Reversible Reactions & Equilib

Cheatsheet Content

### Reversible Reactions - **Definition:** Chemical reactions where products can react to reform reactants. Represented by a double arrow ($\rightleftharpoons$). - **Examples:** - Formation of ammonia: $\text{N}_2(g) + 3\text{H}_2(g) \rightleftharpoons 2\text{NH}_3(g)$ - Dissociation of weak acids: $\text{CH}_3\text{COOH}(aq) \rightleftharpoons \text{CH}_3\text{COO}^-(aq) + \text{H}^+(aq)$ - **Characteristics:** - Never go to completion. - Both forward and reverse reactions occur simultaneously. - Eventually reach a state of dynamic equilibrium. ### Dynamic Equilibrium - **Definition:** A state in a reversible reaction where the rate of the forward reaction equals the rate of the reverse reaction. - **Key Features:** - **Dynamic:** Reactions are still occurring, but there is no net change in concentrations of reactants or products. - **Constant macroscopic properties:** Temperature, pressure, and concentrations remain constant. - **Achieved in a closed system:** No matter can enter or leave. - **Graphical Representation:** - Reactant concentrations decrease and product concentrations increase until equilibrium is reached, after which they remain constant. - Forward reaction rate decreases, reverse reaction rate increases until they become equal. ### Law of Mass Action - **Statement:** At a given temperature, the ratio of product concentrations to reactant concentrations, each raised to the power of their stoichiometric coefficients, is a constant for a reversible reaction at equilibrium. - **General Reaction:** $a\text{A} + b\text{B} \rightleftharpoons c\text{C} + d\text{D}$ - **Equilibrium Expression:** - For concentrations ($K_c$): $K_c = \frac{[\text{C}]^c[\text{D}]^d}{[\text{A}]^a[\text{B}]^b}$ - For partial pressures ($K_p$): $K_p = \frac{(P_{\text{C}})^c(P_{\text{D}})^d}{(P_{\text{A}})^a(P_{\text{B}})^b}$ - **Important Notes:** - Pure solids and pure liquids are *not* included in the equilibrium expression (their concentrations are considered constant). - $K_c$ and $K_p$ are temperature-dependent. ### Equilibrium Constant ($K$) - **Significance:** Provides a quantitative measure of the extent to which a reaction proceeds. - **Magnitude of $K$:** - **$K \gg 1$ (large $K$):** Products are favored at equilibrium. The reaction proceeds almost to completion. - **$K \approx 1$:** Significant amounts of both reactants and products are present at equilibrium. - **$K \ll 1$ (small $K$):** Reactants are favored at equilibrium. The reaction barely proceeds. - **Relationship between $K_p$ and $K_c$:** $K_p = K_c(RT)^{\Delta n}$ Where: - $R$ = ideal gas constant ($0.0821 \text{ L atm mol}^{-1} \text{ K}^{-1}$) - $T$ = absolute temperature (in Kelvin) - $\Delta n$ = (moles of gaseous products) - (moles of gaseous reactants) - **Changing the Direction of Reaction:** - If a reaction is reversed, the new equilibrium constant is the reciprocal of the original: $K' = 1/K$. - If a reaction is multiplied by a factor $n$, the new equilibrium constant is $K^n$. - If reactions are added, their equilibrium constants are multiplied. ### Applications of the Equilibrium Constant - **Predicting the Direction of a Reaction (Reaction Quotient, $Q$):** - $Q$ has the same form as $K$ but uses current (non-equilibrium) concentrations. - If $Q K$: The reaction will proceed in the reverse direction to reach equilibrium. - If $Q = K$: The system is at equilibrium. - **Calculating Equilibrium Concentrations:** - Use initial concentrations, $K$, and an ICE (Initial, Change, Equilibrium) table to determine equilibrium concentrations. - Often involves solving quadratic equations. - **Le Chatelier's Principle:** - Although not directly part of $K$, the equilibrium constant is crucial for understanding how systems respond to stresses (changes in concentration, pressure, temperature). - $K$ only changes with temperature. Changes in concentration or pressure shift the equilibrium position but do not change $K$.