Chemical Equilibria Notes

Exam Information

• End of block quiz opens on Thursday at 05:00.
• Covers gases, gas laws, atomic and molecular structure, periodicity, molecular structure, and equilibrium.
• Thursday session will include problem solutions; students should bring questions or email them beforehand.

Chemical Equilibria

• Definition: Chemical equilibria is a state describing how to determine the concentration of different substances in a chemical reaction. It describes a condition where the rate of the forward reaction equals the rate of the reverse reaction, leading to constant concentrations of reactants and products.
• Ocean Acidification Example:
  • Increased $CO<em>2$ in the atmosphere leads to more dissolved $CO</em>2$ in oceans.
  • Equilibrium exists between gaseous and dissolved $CO_2$.
  • Dissolved $CO<em>2$ affects concentrations of protons ($H^+$, hydrogen carbonate ($HCO</em>3^−$), and carbonate ($CO_3^{2−}$).
  • More dissolved $CO_2$ results in more $H^+$, increasing acidity.
  • Combustion of fossil fuels increases atmospheric $CO_2$.
  • Ocean acidification dissolves coral, harming marine ecosystems.

Reversible Reactions

• Most reactions are reversible, meaning products can revert to reactants.
• Chemical Kinetics: Deals with reaction rates (how fast reactions occur).
• Reactions do not truly "finish"; they reach equilibrium where forward and reverse rates are equal.
• Rate equations include a constant related to speed and molar concentration.
• Square brackets denote concentration in moles per liter (mol/L).
• Reaction rate depends on concentration; more reactant typically leads to a faster reaction.
• At equilibrium, forward and reverse reaction rates are equal, and no further macroscopic change is observed.
• Equilibrium position is influenced by temperature and pressure.

Dynamic Equilibrium

• Reactions are in a dynamic equilibrium where forward and reverse reactions continue at equal rates.
• Example: Dinitrogen tetroxide ($N<em>2O</em>4$) gas in equilibrium with nitrogen dioxide ($NO_2$) gas.
  • $N<em>2O</em>4(g) \\rightleftharpoons 2NO_2(g)$
  • $N<em>2O</em>4$ is colorless, $NO_2$ is brown.
  • At low temperatures, the equilibrium favors $N<em>2O</em>4$ (colorless).
  • At high temperatures, the equilibrium favors $NO_2$ (brown).
• Starting with $N<em>2O</em>4$, its concentration decreases as $NO_2$ forms, until equilibrium is reached.
• The stoichiometric ratio affects the relative positions of reactant and product concentrations at equilibrium.

Equilibrium Favored Reactions

• Reactions can be product-favored (go to completion), reactant-favored, or neither.
• Product-favored reactions consume most reactants to form products.
• Reactant-favored reactions have significant amounts of reactants remaining at equilibrium.

Haber Process

• Haber Process: Production of ammonia ($NH<em>3$) from nitrogen ($N</em>2$) and hydrogen ($H_2$) gas.
  • $N<em>2(g) + 3H</em>2(g) \rightleftharpoons 2NH_3(g)$
• Starting with $N<em>2$ and $H</em>2$, ammonia forms until equilibrium is reached.
• Starting with only ammonia, it decomposes into $N<em>2$ and $H</em>2$ until the same equilibrium ratio is achieved.

Defining Units

• Concentration: Moles per liter (mol/L), denoted by square brackets.
  • Reference concentration: 1 mol/L.
• Partial Pressures:
  • Reference unit: 1 bar.

Equilibrium Constant

• Equilibrium Constant ($K$): Describes the ratio of products to reactants at equilibrium.
• For a generic reaction: $aA + bB \rightleftharpoons cC + dD$
• The equilibrium constant in terms of concentration ($K_c$) is defined as:
  • $K<em>c = \frac{([C]/C</em>0)^c([D]/C<em>0)^d}{([A]/C</em>0)^a([B]/C_0)^b}$
  • Where $C_0$ is the standard concentration (1 mol/L).
  • Simplified: $K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}$
• $K_c$ depends only on reaction stoichiometry.
• It is constant at equilibrium for a given temperature.
• $K_c$ is dimensionless and does not depend on initial concentrations.
• Spectator molecules do not affect $K_c$.
• $K_c$ is temperature-dependent; temperature must be specified.

