Chemistry

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The pH Scale

We usually deal with acid / base solution in the concentration range 10^-1 to 10^-2M. To express the strength of such low concentrations, Sorensen introduced a logarithmic scale known as the pH scale. The term pH is derived from the French word ‘Purissance de hydrogene’ meaning, the power of hydrogen. pH of a solution is defined as the negative logarithm of base 10 of the molar concentration of the hydronium ions present in the solution.

pH = – log₁₀[H₃O⁺] …………. (8.5)

The concentration of H₃O⁺ in a solution of known pH can be calculated using the following expression.

[H₃O⁺] = 10^-pH (or) [H₃O⁺] = antilog of (-pH) …………. (8.6)

Similarly, pOH can also be defined as follows

pOH = -log₁₀[OH^–] …………….. (8.7)

As discussed earlier, in neutral solutions, the concentration of [H₃O⁺] as well as [OH⁺] is equal to 1 × 10^-7M at 25°C . The pH of a neutral solution can be calculated by substituting this H₃O⁺ concentration in the expression (8.5)

pH = – log₁₀[H₃O⁺]
= – log₁₀10^-7
= (-7)(-1)log₁₀10 = +7(1) = 7 [∵log₁₀¹⁰ = 1]

Similary, we can calculate the pOH of a neutral solution using the expression (8.7), it is also equal to 7. The negative sign in the expression (8.5) indicates that when the concentration of [H₃O⁺] increases the pH value decreases.

For example, if the [H₃O⁺] increases from to 10^-7 to 10^-5M the pH value of the solution decreases from 7 to 5. We know that in acidic solution, [H₃O⁺]>[OH^–], i.e; [H₃O⁺]>10^-7. So, we can conclude that acidic solution should have pH value less than 7 and basic solution should have pH value greater than 7.

Relation Between pH and pOH

A relation between pH and pOH can be established using their following definitions

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Ionisation of Water

We have learnt that when an acidic or a basic substance is dissolved in water, depending upon its nature, it can either donate (or) accept a proton. In addition to that the pure water itself has a little tendency to dissociate. i.e, one water molecule donates a proton to an another water molecule. This is known as auto ionisation of water and it is represented as below.

In the above ionisation, one water molecule acts as an acid while the another water molecule acts as a base. The dissociation constant for the above ionisation is given by the following expression

…………… (8.3)

The concentration of pure liquid water is one. i.e, [H₂O]² = 1
∵ K_w = [H₃O⁺][OH^–] …………. (8.4)

Here, K_w represents the ionic product (ionic product constant) of water.

It was experimentally found that the concentration of H₃O⁺ in pure water is 1 × 10^-7 at 25°C. Since the dissociation of water produces equal number of H₃O⁺ and OH^–, the concentration of OH^– is also equal to 1 × 10^-7 at 25°C.

Therefore, the ionic product of water at 25°C is

K_W = [H₃O]⁺[OH^–] …………. (8.4)
K_W = (1 × 10^-7)(1 × 10^-7)
= 1 × 10^-14.

Like all equilibrium constants, K_w is also a constant at a particular temperature. The dissociation of water is an endothermic reaction. With the increase in temperature, the concentration of H₃O⁺ and OH^– also increases, and hence the ionic product also increases.

In neutral aqueous solution like NaCl solution, the concentration of H₃O⁺ is always equal to the concentration of OH^– whereas in case of an aqueous solution of a substance which may behave as an acid (or) a base, the concentration of H₃O⁺ will not equal to
[OH^–].

We can understand this by considering the aqueous HCl as an example. In addition to the auto ionisation of water, the following equilibrium due to the dissociation of HCl can also exist.

HCl + H₂O ⇄ H₃O⁺ + Cl^–

In this case, in addition to the auto ionisation of water, HCl molecules also produces H₃O⁺ ion by donating
a proton to water and hence [H₃O⁺]>[OH^–]. It means that the aqueous HCl solution is acidic. Similarly, in basic solution such as aqueous NH₃, NaOH etc…. [OH^–]>[H₃O⁺].

