Chemical Equilibrium: Reaction Quotient, Equilibrium Calculations, and Le Chatelier's Principle

Chemical Equilibrium

Reaction Quotient (Q) and Equilibrium Constant (Kc)

Chemical equilibrium occurs when the rates of the forward and reverse reactions are equal, resulting in constant concentrations of reactants and products. The reaction quotient (Q) is used to determine the direction in which a reaction will proceed to reach equilibrium, while the equilibrium constant (Kc) describes the ratio of product and reactant concentrations at equilibrium for a given temperature.

• Q is calculated using the same expression as Kc, but with current (not necessarily equilibrium) concentrations.

• Kc is constant at a given temperature and is calculated using equilibrium concentrations.

• The general equilibrium expression for a reaction: $aA + bB \rightleftharpoons cC + dD$ $Q = \frac{[C]^c [D]^d}{[A]^a [B]^b}$

• If Q > Kc, the reaction shifts to the left (toward reactants).

• If Q < Kc, the reaction shifts to the right (toward products).

• If Q = Kc, the system is at equilibrium.

Reaction Quotient Calculations

Calculating Q allows prediction of how a reaction mixture will adjust to reach equilibrium. Example calculations:

• For the reaction COCl2 (g) → CO (g) + Cl2 (g), with Kc = 2.19 × 10-10 at 373 K:

• Given concentrations: [COCl2] = 5.00 × 10-2 M, [CO] = 3.31 × 10-2 M, [Cl2] = 3.31 × 10-6 M

• Calculate Q: $Q = \frac{[CO][Cl_2]}{[COCl_2]}$ $Q = \frac{(3.31 \times 10^{-2})(3.31 \times 10^{-6})}{5.00 \times 10^{-2}} = 2.19 \times 10^{-6}$

• Since Q > Kc, the reaction will shift toward COCl2 (reactants).

Calculating Component Concentrations with Equilibrium Constants

When partial information about concentrations is known, equilibrium expressions can be used to find missing concentrations. The process involves setting up an ICE (Initial, Change, Equilibrium) table and solving for unknowns.

1. Write the equilibrium expression.

2. Create a table of initial concentrations.

3. Indicate changes using a variable (e.g., x).

4. Apply stoichiometry to relate changes.

5. Calculate equilibrium concentrations.

6. Substitute into the equilibrium expression.

7. Solve for the variable.

8. Find equilibrium concentrations.

Example: For CO (g) + H2O (g) → CO2 (g) + H2 (g), Kc = 4.06 at 500 °C, initial [CO] = [H2O] = 0.100 M:

• Let x = change in [CO] and [H2O] (both decrease by x), [CO2] and [H2] increase by x.

• Equilibrium concentrations: [CO] = [H2O] = 0.100 - x, [CO2] = [H2] = x

• Substitute into equilibrium expression: $K_c = \frac{[CO_2][H_2]}{[CO][H_2O]} = \frac{x^2}{(0.100-x)^2} = 4.06$ Solve for x: $x = 0.0668$ Equilibrium: [CO2] = [H2] = 0.0668 M, [CO] = [H2O] = 0.033 M

Using Assumptions in Equilibrium Calculations

When Kc is very small or very large, simplifying assumptions can be made to ease calculations. If the change (x) is much smaller than the initial concentration, it can be neglected in the denominator.

• Always check the validity of the assumption: x should be less than 5% of the initial concentration.

• Example: For 2 N2 (g) + O2 (g) → 2 N2O (g), Kc = 2.0 × 10-37, initial [N2] = 0.0482 M, [O2] = 0.0933 M.

• Assume x is very small, so [N2] ≈ 0.0482 M, [O2] ≈ 0.0933 M.

• Solve for x: $x = 3.29 \times 10^{-21}$, [N2O] = 2x = $6.58 \times 10^{-21}$ M.

Le Chatelier's Principle

Le Chatelier's Principle states that if a system at equilibrium is disturbed, it will shift to counteract the disturbance and reestablish equilibrium. Disturbances include changes in concentration, temperature, and pressure.

• Adding/removing components: The system shifts to consume added substances or replace removed ones.

• Changing temperature: For exothermic reactions, increasing temperature shifts equilibrium toward reactants; for endothermic reactions, toward products.

• Changing pressure/volume: Increasing pressure (decreasing volume) shifts equilibrium toward the side with fewer moles of gas.

• Adding a catalyst: Does not affect equilibrium position, only the rate at which equilibrium is reached.

Examples of Le Chatelier's Principle

• Component addition/removal: For 2 NO (g) + 2 H2 (g) → N2 (g) + 2 H2O (g), adding H2 shifts equilibrium toward products; removing H2 shifts toward reactants.

• Using Q: For C(s) + 2 H2 (g) → CH4 (g), if Q > Kp, the reaction shifts left (CH4 decreases, H2 increases).

• Temperature: For CaC2 (s) + 2 H2O (l) → Ca(OH)2 (s) + C2H2 (g), exothermic reaction; increasing temperature shifts equilibrium left.

• Pressure: For N2O4 (g) → 2 NO2 (g), decreasing volume (increasing pressure) shifts equilibrium toward N2O4 (fewer moles of gas).

Additional info: Changing total pressure by adding an inert gas does not shift equilibrium unless the reaction involves a change in the number of moles of gas.