0.1 = 1 x 10-1 g mole/L
pH = 1
2. After the addition of 5 ml of 0.1N NaOH:
On adding 5 ml of strong base, 5 ml of the HCl solution is neutralized
leaving 5 ml of 0.1N HCl in a total volume of 15 ml.
Normality of HCl = (5/15) x 0.1 = 3.33 x 10-2
pH = - log10 (3.33 x 10-2)
pH = - [log10 3.33 + (-2)]
pH = - ( 0.523-2) = 1.48
3. After the addition of 9.9 ml of 0.1N NaOH:
On adding 9.9 ml of strong base, 9.9 ml of the HCl solution
is
neutralized leaving 0.1 ml of 0.1 N HCl in a total volume of 19.9 ml.
Normality of HCl = (0.1/19.9) x 0.1 = 5.03 x 10-4
pH = - log10 (5.03 x 10-4)
pH = - [log10 5.03 + (-4)]
pH = - (0.702 -4) = 3.30
4. After the addition of 10.1 ml of 0.1 N NaOH:
On adding 10.1 ml of strong base, all the HCl is neutralized leaving
0.1 ml of 0.1 N NaOH in a total volume of 20.1 ml.
Normality of NaOH = (0.1 / 20.1) = 4.98 x 10-4
[OH-] = 4.98 x 10-4
pOH = 3.3
pH = 14-3.3 = 10.70
Determination of pKa
pKa values can be obtained from titration data by the following
methods:
1. By definition, the pKa value is equal to the pH at which the
acid is half titrated. The pKa can, therefore, be obtained from
a knowledge of the end point of the titration.
2. The ratio of salt / acid can be calculated from the
experimental data and a graph prepared of log10 salt / acid
against pH. The intercept on the axis is the pKa value.
Lewis Acids and Bases
Lewis had suggested in 1916 that two atoms are held together in a
chemical bond by sharing a pair of electrons. When each atom
contributed one electron to the bond it was called a covalent bond.
When both electrons come from one of the atoms it was called a
dative covalent bond or coordinate bond. The distinction is not
clear-cut as the diagram at the right shows; although the ammonia
molecule donates a pair of electrons to the hydrogen ion, the
identity of the electrons is lost in the ammonium ion that is formed.
Nevertheless, Lewis suggested that an electron-pair donor be
classified as a base and an electron-pair acceptor be classified as
acid.
MO diagram depicting the formation of a dative covalent bond
between two atoms
The modern definition of a Lewis acid is an atomic or molecular
species that has an empty atomic or molecular orbital of low energy
(LUMO) that can accommodate a pair of electrons, as illustrated in
the molecular orbital diagram at the right.