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Strength of Acids and Bases

The strength of acids and bases can be determined by the concentration of H₃O⁺ (or) OH^– produced per mole of the substance dissolved in H₂O. Generally we classify the acids/bases either as strong or weak. A strong acid is the one that is almost completely dissociated in water while a weak acid is only partially dissociated in water.

Let us quantitatively define the strength of an acid (HA) by considering the following general equilibrium.

The equilibrium constant for the above ionisation is given by the following expression

………… (8.1)

We can omit the concentration of H₂O in the above expression since it is present in large excess and essentially unchanged.

……………. (8.2)

Here, K_a is called the ionisation constant or dissociation constant of the acid. It measures the strength of an acid. Acids such as HCl, HNO₃ etc… are almost completely ionised and hence they have high K_a value (K_a for HCl at 25°C is 2 × 10⁶).

Acids such as formic acid (K_a = 1.8 × 10^-4 at 25°C), acetic acid (1.8 × 10^-5 at 25°C) etc.. are partially ionised in solution and in such cases, there is an equilibrium between the unionised acid molecules and their dissociated ions. Generally, acids with K_a value greater than ten are considered as strong acids and less than one considered as weak acids.

Let us consider the dissociation of HCl in aqueous solution,

As discussed earlier, due to the complete dissociation, the equilibrium lies almost 100% to the right. i.e., the Cl^– ion has only a negligible tendency to accept a proton form H₃O⁺. It means that the conjugate base of a strong acid is a weak base and vice versa. The following table illustrates the relative strength of conjugate acid – base pairs.

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Acids and Bases

The term ‘acid’ is derived from the latin word ‘acidus’ meaning sour. We have already learnt in earlier classes that acid tastes sour, turns the blue litmus to red and reacts with metals such as zinc and produces hydrogen gas. Similarly base tastes bitter and turns the red litmus to blue.

These classical concepts are not adequate to explain the complete behaviour of acids and bases. So, the scientists developed the acid – base concept based on their behaviour.

Let us, learn the concept developed by scientists Arrhenius, Bronsted and Lowry and Lewis to describe the properties of acids and bases.

Arrhenius Concept

One of the earliest theories about acids and bases was proposed by swedish chemist Svante Arrhenius. According to him, an acid is a substance that dissociates to give hydrogen ions in water. For example, HCl, H₂SO₄ etc., are acids. Their dissociation in aqueous solution is expressed as

The H⁺ ion in aqueous solution is highly hydrated and usually represented as H₃O⁺, the simplest hydrate
of proton [H(H₂O)]⁺. We use both H⁺ and H₃O⁺ to mean the same.

Similarly a base is a substance that dissociates to give hydroxyl ions in water. For example, substances like NaOH, Ca(OH)₂ etc., are bases.

Limitations of Arrhenius Concept

• Arrhenius theory does not explain the behaviour of acids and bases in non aqueous solvents such as acetone, Tetrahydrofuran etc.
• This theory does not account for the basicity of the substances like ammonia (NH₃) which do not possess hydroxyl group.

Lowry – Bronsted Theory (Proton Theory)

In 1923, Lowry and Bronsted suggested a more general definition of acids and bases. According to their concept, an acid is defined as a substance that has a tendency to donate a proton to another substance and base is a substance that has a tendency to accept a proton from other substance. In other words, an acid is a proton donor and a base is a proton acceptor.

When hydrogen chloride is dissolved in water, it donates a proton to the later. Thus, HCl behaves as an acid and H₂O is base. The proton transfer from the acid to base can be represented as

HCl + H₂O ⇄ H₃O⁺ + Cl^–

When ammonia is dissolved in water, it accepts a proton from water. In this case, ammonia (NH₃) acts as a base and H₂O is acid. The reaction is represented as

H₂O + NH₃ ⇄ NH⁺₄ + OH^–

Let us consider the reverse reaction in the following equilibrium

H₃O⁺ donates a proton to Cl^– to form HCl i.e., the products also behave as acid and base. In general,
Lowry – Bronsted (acid – base) reaction is represented as

Acid₁ + Base₂ ⇄ Acid₂ + Base₁

The species that remains after the donation of a proton is a base (Base₁) and is called the conjugate base of the Bronsted acid (Acid₁). In other words, chemical species that differ only by a proton are called conjugate acid – base pairs.

