Comprehensive NEET Chemistry Formula Summary: Chapter 6 - Equilibrium

1. Key Formulae from Equilibrium
1.1 Equilibrium Constant Expressions

1. Equilibrium Constant for a General Reaction:

• For a reaction of the type $aA+bB\rightleftharpoons cC+dD$, the equilibrium constant in terms of concentration is: $K_c=\frac{[C{]}^c[D{]}^d}{[A{]}^a[B{]}^b}$
• Explanation: Here, $[A]$, $[B]$, $[C]$, and $[D]$ represent the molar concentrations of the reactants and products at equilibrium. The exponents are the stoichiometric coefficients from the balanced chemical equation.
• Units: The units of $K_c$ depend on the reaction and are typically in terms of $mol/L$ raised to the power of the difference in the sum of the stoichiometric coefficients of products and reactants.

1. Relationship between $K_c$ and $K_p$:

• For gaseous reactions, the equilibrium constant can also be expressed in terms of partial pressures ($K_p$): $K_p=K_c(RT{)}^{\Delta n}$
• Explanation: $\Delta n$ is the difference between the number of moles of gaseous products and reactants. $R$ is the gas constant, and $T$ is the temperature in Kelvin.
• Units: $R$ is usually taken as 0.0831 L·bar·K⁻¹·mol⁻¹ when dealing with pressure in bars.

1.2 Le Chatelier's Principle

1. Effect of Concentration on Equilibrium:

• If the concentration of a reactant or product in a reaction at equilibrium is changed, the system will adjust itself to counteract that change:
• Adding a Reactant: Shifts equilibrium towards the products.
• Removing a Product: Shifts equilibrium towards the products.
• Example: For the reaction $H_2(g)+I_2(g)\rightleftharpoons 2HI(g)$, if more $H_2$ is added, the equilibrium will shift right to produce more $HI$.

1. Effect of Pressure on Gaseous Equilibria:

• For reactions involving gases, increasing the pressure by decreasing the volume will shift the equilibrium towards the side with fewer moles of gas.
• Example: For the reaction $N_2(g)+3H_2(g)\rightleftharpoons 2N{H}_3(g)$, increasing pressure favors the formation of $N{H}_3$ since the product side has fewer moles of gas.

1.3 Common Ion Effect

• Definition: The shift in equilibrium caused by the addition of a compound containing an ion that is already present in the equilibrium mixture. $K_{sp}=[cation]\times [anion]$
• Example: Adding $NaCl$ to a solution of $AgCl$ reduces the solubility of $AgCl$ because of the increased concentration of the common ion $C{l}^{-}$.

1.4 Solubility Product Constant ($K_{sp}$)

• Expression: For a sparingly soluble salt, $AB$, dissociating as: $AB(s)\rightleftharpoons A^{+}(aq)+B^{-}(aq)$ The solubility product constant is given by: $K_{sp}=[A^{+}][B^{-}]$
• Explanation: $K_{sp}$ gives the product of the molar concentrations of the ions, each raised to the power of its stoichiometric coefficient in the dissolution equation.

2. Formula Derivations
2.1 Derivation of $K_p$ from $K_c$

• Start with the ideal gas law: $p=[gas]RT$.
• Substitute into the expression for $K_p$: $K_p=K_c(RT{)}^{\Delta n}$ where $\Delta n=\text{moles of gaseous products}-\text{moles of gaseous reactants}$.

2.2 Derivation of the Equilibrium Constant Expression

• Consider a general reaction: $aA+bB\rightleftharpoons cC+dD$.
• At equilibrium, the rate of the forward reaction equals the rate of the reverse reaction. The expression for $K_c$ is derived by equating these rates and simplifying to obtain the ratio of the product concentrations to the reactant concentrations, each raised to the power of their coefficients.

3. Example Applications
3.1 Example Problem on $K_c$

• Problem: For the reaction $H_2(g)+I_2(g)\rightleftharpoons 2HI(g)$ at equilibrium, $[H_2]=0.2M$, $[I_2]=0.2M$, and $[HI]=0.4M$. Calculate $K_c$.
• Solution: $K_c=\frac{[HI{]}^2}{[H_2][I_2]}=\frac{(0.4{)}^2}{(0.2)(0.2)}=4$

3.2 Application of Le Chatelier’s Principle

• Problem: What happens if the pressure is increased for the reaction $N_2(g)+3H_2(g)\rightleftharpoons 2N{H}_3(g)$?
• Solution: The equilibrium will shift towards the side with fewer moles of gas (towards $N{H}_3$), increasing the yield of ammonia.

4. Common Mistakes

• Misinterpretation of Equilibrium Constant: Students often forget that $K_c$ and $K_p$ are temperature-dependent and should not be used interchangeably unless specifically converted.
• Incorrect Unit Handling: Always check the units when calculating $K_c$ or $K_p$, especially when dealing with different phases (gases vs. aqueous).

This summary provides an essential overview of key formulae and concepts from the chapter on Equilibrium, along with practical applications, common errors, and strategies to avoid them, designed for NEET UG Chemistry preparation.