Chemical processes and physical transformations often reach a state of dynamic equilibrium where the rate of the forward process equals the rate of the reverse process. At this stage, the concentrations of reactants and products remain constant over time.
Based on the extent to which reactions proceed to reach equilibrium, they can be classified into three groups:
Equilibrium can be established in physical state transformations. These are characterized by a constant value of a physical parameter at a given temperature.
At the melting point of a substance, the solid and liquid phases coexist in dynamic equilibrium. For example, at $273\text{ K}$ and $1\text{ atm}$:
H2O (s) <=> H2O (l)
The temperature at which this occurs under standard atmospheric pressure is called the normal melting point or normal freezing point.
In a closed vessel, liquid evaporates until the rate of condensation equals the rate of evaporation:
H2O (l) <=> H2O (g)
The pressure exerted by the vapour at this stage is the equilibrium vapour pressure. The temperature at which the vapour pressure equals atmospheric pressure is the normal boiling point.
Sublimable solids establish equilibrium directly with their vapour phase in a closed system:
I2 (solid) <=> I2 (vapour)
Other examples include Camphor and Ammonium Chloride ($NH_4Cl$).
Sugar (solid) <=> Sugar (solution)
CO2 (gas) <=> CO2 (in solution)
Analogous to physical systems, chemical reactions in closed vessels attain dynamic equilibrium when the rates of forward and reverse reactions become equal.
The dynamic nature of chemical equilibrium can be demonstrated by the synthesis of ammonia using Haber's process with deuterium ($D_2$) instead of dihydrogen ($H_2$). Scrambling of hydrogen and deuterium atoms occurs, proving that both forward and reverse reactions continue to take place at equilibrium.
Aim: To visualize dynamic equilibrium using a simple water transfer model.
Materials Required: Two $100\text{ mL}$ measuring cylinders, two glass tubes of equal or different diameters.
Procedure: Fill cylinder 1 with colored water and keep cylinder 2 empty. Use the tubes to simultaneously transfer water from cylinder 1 to 2, and from cylinder 2 to 1. Repeat until the water levels in both cylinders become constant.
Observation: After several transfers, the water levels in both cylinders reach a constant state, even though water transfer continues in both directions.
Inference: This constancy represents a state of dynamic equilibrium where the rate of transfer in both directions is equal.
The Law of Mass Action states that the rate of a chemical reaction is proportional to the active masses (molar concentrations) of the reacting substances.
For a general reversible reaction:
$$aA + bB \rightleftharpoons cC + dD$$
The equilibrium constant expression is written as:
$$K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}$$
Where $[A]$, $[B]$, $[C]$, and $[D]$ are the equilibrium molar concentrations.
All reactants and products are in the same phase. For gaseous systems, the equilibrium constant can be expressed in terms of partial pressures ($K_p$):
$$K_p = \frac{(p_C)^c(p_D)^d}{(p_A)^a(p_B)^b}$$
The relationship between $K_p$ and $K_c$ is given by:
$$K_p = K_c(RT)^{\Delta n}$$
Where $\Delta n = (\text{moles of gaseous products}) - (\text{moles of gaseous reactants})$.
Reactants and products are present in more than one phase. The concentrations of pure solids and pure liquids are constant and are omitted from the equilibrium constant expression. For example, for the thermal decomposition of calcium carbonate:
$$CaCO_3(s) \rightleftharpoons CaO(s) + CO_2(g)$$
$$K_c = [CO_2(g)] \quad \text{and} \quad K_p = p_{CO_2}$$
The thermodynamic state of a system is related to the equilibrium constant by the equation:
$$\Delta G = \Delta G^\ominus + RT \ln Q$$
At equilibrium, $\Delta G = 0$ and $Q = K$, which yields:
$$\Delta G^\ominus = -RT \ln K$$
$$K = e^{-\Delta G^\ominus / RT}$$
Le Chatelier's Principle states that if a system at equilibrium is subjected to a change in concentration, temperature, or pressure, the system will shift in a direction that tends to undo or counteract the effect of that change.
Adding a reactant or removing a product shifts the equilibrium in the forward direction. Removing a reactant or adding a product shifts it in the reverse direction.
Experiment: Reaction of $Fe^{3+}$ and $SCN^-$ ions:
$$Fe^{3+}(aq) + SCN^-(aq) \rightleftharpoons [Fe(SCN)]^{2+}(aq) \quad (\text{Deep Red})$$
An increase in pressure shifts the equilibrium toward the side with fewer moles of gas. It has no significant effect on solids or liquids.
An increase in temperature favors the endothermic reaction, while a decrease in temperature favors the exothermic reaction.
Experiment: Nitrogen dioxide dimerization:
$$2NO_2(g) \rightleftharpoons N_2O_4(g) \quad \Delta H = -57.2\text{ kJ/mol}$$
A catalyst increases the rate of both forward and reverse reactions equally by lowering the activation energy. It does not affect the equilibrium composition or the value of the equilibrium constant.
Equilibrium established between ions and unionized molecules in solution is called ionic equilibrium. Substances that conduct electricity in aqueous solutions are called electrolytes.
Acids dissociate in water to give hydrogen ions ($H^+$ or hydronium ions $H_3O^+$), and bases produce hydroxyl ions ($OH^-$).
An acid is a proton donor, and a base is a proton acceptor. When an acid loses a proton, it forms its conjugate base. When a base gains a proton, it forms its conjugate acid.
An acid is an electron pair acceptor (e.g., $BF_3$, $AlCl_3$, $H^+$), and a base is an electron pair donor (e.g., $NH_3$, $H_2O$, $OH^-$).
Water undergoes self-ionization:
$$H_2O(l) + H_2O(l) \rightleftharpoons H_3O^+(aq) + OH^-(aq)$$
The ionic product constant of water is:
$$K_w = [H^+][OH^-] = 1.0 \times 10^{-14} \quad \text{at } 298\text{ K}$$
The acidity or basicity of a solution is expressed using the pH scale:
$$\text{pH} = -\log[H^+]$$
At $298\text{ K}$:
For a weak acid $HX$:
$$K_a = \frac{c\alpha^2}{1-\alpha}$$
Where $c$ is the initial concentration and $\alpha$ is the degree of ionization. Similarly, for a weak base:
$$K_b = \frac{c\alpha^2}{1-\alpha}$$
For a conjugate acid-base pair:
$$K_a \times K_b = K_w$$
The suppression of the ionization of a weak electrolyte by the addition of a strong electrolyte containing a common ion is called the common ion effect. For example, adding acetate ions to acetic acid solution decreases $[H^+]$.
The interaction of anions or cations of a salt with water to affect the pH of the solution is called salt hydrolysis:
Solutions that resist changes in pH upon dilution or the addition of small amounts of acid or alkali are called buffer solutions.
For an acidic buffer (weak acid + its salt):
$$\text{pH} = pK_a + \log\frac{[\text{Salt}]}{[\text{Acid}]}$$
For a basic buffer (weak base + its salt):
$$\text{pOH} = pK_b + \log\frac{[\text{Salt}]}{[\text{Base}]}$$
For a sparingly soluble salt $M_xX_y$ in equilibrium with its saturated solution:
$$M_xX_y(s) \rightleftharpoons xM^{p+}(aq) + yX^{q-}(aq)$$
The solubility product constant ($K_{sp}$) is given by:
$$K_{sp} = [M^{p+}]^x[X^{q-}]^y$$
If the ionic product ($I_P$) exceeds $K_{sp}$, precipitation occurs. If $I_P < K_{sp}$, more salt dissolves.