Define pH and pOH scale

Definition of pH and pOH in chemistry

From the definition of pH and pOH, we were given a very good idea about acid-base properties and largely used in analytical chemistry.

Hydrogen ion plays a key role in the acid-base properties. And Hydrogen ion in acid chemistry represented as H3O+ ion or hydronium ion.

H+ + H2O → H3O+

The ionic radius of the naked hydrogen ion
= ~10-13 cm
= 10-15 m, which is very small.

Thus the charge/radius ratio ~105, which is very high.

According to Fajan’s rule, hydrogen ion plays a key role in polarizing other ions or molecules.

In H3O+ there assumed to coordinate bonds from water oxygen to the proton, thus giving the proton a helium electron configuration.

Is water is acidic or basic?

Water molecule ionizing weakly to form hydrogen ion and hydroxyl ions. Thus there will always be an equilibrium between hydrogen and hydroxyl ions in the water molecule.

H2O ⇄ H+ + OH

But when hydrogen ion solvated in water to form hydronium ion or simply hydrogen ion.

At equilibrium for dissociation of water will have its own equilibrium constant value.

k=\frac{C_{H^{+}}\times C_{OH^{-}}}{C_{H_{2}O}}

or, k\times C_{H_{2}O}=C_{H^{+}}\times C_{OH^{-}}

where CH₂O = concentrations of water solution.

But in any dilute aqueous solution, the concentration of water molecules = 55.5 moles/liter, can be taken as a constant.

Thus k × CH₂O = Kw = CH⁺ × COH⁻

where Kw = dissociation constant of water or ionic product of water.

The concentration of hydrogen ion and hydroxyl ion in pure water has been determined by 10-7 M each.

∴ Kw = CH⁺ × COH⁻
= 10-7 × 10-7
= 1.0 × 10-14 M

Thus the above relation tells us that in aqueous solution the concentration of hydrogen ion and hydroxyl ion are inversely proportional to each other.

To maintain constant Kw, if hydrogen ion concentration increases 100 fold than hydroxyl ion concentration decrease 100 fold.

Ionization of water endothermic or exothermic

Chemical reactions in which heat absorbed by the system from the surroundings are known as endothermic reactions.

Thus ionization of water into hydrogen and hydroxyl ion is an endothermic chemical reaction because heat absorbed from the surroundings for ionization of water.

H2O + 13.7 kcal → H+ + OH

Le Chatelier principle-acid base

If a system in equilibrium, a change in any factors that determine the condition of equilibrium shifts in such a way as to minimize the effect of this change.

According to Le-Chatelier’s principle, increasing temperature will facilitate dissociation and giving higher values of Kw.

TemperatureKw values
200C0.68 × 10-14
250C1.00 × 10-14
600C9.55 × 10-14

What is the definition of pH?

The dissociation constant of pure water is very low value. Thus the expression of the concentrations of hydrogen ion and hydroxyl ion of a solution in terms of such low figures not much convenient and meaningful.

So, Sorensen proposed the use of a term known as pH to measure the concentration of hydrogen ion in acid and alkali solution.

P^{H}=-log\, \left ( C_{H^{+}} \right )=log\, \frac{1}{C_{H^{+}}}

In acid chemistry, this provides the relation between the concentration of hydrogen ion in the solution and pH of this solution.

If the concentration of hydrogen ion= 10-1 M.

∴ pH = – log(10-1) = 1

When CH⁺ = 10-14 M
pH = – log(10-14) = 14

For such solutions having hydrogen ion concentration in the range of 10-1 M to 10-14 M.

Thus to express the acidity in terms of pH rather than hydrogen ion concentrations is more convenient and meaningful.

The pH of 0.01 m sulfuric acid

Sulfuric acid is a dibasic acid. Molarity of sulfuric acid = 2 × molarity of the sulfuric acid solution.

Thus 0.1 m and 0.2 N sulfuric acids are the same. So the pH of the solution

∴ pH of 0.1 or 0.2 H2SO4 = – log (0.2)
= 0.699

The study of pH identified the acidic and basic properties of the solution.

Hence with the increasing concentration of hydrogen ion, pH values decrease. If the acidity of a solution goes down 100 fold, the pH goes up by the two units.

What is the pH of a solution of 0.02 M HCl?

Hydrochloric acid is a strong electrolyte and completely dissociated in the solution.

Thus the concentration of  hydrogen ion
CH⁺ = CHCl = 0.002 = 2×10-3 M

∴ pH = – log CH⁺
= – log (2×10-3) = (3 – log2)
= 2.7

What is the pH of 0.02 m acetic acid?

Acetic acid is a weak acid. Thus the concentration of hydrogen ion in acetic acid

=\sqrt{K_{a}\times C_{CH_{3}COOH}}

=\sqrt{2\times 10^{-5}\times 2\times 10^{-3}}=2\times 10^{-4}

∴ pH of 0.002 acetic acid
= – log (CH⁺) = -log (2 × 10⁻⁴)
= 3.7

What is the pOH of the solution?

The concentration of hydroxide ion also expressed as the concentration of hydrogen ion in the solution and it is expressed as the pOH of the alkaline solution.

P^{OH}=-\, logC_{OH^{-}}=log\, \left ( \frac{1}{C_{OH^{-}}} \right )

When the acidity of a solution goes down 100 fold its pH goes up by two units. Thus a solution of pH = 1, has hydrogen ion concentration 100 times greater than that of pH = 3.

Same way for OH ions, If the pOH will go down by two units then pOH goes from 13 to 11.

Show that pH + pOH = pKw = 14

Previously we study the product of hydrogen ion and hydroxyl ion has constant.

Thus CH⁺ × COH⁻ = 10-14
or, log(CH⁺ × COH⁻) = log(10-14)
∴ log (CH⁺) + log(COH⁻) = -14

Again from the definition
– log CH⁺ = pH and -logCOH⁻ = pOH

∴ pH + pOH = 14

pH scale of acids and bases

Now we can proceed to differentiate between neutral, acidic or basic on the basis of relative concentrations of hydrogen and hydroxyl ions.

But if the concentration on the basis of the pH of the solution, it constructed the pH and pOH scale of the solution.


What is the pH value of a neutral solution?

A neutral solution is one where the concentrations of hydrogen and hydroxyl ions are equal.

Thus CH⁺ = COH⁻ = 10-7 M

From the definition of pH and pOH
– log (CH⁺) = – log (COH⁻) = – log (10-7)
= 7

So the pH and pOH of the neutral solution = 7.

pH value of an acidic solution

An acidic solution has the concentration of hydrogen ion greater then hydroxyl ion.

∴ CH⁺ 〉COH⁻
Thus CH⁺ 〉 10-7 M
and COH⁻ 〈 10-7 M

From the definition of pH and pOH
– log (CH⁺) 〉- log (10-7)
∴ pH 〈 7

– log (COH⁻) 〈 – log (10-7)
∴ pOH 〉 7

pH value of the alkaline solution


Thus COH⁻ 〉10-7 M
and CH⁺〈 10-7 M

From the definition of pH and pOH
CH⁺ 〈 10⁻⁷ M
∴ pH 〉 7

Thus a mathematical definition of pH and pOH scale provides a negative value when hydrogen ion exceeds 1 M.

However, pH measurements of such concentrated solutions are avoided as these solutions are not likely to be dissociated fully.

Thus pH and pOH scale play the key role in acid chemistry to recognize the acid-base solution. From this study, we easily detect the substances or solutions as acidic or basic.