Introduction
Chemical equilibrium is a fundamental concept in chemistry that describes the state of a reversible reaction where the rate of the forward reaction equals the rate of the backward reaction. This balance results in no net change in the concentration of reactants and products over time. Understanding chemical equilibrium is crucial for solving problems in JEE Main Chemistry, as it forms the basis for various topics, including reaction kinetics, thermodynamics, and acid-base chemistry.
Dynamic Nature of Chemical Equilibrium
Reversible Reactions
Reversible reactions are those that can proceed in both forward and backward directions. For example:
$$ \text{A} + \text{B} \rightleftharpoons \text{C} + \text{D} $$
In this reaction, A and B react to form C and D, and simultaneously, C and D react to form A and B.
Dynamic Equilibrium
At equilibrium, the concentrations of reactants and products remain constant, but the reactions continue to occur. This is known as dynamic equilibrium. The rates of the forward and backward reactions are equal, leading to a stable system.
Remember, equilibrium does not mean the reactants and products are in equal concentrations, but that their rates of formation are equal.
The Equilibrium Constant ($K$)
Expression of $K$
For a general reaction:
$$ a\text{A} + b\text{B} \rightleftharpoons c\text{C} + d\text{D} $$
The equilibrium constant ($K$) is given by:
$$ K = \frac{[\text{C}]^c [\text{D}]^d}{[\text{A}]^a [\text{B}]^b} $$
where $[\text{C}]$, $[\text{D}]$, $[\text{A}]$, and $[\text{B}]$ are the molar concentrations of the respective species at equilibrium.
Types of Equilibrium Constants
- $K_c$: Equilibrium constant in terms of concentration (mol/L).
- $K_p$: Equilibrium constant in terms of partial pressure (atm).
The relationship between $K_c$ and $K_p$ for a gaseous reaction is given by:
$$ K_p = K_c (RT)^{\Delta n} $$
where $R$ is the gas constant, $T$ is the temperature in Kelvin, and $\Delta n$ is the change in the number of moles of gas ($\Delta n = \text{moles of gaseous products} - \text{moles of gaseous reactants}$).
For the reaction $2\text{NO}_2(g) \rightleftharpoons 2\text{NO}(g) + \text{O}_2(g)$, the relationship between $K_c$ and $K_p$ can be calculated as follows:
$$ \Delta n = (2 + 1) - 2 = 1 $$
Thus,
$$ K_p = K_c (RT) $$
Le Chatelier's Principle
Le Chatelier's Principle states that if a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium moves to counteract the change.
Effects of Changing Conditions
- Concentration: Increasing the concentration of reactants shifts the equilibrium to the right (toward products), while increasing the concentration of products shifts it to the left (toward reactants).
- Pressure: For gaseous reactions, increasing pressure shifts the equilibrium toward the side with fewer moles of gas, while decreasing pressure shifts it toward the side with more moles of gas.
- Temperature: For endothermic reactions, increasing temperature shifts the equilibrium to the right, while for exothermic reactions, increasing temperature shifts it to the left.
Le Chatelier's Principle helps predict the direction of the shift but does not quantify the extent of the shift.
Reaction Quotient ($Q$)
The reaction quotient ($Q$) has the same form as the equilibrium constant but is calculated using initial concentrations or pressures.
- If $Q = K$, the system is at equilibrium.
- If $Q
< K$, the reaction will proceed in the forward direction.
- If $Q >
K$, the reaction will proceed in the backward direction.
Do not confuse $Q$ with $K$. $Q$ is calculated with initial conditions, while $K$ is calculated at equilibrium.
Factors Affecting Equilibrium
Catalysts
Catalysts increase the rate of both the forward and backward reactions equally, thus they do not affect the position of equilibrium but help the system reach equilibrium faster.
Inert Gases
Adding an inert gas at constant volume does not affect the equilibrium position because it does not change the partial pressures of the reacting gases.
Applications of Equilibrium Concepts
Solubility Product ($K_{sp}$)
For a sparingly soluble salt $AB$:
$$ AB(s) \rightleftharpoons A^+(aq) + B^-(aq) $$
The solubility product constant ($K_{sp}$) is given by:
$$ K_{sp} = [A^+][B^-] $$
For $AgCl$, $K_{sp} = [Ag^+][Cl^-]$. If $K_{sp} = 1.8 \times 10^{-10}$, and $[Ag^+] = [Cl^-] = s$, then:
$$ s^2 = 1.8 \times 10^{-10} $$
Thus,
$$ s = \sqrt{1.8 \times 10^{-10}} = 1.34 \times 10^{-5} \text{ M} $$
Common Ion Effect
The common ion effect states that the solubility of a salt decreases in the presence of a common ion. For example, the solubility of $AgCl$ decreases in the presence of $NaCl$ because $Cl^-$ ions are common to both.
Conclusion
Chemical equilibrium is a vital concept in chemistry that balances the rates of forward and backward reactions. Understanding how to manipulate and calculate equilibrium constants, apply Le Chatelier's Principle, and use the reaction quotient are essential skills for mastering this topic in JEE Main Chemistry. Practice with various problems and real-world examples to solidify your understanding and application of these principles.
