Concept of pH and pOH scale

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pH and pOH in aqueous solution

The concept of pH and pOH plays a key role in an acid-base neutralization reaction. In aqueous solution hydrogen ion represented as H₃O⁺.

A naked hydrogen ion has a vanishingly small size ( radius ~10⁻¹³ cm =10⁻¹⁵ Å) and therefore has a very high (charge/radius) ratio(~10⁵). The hydrogen ion is most effective in polarizing other ions or molecules according to Fajan's rules.

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

pH of acid in water solution

Perchloric acid reacts vigorously with water and It gives a series of hydrates.
HClO₄ (112°C)

HClO₄, H₂O (+ 50°C)

HClO₄, 2H₂O (- 17.8°C)

HClO₄, 3H₂O (- 37°C )

HClO₄, 3.5H₂O (- 41.4°C)

Most remarkable hydrates of perchloric acid are monohydrates, melting at a much higher temperature than the covalent anhydrous acid. Monohydrates of perchloric acid very stable and can be heated to around 100⁰C without decomposition.

The monohydrate about ten times vicious then anhydrous acid. It has the same crystal lattice as the ionic ammonium perchlorate and it shows an ionic compound.
 [H₃O⁺][ClO₄]

Hydrogen ions in water in equilibrium

We know that water dissociates weakly to hydrogen ion and hydroxyl ions. Regardless of what other ions are present in water, there will always be an equilibrium between hydrogen and hydroxyl ions.

H₂O ⇄ H⁺ + OH⁻

Hydrogen ion solvated in water to form hydronium ion or simply we will write H⁺ only. Equilibrium for dissociation of water will have its own equilibrium constant.

K = ([H⁺] × [OH⁻])/[H₂O]
or, K × [H₂O] = [H⁺] × [OH⁻]


The square brackets indicate concentrations. Recognizing the fact that in any dilute aqueous solution, the concentration of water molecules (55.5 moles/liter) greatly exceeds that of any other ion, the concentration of water can is taken as a constant.

K×[H₂O] = Kw = [H⁺]×[OH⁻]

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 = [H⁺] × [OH⁻]
= 10⁻⁷ × 10⁻⁷
= 1.0 × 10⁻¹⁴ M
Concept of ionic product of water
Ionic product of water
The above relation tells us that in aqueous solution the concentration of H⁺ and OH⁻ are inversely proportional to each other.

If H⁺ concentration increases 100 fold, that of OH⁻ has to decrease 100 fold to maintain Kw constant.

Water into hydrogen and hydroxyl ion

Dissociation of water into hydrogen and hydroxyl ion is an endothermic reaction.

Endothermic reaction

Chemical reactions in which heat is absorbed by the system from the surroundings are known as endothermic reactions.
H₂O + 13.7 kcal → H⁺ + OH⁻

Le-Chatelier's Principle

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

Thus according to Le-Chatelier’s principle, increasing temperature will facilitate dissociation, thus giving higher values of Kw. The value of Kw at 20⁰ C, 25⁰ C, and 60⁰ C are 0.68×10⁻¹⁴, 1.00×10⁻¹⁴, and 9.55×10⁻¹⁴ respectively.

The pH scale of acid and alkali solutions

The dissociation of water, Kw, has such low value that expressing the concentrations of H⁺ and OH⁻ ions of a solution in terms of such low figures is not much convenient and meaningful.

Such expressions necessarily have to involve the negative power of the base 10. Sorensen proposed the use of a term known as pH, defined as:

pH = - log[H⁺] = log(1/[H⁺])

Thus for a solution having H⁺ concentration, 10⁻¹ M has a pH = 1And for a solution having H⁺ concentration, 10⁻¹⁴ M has a pH = 14.

For such solutions having H⁺ concentration in the range of 10⁻¹ M to 10⁻¹⁴ M is more convenient and meaningful to express the acidity in terms of pH rather than H⁺ concentrations.

The use of small fractions or negative exponents can thus be avoided. For monobasic acid molarity and normality are the same while they are different for poly-basic acid.

Thus 0.1 M H₂SO₄ is really 0.2 N H₂SO₄ and the pH of the solution is,

pH = -log[H⁺] = -log(0.2)
= 0.699



It follows from these relations that the lower the pH, the more acidic the solution is. If the acidity of a solution goes down 100 fold its pH goes up by the two units. For example, a solution of pH 1 has [H⁺] which is 100 times greater than that of pH 3.

How to calculate the pH of the acid solution?

