Representations of Equilibrium (College Board AP Chemistry)

A₂ (g) + 2B (g) ⇌ A₂B₂ (g)

Gases A₂ and B are placed in an empty 1.00 L rigid vessel at a constant temperature of 25°C. The particle diagram below represents the contents of the vessel after equilibrium is established. Assume that each particle in the diagram represents 1 mole. Based on this information, what is the equilibrium constant, K_c, for the reaction above at 25°C?

Answer:

• For the generic equation

aA + bB ⇌ cC + dD

The equilibrium expression for K_c is

• So the equilibrium expression for K_c for the given reaction is

 

• Each particle in the diagram represents 1.00 mole and the total volume of the container is 1.00 L
• Therefore, the number of particles of a species in the diagram also represents the concentration of that species at equilibrium in mol/L
• The equilibrium concentrations are
  • [A₂B₂]_eq = 4.00 mol/L
  • [A₂]_eq = 2.00 mol/L
  • [B]_eq = 4.00 mol/L
• Substituting the concentrations into the equilibrium expression

${\mathrm{K}}_{\mathrm{c}}=\frac{4.00}{32.00}$

${\mathrm{K}}_{\mathrm{c}}=0.125$

2X (g) ⇌ Y (g)

At 25°C, the equilibrium constant, K_c, for the reaction shown above is 15. Which of the following particle diagrams best represents the system at equilibrium? Assume that each particle in the diagrams represents a concentration of 0.1 M.

Answer:

Step 1: Determine the expression for Q

• For the generic equation

aA + bB ⇌ cC + dD

The equilibrium expression for Q_c is

${\mathrm{Q}}_{\mathrm{c}}=\frac{{\left[\mathrm{C}\right]}^{\mathrm{c}}{\left[\mathrm{D}\right]}^{\mathrm{d}}}{{\left[\mathrm{A}\right]}^{\mathrm{a}}{\left[\mathrm{B}\right]}^{\mathrm{b}}}$

• So the expression for Q_c for the given reaction is

${\mathrm{Q}}_{\mathrm{c}}=\frac{\left[\mathrm{Y}\right]}{{\left[\mathrm{X}\right]}^2}$

Step 2: Solve for Q

• Diagram A
  • [Y] = 0.4 M
  • [X] = 0.4 M

${\mathrm{Q}}_{\mathrm{c}}=\frac{0.4}{{\left(0.4\right)}^2}$

${\mathrm{Q}}_{\mathrm{c}}=\frac{0.4}{0.16}$

${\mathrm{Q}}_{\mathrm{c}}=2.5$

• Diagram B
  • [Y] = 0.3 M
  • [X] = 0.5 M

${\mathrm{Q}}_{\mathrm{c}}=\frac{0.3}{{\left(0.5\right)}^2}$

${\mathrm{Q}}_{\mathrm{c}}=\frac{0.3}{0.25}$

${\mathrm{Q}}_{\mathrm{c}}=1.2$

• Diagram C
  • [Y] = 0.6 M
  • [X] = 0.2 M

${\mathrm{Q}}_{\mathrm{c}}=\frac{0.6}{{\left(0.2\right)}^2}$

${\mathrm{Q}}_{\mathrm{c}}=\frac{0.6}{0.04}$

${\mathrm{Q}}_{\mathrm{c}}=15$

• Diagram D
  • [Y] = 0.5 M
  • [X] = 0.3 M

 ${\mathrm{Q}}_{\mathrm{c}}=\frac{0.5}{{\left(0.3\right)}^2}$

${\mathrm{Q}}_{\mathrm{c}}=\frac{0.5}{0.09}$

${\mathrm{Q}}_{\mathrm{c}}=5.6$

• A system is in equilibrium when Q = K
• So diagram C best represents the system at equilibrium