\( \newcommand{\xrightleftharpoons}[2]{\overset{#1}{\underset{#2}{\rightleftharpoons}}} \) \( \newcommand{\conc}[1]{\left[\mathrm{#1}\right]} \) \( \newcommand{\chem}[1]{\mathrm{#1}} \)

Chapter 12
Chemical Kinetics

Shaun Williams, PhD

Chemical Equilibrium

The Changes with Time in the Rates of Forward and Reverse Reactions

The rate of the forward reaction exponentially falls as the reactants get used up. The rate of the reverse reaction exponentially rises as products are produced. Evertually these rates have the same value (and from the time on) which is the time that the equilibrium is established.

Consider the following reaction at equilibrium

$$ j\chem{A}+k\chem{B}\rightleftharpoons l\chem{C}+m\chem{D} $$ $$ K=\frac{\conc{C}^l\conc{D}^m}{\conc{A}^j\conc{B}^k} $$

Conclusions About the Equilibrium Expression

Example

$$\chem{N_2(g)+3H_2(g)\rightleftharpoons 2NH_3(s)} $$ $$ \begin{align} K &= \frac{\conc{NH_3}^2}{\conc{N_2}\conc{H_2}^3} \\ K_\mathrm{P} &= \frac{\left(P_\chem{NH_3}\right)^2}{\left(P_\chem{N_2}\right)\left(P_\chem{H_2}\right)^3} \end{align} $$

The Relationship Between \(K\) and \(K_\mathrm{P}\)

$$ K_\mathrm{P}=K\left(RT\right)^{\Delta n} $$

Types of Equilibria

Heterogeneous Equilibria

$$ \chem{2KClO_3(s) \rightleftharpoons 2KCl(s)+3O_2(g)} $$ $$ K=\conc{O_2}^3 $$

The Extent of a Reaction

Reaction Quotient, \(Q\)

Set Up ICE Table

$$ \chem{Fe^{3+}(aq)+SCN^-(aq) \rightleftharpoons FeSCN^{2+}(aq)} $$ $$ \begin{align} & \chem{Fe^{3+}(aq)} & + & \chem{SCN^-(aq)} & \rightleftharpoons & \chem{FeSCN^{2+}(aq)} \\ \mathrm{Initial}\;\; & 6.00 & & 10.00 & & 0.00 \\ \mathrm{Change}\;\; & -4.00 & & -4.00 & & +4.00 \\ \mathrm{Equilibrium}\;\; & 2.00 & & 6.00 & & 4.00 \end{align} $$ $$ K=\frac{\conc{FeSCN^{2+}}}{\conc{Fe^{3+}}\conc{SCN^-}} = \frac{(4.00\,\mathrm{M})}{(2.00\,\mathrm{M})(6.00\,\mathrm{M})} = 0.333 $$

Solving Equilibrium Problems

  1. Write the balanced equation for the reaction.
  2. Write the equilibrium expression using the law of mass action.
  3. List the initial concentrations.
  4. Calculate \(Q\), and determine the direction of the shift to equilibrium.
  5. Define the change needed to reach equilibrium, and define the equilibrium concentrations by applying the change to the initial concentrations.
  6. Substitute the equilibrium concentrations into the equilibrium expression, and solve for the unknown.
  7. Check your calculated equilibrium concentrations by making sure they give the correct value of \(K\).

Le Châtelier's Principle

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