}]]}]}]}] 30:T2066,

### Introduction to Equilibrium - **Reversible Reactions:** Reactions that proceed in both forward and reverse directions simultaneously. - Represented by double arrows: $A + B \rightleftharpoons C + D$ - **Dynamic Equilibrium:** A state where the rate of the forward reaction equals the rate of the reverse reaction. - Concentrations of reactants and products remain constant, but the reactions are still occurring. ### Law of Mass Action & Equilibrium Constant ($K_c$) - **Law of Mass Action:** At a given temperature, the ratio of product of molar concentrations of products to that of reactants, with each concentration term raised to the power of its stoichiometric coefficient, is constant. - For a general reversible reaction: $aA + bB \rightleftharpoons cC + dD$ - **Equilibrium Constant, $K_c$**: $$K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}$$ - Square brackets denote molar concentrations (mol/L). - $K_c$ is constant at a given temperature. ### Equilibrium Constant for Gaseous Reactions ($K_p$) - For gaseous reactions, partial pressures can be used instead of molar concentrations. - **Partial Pressure:** Pressure exerted by individual gas in a mixture. - **Relationship between $K_p$ and $K_c$**: $$K_p = K_c(RT)^{\Delta n_g}$$ - $R$ = gas constant ($0.0831 \text{ L bar K}^{-1} \text{ mol}^{-1}$) - $T$ = temperature in Kelvin - $\Delta n_g$ = (moles of gaseous products) - (moles of gaseous reactants) ### Characteristics of Equilibrium Constant - $K_c$ is constant for a reaction at a specific temperature. - If $K_c > 10^3$: Products largely favored, reaction proceeds almost to completion. - If $K_c < 10^{-3}$: Reactants largely favored, reaction proceeds rarely. - If $10^{-3} < K_c < 10^3$: Appreciable concentrations of both reactants and products. - **Reverse Reaction:** $K_{c}' = 1/K_c$ - **Multiplying by a factor 'n':** $K_{c}'' = (K_c)^n$ - **Adding Reactions:** The overall $K_c$ is the product of individual $K_c$ values. ### Reaction Quotient ($Q_c$) - **Definition:** Calculated similarly to $K_c$, but using non-equilibrium concentrations. $$Q_c = \frac{[C]^c[D]^d}{[A]^a[B]^b} \text{ (at any time 't')}$$ - **Predicting Reaction Direction:** - If $Q_c < K_c$: Net reaction proceeds in the forward direction. - If $Q_c > K_c$: Net reaction proceeds in the reverse direction. - If $Q_c = K_c$: System is at equilibrium. ### Le Chatelier's Principle - **Statement:** If a change of condition (temperature, pressure, concentration) is applied to a system in equilibrium, the system will shift in a direction that counteracts the change. #### Effect of Concentration Change - **Adding reactant:** Equilibrium shifts to the right (forward direction). - **Removing reactant:** Equilibrium shifts to the left (reverse direction). - **Adding product:** Equilibrium shifts to the left (reverse direction). - **Removing product:** Equilibrium shifts to the right (forward direction). #### Effect of Pressure Change (for gaseous reactions) - **Increasing pressure:** Equilibrium shifts to the side with fewer moles of gas. - **Decreasing pressure:** Equilibrium shifts to the side with more moles of gas. - **Adding inert gas (at constant volume):** No effect on equilibrium. #### Effect of Temperature Change - **For Endothermic Reactions ($\Delta H > 0$):** - Increasing temperature: Equilibrium shifts to the right (forward direction). - Decreasing temperature: Equilibrium shifts to the left