0.002 M hydrochloric acid solution

Since HCl is a strong electrolyte and completely dissociated.
Thus, [H⁺] = [HCl] = 0.002= 2×10⁻³ M
∴ pH = - log[H⁺]
= - log(2×10⁻³)
= (3 - log2)
= 2.7

0.002 M sulfuric acid solution

For sulfuric acid, [H⁺] = 2[H₂SO₄]
= 2 × 0.002 = 4 × 10⁻³ M
pH = -log[H⁺] = - log(4×10⁻³)
= (3 - log4)
= 2.4

0.002 M acetic acid solution

Acetic acid [H⁺] = √(Ka× [CH₃COOH]
= √(2 × 10-5× 2 × 10⁻³)
= 2 × 10⁻⁴
Thus, pH = - log[H⁺]
= -log(2 × 10⁻⁴)
= (4 - log2)
= 3.7

pOH of an alkali solution

The corresponding expression for the hydroxide ion is,
pOH = - log[OH-]

If the acidity of a solution goes down 100 fold its pH goes up by two units. A solution of pH 1 has [H⁺] which is 100 times greater than that of pH 3. Taking the case of OH⁻ ions, the pOH will go down by two units (from 13 to 11).
The product of [H⁺] and [OH⁻] is 10⁻¹⁴ and that this has to remain constant.
Thus, [H⁺] [OH⁻] = 10⁻¹⁴
or, log[H⁺] [OH⁻] = log10⁻¹⁴
or, log[H⁺] + log[OH⁻] = -14
or, -log[H⁺] - log[OH⁻] = 14

pH + pOH = 14

We have from the definition,
pH = -log[H⁺] and pOH = -log [OH⁻]

pH scale of an acidic, basic and neutral solution

We can now proceed to differentiate between neutral, acidic or basic on the basis of relative concentrations of H⁺ and OH⁻ ions on the one hand, and on the basis of pH on the other.
pH scale of acids bases
pH scale of acids bases
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pH and pOH of a neutral solution

A neutral solution is one in which the concentrations of H+ and OH- ions are equal.
Thus, [H⁺] = [OH⁻] = 10⁻⁷ M
In terms of pH, we have the following relations,
[H⁺] = 10⁻⁷ M
or, pH = 7

pH and pOH of acidic solution

[H⁺] 〉[OH⁻]
or, [H⁺] 〉 10⁻⁷ M
and [OH⁻] 〈 10⁻⁷ M
In terms of pH, we have the following relations,
[H⁺] 〉 10⁻⁷ M
or, pH 〈 7

pH and pOH of basic solution

[H⁺]〈 [OH⁻]
or, [OH⁻] 〉10⁻⁷M
and [H⁺]〈 10⁻⁷M
In terms of pH, we have the following relations,
[H⁺] 〈 10⁻⁷ M
or, pH 〉 7

A mathematical definition of pH provides a negative value when [H⁺] exceeds 1 M. However pH measurements of such concentrated solutions are avoided as these solutions are not likely to be dissociated fully.

The concentration of such strongly acid solutions is best expressed in terms of molarity than in terms of pH.

Problems solutions

Problem

Calculate the [H⁺], [OH⁻] and pH of a solution obtained by dissolving 28 gm KOH to make 200 ml of a solution.

Solution
[OH⁻] = (28×1000)/(56×200)
= 2.5M
(Molecular Weight of KOH = 56 gm)
[H⁺] = (1 × 10⁻¹⁴)/[OH⁻]
= (1 × 10⁻¹⁴)/(2.5)
= 4 × 10⁻¹⁵
pH = - log[H⁺]
= - log4 × 10⁻¹⁵
= (15 - log4)
Problem

Calculate the [H⁺], [OH⁻] and pH of a solution prepared by diluting 20 ml of 0.1M HCl to one lit.

Solution
[H⁺] = (20 × 0.1)/1000 = 0.002 = 2×10⁻³
[OH⁻] = (1 × 10⁻¹⁴)/[H⁺]
= (1×10⁻¹⁴)/(2×10⁻³)
= 0.5 × 10⁻¹¹
pH = - log[H⁺]
= - log(2 × 10⁻³)
= (3 - log2)
= 2.7
Problem

The pH of a solution is 4.5. Calculate the concentration of H⁺ ion.

Solution
We have from the definition,
pH = - log[H⁺] = 4.5
or, log[H⁺] = - 4.5
∴ [H⁺] = 3.16 × 10⁻⁵

Concept of pH and pOH, dissociation of water, pH and pOH of the acidic, basic and neutral solution, related problems solutions

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