Concept of pH and pOH

Concept of pH and pOH
pH scale
The concept of pH and pOH plays a key role in an acid-base neutralization reaction. In an aqueous medium, it is usually 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). It is expected to be the most effective in polarizing other ions or molecules according to Fajan's rules.

In HO₃⁺ there are assumed to coordinate bonds from water oxygen to the proton, thus giving the proton a helium electronic configuration.

Evidence of pH concept

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

HClO₄, H₂O (+ 50°C)

HClO₄, 2H₂O (- 17.8°C)

HClO₄, 3H₂O (- 37°C )

HClO₄, 3.5H₂O (- 41.4°C)

Of these hydrates the most remarkable is the monohydrate, melting at the much higher temperature than the covalent anhydrous acid. It is very stable and can be heated to around 100⁰C without decomposition.

The monohydrate is about ten times vicious as the anhydrous acid. It has the same crystal lattice as the ionic ammonium perchlorate, showing that it is an ionic compound, [H₃O⁺][ClO₄].

Water as an acid and as a base

We know that water dissociates weakly to H⁺ and OH⁻ ions. Regardless of what other ions are present in water, there will always be an equilibrium between H⁺ and OH⁻ ions.

H₂O ⇄ H⁺ + OH⁻

The proton, however, will be solvated and is usually written as [H₃O⁺]. For simplicity, we will write H⁺ only. The above equilibrium 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, [H₂O] can be taken as a constant. Hence,

K×[H₂O] = Kw = [H⁺]×[OH⁻]

Where Kw is the dissociation constant of water (ionic product of water). The value of H⁺ in pure water has been determined as 10⁻⁷ M so that Kw becomes,

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.

Dissociation of water into H⁺ and OH⁻

Dissociation of water into H⁺ and OH⁻ ions are an endothermic reaction.

Endothermic reaction

The 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.

Concept of pH

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.

Calculation of pH

0.002 M HCl 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 H₂SO₄ solution

For H₂SO₄, [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

For 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

Concept of pOH

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⁻]

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 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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