Hydronium ion concentration in molarity is more conveniently expressed on a logarithmic scale known as the pH scale. The pH of a solution is defined as the negative logarithm to base 10 of the activity aH+  ( ) of hydrogen.

In dilute solutions (< 0.01 M), activity of hydrogen ion (H+ ) is equal in magnitude to molarity represented by [H+ ].

It should be noted that activity has no units and is defined as: = [H+ ] / mol L–1

From the definition of pH, the following can be written, pH = – log aH+ = – log {[H+] / mol L–1}

Thus, an acidic solution of HCl (10–2 M) will have a pH = 2. Similarly, a basic solution of NaOH having [OH– ] =10–4 M and [H3O+ ] = 10–10 M will have a pH = 10. At 25 °C,

pure water has a concentration of hydrogen ions, [H+ ] = 10–7 M. Hence, the pH of pure water is given as: pH = –log(10–7) = 7

Acidic solutions possess a concentration of hydrogen ions, [H+ ] > 10–7 M, while basic solutions possess a concentration of hydrogen ions, [H+ ] < 10–7 M. thus,

we can summarise that

Acidic solution has pH < 7

Basic solution has pH > 7

Neutral solution has pH = 7

Kw = [H3O+ ] [OH– ] = 10–14

Taking negative logarithm on both sides of equation, we obtain

–log Kw = – log {[H3O+ ] [OH– ]}

= – log [H3O+] – log [OH– ]

= – log 10–14

pKw = pH + pOH = 14

Kw may change with temperature the variations in pH with temperature are so small.

It should be noted that as the pH scale is logarithmic, a change in pH by just one unit also means change in [H+ ] by a factor of 10. The hydrogen ion concentration, [H+] changes by a factor of 100, the value of pH changes by 2 units.

The pH of a solution can be found roughly with the help of pH paper that has different colour in solutions of different pH.

The pH in the range of 1-14 can be determined with an accuracy of ~0.5 using pH paper.

For greater accuracy pH meters are used.

pH meter is a device that measures the pH-dependent electrical potential of the test solution within 0.001 precision.

Ionisation constant of weak acid and base

At a given temperature T, Ka is a measure of the strength of the acid HX.

larger the value of Ka, the stronger is the acid.

Ka is a dimensionless quantity with the understanding that the standard state concentration of all species is 1M.

 

A general step-wise approach can be adopted to evaluate the pH of the weak electrolyte as follows:

Step 1. The species present before dissociation are identified as Brönsted-Lowry acids / bases.

Step 2. Balanced equations for all possible reactions i.e., with a species acting both as acid as well as base are written.

Step 3. The reaction with the higher Ka  is identified as the primary reaction whilst the other is a subsidiary reaction.

Step 4. Enlist in a tabular form the following values for each of the species in the primary reaction

(a) Initial concentration, c.

(b) Change in concentration on proceeding to equilibrium in terms of α, degree of ionization.

(c) Equilibrium concentration.

Step 5. Substitute equilibrium concentrations into equilibrium constant equation for principal reaction and solve for α.

Step 6. Calculate the concentration of species in principal reaction.

Step 7. Calculate pH = – log[H3O+].

 

In a weak base there is partial ionization of MOH into M+ and OH– ,.

The equilibrium constant for base ionization is called base ionization constant and is represented by Kb.

It can be expressed in terms of concentration in molarity of various species in equilibrium.

Relation between Ka and Kb

Ka and Kb represent the strength of an acid and a base.

In case of a conjugate acid-base pair, they are related in a simple manner so that if one is known, the other can be deduced.

The equilibrium constant is equal to the product of equilibrium constants Ka and Kb for the reactions added.

The equilibrium constant for a net reaction obtained after adding two (or more) reactions equals the product of  the equilibrium constants for individual.

A strong acid will have a weak conjugate base and vice-versa.

Acids like oxalic acid, sulphuric acid and phosphoric acids have more than one ionizable proton per molecule of the acid.

Ka1 and Ka2 are called the first and second ionization constants respectively of the acid H2 X.

For tribasic acids like H3PO4 have three ionization constants.

Higher order ionization constants (Ka2 , Ka3 ) are smaller than the lower order ionization constant (Ka1 ) of a polyprotic acid.

It is more difficult to remove a positively charged proton from a negative ion due to electrostatic forces.

H2CO3 as compared from a negatively charged HCO3 – .

It is more difficult to remove a proton from a doubly charged HPO4 2– anion as compared to H2PO4 – .

Polyprotic acid solutions contain a mixture of acids like H2A, HA– and A2– in case of a diprotic acid.

The extent of dissociation of an acid depends on the strength and polarity of the H-A bond.

When strength of H-A bond decreases, that is, the energy required to break the bond decreases, HA becomes a stronger acid.

When the H-A bond becomes more polar i.e., the electronegativity difference between the atoms H and A increases and

There is marked charge separation, cleavage of the bond becomes easier thereby increasing the acidity.

While comparing elements in the same group of the periodic table, H-A bond strength is a more important factor in determining acidity than its polar nature.

As the size of A increases down the group, H-A bond strength decreases and so the acid strength increases.

Elements in the same row of the periodic table, H-A bond polarity becomes the deciding factor for determining the acid strength.

As the electronegativity of A increases, the strength of the acid also  increases.