Equilibrium Constant Examples

• Haber Reaction:
  • $N<em>2(g) + 3H</em>2(g) \rightleftharpoons 2NH_3(g)$
  • $K<em>c = \frac{[NH</em>3]^2}{[N<em>2][H</em>2]^3}$
• Another Example:
  • $4NO<em>2(g) + O</em>2(g) \rightleftharpoons 2N<em>2O</em>5(g)$
  • $K<em>c = \frac{[N</em>2O<em>5]^2}{[NO</em>2]^4[O_2]}$

Equilibrium Constant in terms of Pressures

• For gas phase reactions, can use equilibrium constant in terms of pressure ($K_p$).
• For a generic gas phase reaction: $aA(g) + bB(g) \rightleftharpoons cC(g) + dD(g)$
  • $K<em>p = \frac{(P</em>C/P<em>0)^c(P</em>D/P<em>0)^d}{(P</em>A/P<em>0)^a(P</em>B/P_0)^b}$
  • Where $P_0$ is the standard pressure (1 bar).
  • Simplified: $K<em>p = \frac{P</em>C^cP<em>D^d}{P</em>A^aP_B^b}$
• Ideal Gas Equation: $n/V = P/RT$
• Relationship between $K<em>p$ and $K</em>c$:
  • $K<em>p = K</em>c(RT/P_0)^{\Delta n}$
  • Where $\Delta n$ is the change in the number of moles of gas (products - reactants).

Using Equilibrium Constant in terms of Pressures

• Conversion between $K<em>c$ and $K</em>p$:
  • Need to pay attention to the units of $R$ and pressure.
  • Values of $R$ vary depending on pressure units (e.g., L⋅atm/mol⋅K or L⋅bar/mol⋅K).

Reactions with Solids

• For reactions involving solids, the concentration of a solid is constant and does not change during the reaction.
• Therefore, solids are not included in the equilibrium constant expression.
• Example: Oxidation of sulfur:
  • $S(s) + O<em>2(g) \rightleftharpoons SO</em>2(g)$
  • $K<em>c = \frac{[SO</em>2]^8}{[O_2]^8}$
  • Sulfur (S) is not included in the equilibrium expression because it is a solid.

Reactions with Aqueous Solutions

• For aqueous solutions, the concentration of water is considered constant in dilute solutions.
• Water is not included in the equilibrium constant expression.
• Example: Ammonia in water:
  • $NH<em>3(g) + H</em>2O(l) \rightleftharpoons NH_4^+(aq) + OH^-(aq)$
  • $K<em>c = \frac{[NH</em>4^+][OH^-]}{[NH<em>3][H</em>2O]}$
  • Water is not included in the equilibrium expression because its concentration is constant.

Tips and Tricks For Equilibria

• Reversing Reactions:
  • If a reaction is reversed, the new equilibrium constant is the inverse of the original.
  • If the original reaction has equilibrium constant $K$, the reversed reaction has equilibrium constant $1/K$.
  • Example: $N<em>2O</em>4(g) \rightleftharpoons 2NO<em>2(g)$, $K</em>1$
  • Reversed: $2NO<em>2(g) \rightleftharpoons N</em>2O<em>4(g)$, $K</em>2 = 1/K_1$
• Multiplying Reactions:
  • If a reaction is multiplied by a factor, the equilibrium constant is raised to the power of that factor.
  • Example: $N<em>2(g) + 3H</em>2(g) \rightleftharpoons 2NH<em>3(g)$, $K</em>1$
  • Multiplied by 1/2: $1/2 N<em>2(g) + 3/2 H</em>2(g) \rightleftharpoons NH<em>3(g)$, $K</em>2 = (K_1)^{1/2}$

Multi-Step Reactions

• If a reaction can be written as a series of steps, the overall equilibrium constant is the product of the equilibrium constants for each step.
• Example:
  • Step 1: $AgCl(s) \rightleftharpoons Ag^+(aq) + Cl^-(aq)$, $K_1$
  • Step 2: $Ag^+(aq) + 2NH<em>3(aq) \rightleftharpoons [Ag(NH</em>3)<em>2]^+(aq)$, $K</em>2$
  • Overall: $AgCl(s) + 2NH<em>3(aq) \rightleftharpoons [Ag(NH</em>3)<em>2]^+(aq) + Cl^-(aq)$, $K</em>3 = K<em>1 \times K</em>2$