HCl and Cl^–, H₂O and H₃O⁺ are two conjugate acid – base pairs, i.e; Cl^– is the conjugate base of the acid HCl. (or) HCl is conjugate acid of Cl^–. Similarly H₃O⁺ is the conjugate acid of H₂O.

Limitations of Lowry – Bronsted Theory

(i) Substances like BF₃, AlCl₃ etc., that do not donate protons are known to behave as acids.

Lewis Concept

In 1923, Gilbert. N. Lewis proposed a more generalised concept of acids and bases. He considered the electron pair to define a species as an acid (or) a base. According to him, an acid is a species that accepts an electron pair while base is a species that donates an electron pair. We call such species as Lewis acids and bases.

A Lewis acid is a positive ion (or) an electron deficient molecule and a Lewis base is a anion (or) neutral molecule with at least one lone pair of electrons.

Les us consider the reaction between Boron tri flouride and ammonia.

Here, boron has a vacant 2p orbital to accept the lone pair of electrons donated by ammonia to form a new coordinate covalent bond. We have already learnt that in coordination compounds, the Ligands act as a Lewis base and the central metal atom or ion that accepts a pair of electrons from the ligand behaves as a Lewis acid.

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Factors Affecting the Reaction Rate

The rate of a reaction is affected by the following factors.

1. Nature and State of the Reactant
2. Concentration of the Reactant
3. Surface Area of the Reactant
4. Temperature of the Reaction
5. Presence of a Catalyst

Nature and State of the Reactant:

We know that a chemical reaction involves breaking of certain existing bonds of the reactant and forming new bonds which lead to the product. The net energy involved in this process is dependent on the nature of the reactant and hence the rates are different for different reactants.

Let us compare the following two reactions that you carried out in volumetric analysis.

1. Redox reaction between ferrous ammonium sulphate (FAS) and KMnO₄
2. Redox reaction between oxalic acid and KMnO₄

The oxidation of oxalate ion by KMnO₄ is relatively slow compared to the reaction between KMnO₄ and Fe²⁺. In fact heating is required between KMnO₄ and Oxolate ion and is carried out at around 60°C.

The physical state of the reactant also plays an important role to influence the rate of reactions. Gas phase reactions are faster as compared to the reactions involving solid or liquid reactants. For example, reaction of sodium metal with iodine vapours is faster than the reaction between solid sodium and solid iodine.

Let us consider another example that you carried out in inorganic qualitative analysis of lead salts. If you mix the aqueous solution of colorless potassium iodide with the colorless solution of lead nitrate, precipitation of yellow lead iodide take place instantaneously, whereas if you mix the solid lead nitrate with solid potassium iodide, yellow coloration will appear slowly.

Concentration of the Reactants:

The rate of a reaction increases with the increase in the concentration of the reactants. The effect of concentration is explained on the basis of collision theory of reaction rates. According to this theory, the rate of a reaction depends upon the number of collisions between the reacting molecules. Higher the concentration, greater is the possibility for collision and hence the rate.

Effect of Surface Area of the Reactant:

In heterogeneous reactions, the surface areas of the solid reactants play an important role in deciding the rate. For a given mass of a reactant, when the particle size decreases surface area increases. Increase in surface area of reactant leads to more collisions per litre per second, and hence the rate of reaction is increased. For example, powdered calcium carbonate reacts much faster with dilute HCl than with the same mass of CaCO₃ as marble.

Effect of Presence of Catalyst:

So far we have learnt, that rate of reaction can be increased to certain extent by increasing the concentration, temperature and surface area of the reactant. However significant changes in the reaction can be brought out by the addition of a substance called catalyst.

A catalyst is substance which alters the rate of a reaction without itself undergoing any permanent chemical change. They may participate in the reaction, but again regenerated at the end of the reaction. In the presence of a catalyst, the energy of activation is lowered and hence, greater number of molecules can cross the energy barrier and change over to products, thereby increasing the rate of the reaction.