Reversible Reactions and Chemical Equilibrium Study Notes

Reversible Reactions and Dynamic Equilibrium

• Many reactions proceed in both forward and reverse directions and are termed reversible.
• For a reaction $A + B \rightleftharpoons C + D$, equilibrium is established when the rate of the forward reaction equals the rate of the backward reaction.
• A dynamic equilibrium is characterized by a continual exchange of species with no observable change in concentration.
• Once established, the concentrations of reactants and products remain constant over time.

The Law of Mass Action

• Put forward by Guldberg and Waage.
• It states that at a constant temperature, the rate of a reaction is proportional to the active masses of each reactant.
• Active mass is interpreted as the concentration of a substance raised to a power corresponding to its stoichiometric coefficient in the balanced equation.
• For the general reaction $aA + bB \rightleftharpoons cC + dD$:
  • Rate of forward reaction: $r_1 = K_1[A]^a [B]^b$
  • Rate of backward reaction: $r_2 = K_2[C]^c [D]^d$
  • At equilibrium ($r_1 = r_2$): $K = \frac{[C]^c[D]^d}{[A]^a[B]^b}$, where $K$ is the equilibrium constant.

Homogeneous and Heterogeneous Equilibria

• Homogeneous Equilibrium: All reactants and products are in the same physical state (e.g., all gases).
• Heterogeneous Equilibrium: The substances involved are in different phases.
• In heterogeneous systems, the active mass of a solid is constant at a constant temperature because its vapor pressure is independent of the amount of solid present.
• The equilibrium constant expression for heterogeneous systems only includes gaseous species; solid and liquid species are omitted.
• Example: for $CaCO_3(s) \rightleftharpoons CaO(s) + CO_2(g)$, the equilibrium constant is determined solely by the pressure of the gas: $K_p = P(CO_2)$.

Equilibrium Constants $K_c$ and $K_p$

• $K_c$ is expressed in terms of molar concentrations ($mol\,dm^{-3}$).
• $K_p$ is expressed in terms of partial pressures for gaseous reactions.
• Relationship between $K_p$ and $K_c$ derived from the ideal gas equation ($PV = nRT$):
  • $K_p = K_c(RT)^{\Delta n}$
  • where $\Delta n = (c + d) - (a + b)$, representing the difference in stoichiometric coefficients of gaseous products and reactants.

Multiple Equilibria

• If a reaction proceeds through a series of steps (reaction mechanism), each step has its own equilibrium constant.
• The overall equilibrium constant for the reaction is the product of the equilibrium constants of the individual steps:
  • $K = K_1 \times K_2 \times ...$

Solved Problems

• Haber Process: For $N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)$ with equilibrium concentrations $[N_2] = 0.30\,mol\,L^{-1}$, $[H_2] = 0.10\,mol\,L^{-1}$, and $[NH_3] = 0.20\,mol\,L^{-1}$, the calculated $K = 1.3 \times 10^2$.
• Nitrogen Oxide Reaction: For $2NO(g) + O_2(g) \rightleftharpoons 2NO_2(g)$ where $K = 5.0 \times 10^{-5}$. If $[NO_2] = [NO]$, then $[O_2] = \frac{1}{5.0 \times 10^{-5}} = 2 \times 10^4\,mole\,L^{-1}$.
• Esterification Calculations:
  • For ethanol and acetic acid reacting to form ethyl acetate and water, starting with $138\,g$ ethanol and $120\,g$ acetic acid, the mass of ethyl acetate at equilibrium is $138.2\,g$.
  • When $2\,mol$ ethanoic acid is mixed with $1\,mol$ ethanol ($K = 4.0$), the amount of ester produced is $0.845\,mol$.
• Constant Conversion: For the reaction $2NOCl(g) \rightleftharpoons 2NO(g) + Cl_2(g)$, given $K_c = 4.4 \times 10^{-4}$ at $500\,K$, the partial pressure constant is calculated as $K_p = 1.8 \times 10^{-2}$.