Ionic equilibrium

Ionic equilibrium is an important concept of chemistry and it was developed by the Swedish chemist Svante Arrhenius. Arrhenius published his work around the year 1887. In his discovery he tell us that understanding the ionic equilibrium is very important because it is very helpful in determining the behavior of electrolytes in the Solutions and also the conductivity and reactivity of electrolytes. Understanding of ionic equilibrium has applications in various fields such as physical chemistry, Environmental science, and industrial processes. The discovery of Arrhenius is also useful in understanding the properties of solutions and in the Acid-base reactions.

Ionic Equilibrium

Ionic equilibrium refers to the state in which the concentrations of ions in a solution remain constant over time. It occurs in two types of substances.

Types of substances

Substances are of two types:

• Non-Electrolyte: Their aqueous solution or molten state does not conduct electricity. For example, a solution of urea, glucose, sugar, glycerine, etc.
• Electrolyte: Their aqueous or molten state conducts electricity.

Strong Electrolyte: These are much ionized in water, and hence show more conduction. For example, Strong acids like HCI, H₂SO₄, HNO₃, strong bases like MOH, MOH₂. For example, KOH, NaOH, etc., and salt of strong acid or strong base like NaCl, CH₃COONa, NH₄X, etc.
Weak Electrolyte: These are less ionized in water so show less conduction. For example, weak acids like CH₃COOH, HCN, H₃PO₄, H₂CO₃, weak bases like NH₄OH, and their salts like NH₂CN, CH₃COONH₄, etc.
Degree of ionization: It is the extent to which an electrolyte gets ionized in a solvent. It is shown by $\alpha$ or x.

$\alpha=\frac{\text { number of molecules dissociated }}{\text { total number of molecules }}$

$\alpha$ depends on the following factors:

• Nature of solute and solvent: For strong electrolytes, $\alpha$ is more than that for weak electrolytes.
• $\alpha$ is directly proportional to the dielectric constant of the solvent.
• The degree of dissociation of weak electrolyte ∝ Dilution
• - $\alpha \propto 1$ /Concentration
• - $\alpha \propto$ Temperature

Equilibrium constant

It is the ratio of the rate of forward and backward reaction at a particular temperature or it is the ratio of active masses of the reactants to that of active masses of products at a particular temperature raised to their stoichiometric coefficients. It is denoted by K_c or K_p. The distinction between K_eq and K_c is that the expression of K_eq involves all the species (whether they are pure solids, pure liquids, gases, solvents, or solutions) while the expression K_c involves only those species whose concentration is a variable (gases and solution). It means K_c is devoid of pure components (like pure solids and pure liquids) and solvents.

Equilibrium constant in terms of Concentration

For a reaction:
$
\begin{aligned}
& \mathrm{mA}+\mathrm{nB} \rightleftharpoons \mathrm{pC}+\mathrm{qD} \\
& \mathrm{r}_{\text {forward }} \propto[\mathrm{A}]^{\mathrm{m}}[\mathrm{B}]^{\mathrm{n}}=\mathrm{K}_{\mathrm{f}}[\mathrm{A}]^{\mathrm{m}}[\mathrm{B}]^{\mathrm{n}} \\
& \mathrm{r}_{\text {backward }} \propto[\mathrm{C}]^{\mathrm{p}}[\mathrm{D}]^{\mathrm{q}}=\mathrm{K}_{\mathrm{b}}[\mathrm{C}]^{\mathrm{p}}[\mathrm{D}]^{\mathrm{q}}
\end{aligned}
$

We know that at equilibrium
$
\begin{aligned}
& \mathrm{r}_{\mathrm{f}}=\mathrm{r}_{\mathrm{b}} \\
& \mathrm{K}_{\mathrm{f}}[\mathrm{A}]^{\mathrm{m}}[\mathrm{B}]^{\mathrm{n}}=\mathrm{K}_{\mathrm{b}}[\mathrm{C}]^{\mathrm{p}}[\mathrm{D}]^{\mathrm{q}} \\
& \frac{\mathrm{K}_{\mathrm{f}}}{\mathrm{K}_{\mathrm{b}}}=\frac{[\mathrm{C}]^{\mathrm{p}}[\mathrm{D}]^{\mathrm{q}}}{[\mathrm{A}]^{\mathrm{m}}[\mathrm{B}]^{\mathrm{n}}} \quad \text { (at constant temperature) } \\
& \frac{\mathrm{K}_{\mathrm{f}}}{\mathrm{K}_{\mathrm{b}}}=\frac{[\mathrm{C}]^{\mathrm{p}}[\mathrm{D}]^{\mathrm{q}}}{[\mathrm{A}]^{\mathrm{m}}[\mathrm{B}]^{\mathrm{n}}}=\mathrm{K}_{\mathrm{c}}
\end{aligned}
$

The above expression gives us the value of Kc as the activity or the active mass is expressed in terms of the concentrations (c) or the molarity.

