# Define pH and pOH scale or chart

## Definition of the pH scale

The dissociation constant of pure water is very low. 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. Sorensen proposed the use of a term known as pH scale or chart to measure the concentration of hydrogen ion in acid and alkali solution.

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

 Concentration pH values CH⁺ = 10-1 M 1 CH⁺ = 10-14 M 14

If a solution having concentrations of H+ ion in the range of 10-1 M to 10-14 M, the pH range of this solution is 1 to 14. Thus to express the acidity in terms of pH rather than the concentration of H+ ion is more convenient and meaningful.

#### pOH for acids and alkalies

The concentration of hydroxide ion also expressed as the pOH of the alkaline solution.

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

When the acidity of a solution goes down 100 fold its pH goes up by two units.

1. Thus a solution of pH = 1, has H+ concentration 100 times greater than that of pH = 3.
2. Same way, if OH ion concentration will go down by two units then pOH goes from 13 to 11.

### pH chart for acids and bases

Now we can proceed to differentiate between neutral, acidic and basic solution on the basis of relative concentrations of H+ and OH ions. But if the concentration based on the pH of the solution, it constructed the pH and pOH chart.

#### The pH of the neutral solution

A neutral solution is one where the concentrations of H+ and OH- are equal.

∴ CH⁺ = COH⁻ = 10-7 M
or, -log (CH⁺) = -log (COH⁻) = -log (10-7) M

Agin from the definition of pH and pOH
pH = -log (CH⁺) and pOH = -log (COH⁻)

∴ pH = pOH = 7

Thus the pH for a neutral solution = 7, where pH and pOH are the same values.

#### 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
∴ pH < 7 and pOH > 7

Thus for an acidic solution pH range one to less than seven and pOH range greater than seven to fourteen.

#### pH value of the alkaline solution

In alkaline solution, the concentration of H+ less than OH

CH⁺ < COH⁻
Thus COH⁻ > 10-7 M and CH⁺ < 10-7 M
or, pOH < 7 and pH > 7

#### Ionic product of water

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

H2O ⇄ H+ + OH-

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

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

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

where CH₂O = concentrations of water and CH⁺ and COH⁻ are the concentration of hydrogen and hydroxyl ions.

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

∴ k × CH₂O = Kw = CH⁺ × COH⁻
where Kw = ionic product of water.

#### For pure water, pH + pOH = pKw = 14

Previously we see that the product of H+ and OH has constant having the value 10-14.

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

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

∴ pH + pOH = 14

#### pH scale of pure water

The concentration of H+ and OH in pure water has been determined from the ionic product of water. Ionic product of pure water =14 and the concentration of H+ and OH are the same.

pKw = pH + pOH =14
or, Kw = CH⁺ × COH⁻ =10-7 × 10-7
= 10-14

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 is endothermic

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

A specific heat absorbed from the surroundings for ionization of water. Thus it is an endothermic reaction.

$H_{2}O\xrightarrow{+13.7\,&space;Kcal}H^{+}+OH^{-}$

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

#### 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.

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

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

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

∴ CH⁺ = CHCl = 0.002 = 2×10-3 M

Thus the pH of HCl = – 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 and the concentration of hydrogen ion in 0.02 m acetic acid

$C_{H^{+}}=\sqrt{K_{a}\times&space;C_{CH_{3}COOH}}$

$=\sqrt{2\times&space;10^{-5}\times&space;2\times&space;10^{-3}}=2\times&space;10^{-4}$

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

#### A mathematical definition of the pH and pOH scales

The mathematical definition of pH and pOH scales provides a negative value when hydrogen ion when the concentration of H+ exceeds 1 M.

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