Recommended topic video on ( Ionic Equilibrium)

Some Some Examples

1. The set of Ionic species formed by hydration of hydroxyl ions are :

1) $\left(\right.$ correct) $\mathrm{H}_3 \mathrm{O}_2^{-}, \mathrm{H}_5 \mathrm{O}_3^{-}, \mathrm{H}_7 \mathrm{O}_4^{-}$
2) $\mathrm{H}_5 \mathrm{O}_2^{+}, \mathrm{H}_7 \mathrm{O}_3^{+}$
3)Only $\mathrm{H}_3 \mathrm{O}_2^{-}$
4)Only $\mathrm{H}_5 \mathrm{O}_2^{+}$

Solution

As we have learned

Hydronium and hydroxyl ions -

In an aqueous solution the hydronium ion is further hydrated to give species like H₅O₂⁺, H₇O₃^+, and H₉O₄⁺ similarly hydroxyl ions are hydrated to give several ionic species like H₃O₂^-, H₅O₃^- and H₇O₄^- etc.

Hence, the answer is the option (1)

2. Which among the following is a salt but not a strong electrolyte

1) NaCl
2) KCl
3) $\left(\right.$ correct) $\mathrm{HgCl}_2$
4) NaBr

Solution

Substances that are largely dissociated to form a highly conducting solution in water are strong electrolytes. Almost all other salts are strong electrolytes.

Hence, the answer is the option (3).

3. Which among the following is NOT a weak electrolyte

1) HCN
2) $\mathrm{H}_3 \mathrm{BO}_3$
3) (correct) $\mathrm{RSO}_3 \mathrm{H}$
4) $\mathrm{NH}_4 \mathrm{OH}$

Solution

Substances that dissociate only to a small extent in an aqueous solution forming low-conducting liquid are weak electrolytes. All organic acids are weak electrolytes except Sulphonic acid (RSO₃H).

Hence, the answer is the option (3).

4. The species present in the solution when CO₂ is dissolved in water are :

$\begin{aligned} & \text { 1) (correct) } \mathrm{CO}_2, \mathrm{H}_2 \mathrm{CO}_3, \mathrm{HCO}_3^{-}, \mathrm{CO}_3^{2-} \\ & \text { 2) } \mathrm{H}_2 \mathrm{CO}_3, \mathrm{CO}_3^{2-} \\ & \text { 3) } \mathrm{HCO}_3^{-}, \mathrm{CO}_3^{2-} \\ & \text { 4) } \mathrm{CO}_2, \mathrm{H}_2 \mathrm{CO}_3\end{aligned}$

Solution

When $\mathrm{CO}_2$ is dissolved in water then, $\mathrm{H}_2 \mathrm{CO}_3$ is formed and dissociates in the manner as given below
$
\begin{aligned}
& \mathrm{H}_2 \mathrm{CO}_3 \rightleftharpoons \mathrm{H}^{+}+\mathrm{HCO}_3^{-} \\
& \mathrm{HCO}_3^{-} \rightleftharpoons \mathrm{H}^{+}+\mathrm{CO}_3^{2-}
\end{aligned}
$

All of these species will be present at equilibrium.

All of these species will be present at equilibrium.

Hence, the answer is the option (1).

5. Which of the following is the unit of ionic mobility?

1) $m V^{-1} s^{-2}$
2) $m s^{-2}$
3) $m^2 V^{-1} s^{-2}$
4) (correct) $m^2 V^{-1} s^{-1}$

Solution

Ionic Mobility is defined as the speed of an ion under one unit of potential gradient,

$\begin{aligned} & \text { Ionic Mobility }=\frac{\text { Speed of ions }}{\text { Potential gradient }} \\ & \text { Ionic Mobility }=\frac{\mathrm{m} / \mathrm{s}}{\mathrm{V} / \mathrm{m}} \\ & =\frac{\mathrm{m}^2}{\mathrm{Vs}}\end{aligned}$

Summary

Ionic equilibrium is the equilibrium established between the unionized molecules and the ions in a solution of weak electrolytes. Ionic equilibrium involves the balance between the dissociation of an ionic compound into its constituent ions and the combination of these ions into the initial compound when an ionic compound dissolves in water, it dissociates into its positive and negative ions. For example, sodium chloride (NaCl) separates into Na⁺ and Cl⁻ ions. Ions in solution can recombine to form the original ionic compound. This process is reversible and depends on the concentration of the ions. In ionic equilibrium we also study the common Ion Effect which is that the presence of a common ion in the solution can change the position of equilibrium, often reducing the solubility of a sparingly soluble salt.