Lesson 7.5: Quantitative Changes in Chemical Equilibrium Systems (12 Chem)

Quantitative Changes in Equilibrium Systems

Introduction to Chemical Equilibrium

Chemical equilibrium occurs when the rates of the forward and reverse reactions are equal, resulting in constant concentrations of reactants and products. Quantitative analysis of equilibrium systems allows chemists to predict how changes in conditions affect the position of equilibrium and the concentrations of substances involved.

Equilibrium Law and Equilibrium Constant (K)

The equilibrium law expresses the relationship between the concentrations of reactants and products at equilibrium for a reversible reaction. The equilibrium constant (K) is a numerical value that characterizes the extent of a reaction at equilibrium.

• Equilibrium Constant Expression: For a general reaction: $aA + bB \rightleftharpoons cC + dD$ The equilibrium constant is: $K = \frac{[C]^c [D]^d}{[A]^a [B]^b}$

• K does not change with concentration, but changes with temperature.

• The magnitude of K indicates the extent of the reaction: - Large K: Products favored - Small K: Reactants favored

Quantitative Shifts in Equilibrium

When the concentration of a reactant or product is changed, the equilibrium system shifts to restore the value of K. This shift can be predicted and calculated using the equilibrium law and ICE tables (Initial, Change, Equilibrium).

• Example: Dissolving CO2 in water forms carbonic acid, which is crucial for maintaining blood pH. Administering hydrogen carbonate ions shifts the equilibrium to reduce acid concentration and raise pH.

• ICE Table: Used to track changes in concentrations as the system moves toward equilibrium.

Trial and Error & Algebraic Approach to Equilibrium

To determine equilibrium concentrations, one can use trial and error or algebraic methods. The ICE table is a systematic way to organize initial amounts, changes, and equilibrium values.

• Trial and Error: Guess the amount reacted, check if the equilibrium expression yields K.

• Algebraic Method: Use variables (e.g., x) to represent changes, solve for x using the equilibrium constant.

Reaction Quotient (Q)

The reaction quotient (Q) is calculated using the same expression as K, but with instantaneous concentrations (concentrations at a moment in time). Q indicates whether a system is at equilibrium and predicts the direction of shift.

• Q < K: System shifts right (toward products).

• Q = K: System is at equilibrium.

• Q > K: System shifts left (toward reactants).

Using Q to Predict Equilibrium Shifts

By comparing Q and K, chemists can determine if a reaction mixture is at equilibrium and, if not, which direction the reaction will proceed.

• Example: For ammonia synthesis: $N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)$ $Q = \frac{[NH_3]^2}{[N_2][H_2]^3}$ (products over reactants)

• Calculate Q using initial concentrations, compare to K, and predict the shift.

Calculating Equilibrium Concentrations

Equilibrium concentrations can be determined from initial concentrations and either the equilibrium constant or one equilibrium concentration. ICE tables and algebraic equations are used for these calculations.

• Stepwise Approach:

  1. Convert amounts to concentrations.

  2. Set up the ICE table.

  3. Write the equilibrium constant expression.

  4. Solve for unknowns (often using quadratic or cubic equations).

  5. Check results by substituting back into the equilibrium expression.

Solving Complex Equilibrium Problems

For reactions with small equilibrium constants or complex stoichiometry, simplifying assumptions ("hundred rule") can be used if justified. Otherwise, quadratic or cubic equations must be solved.

• Hundred Rule: If the initial concentration is at least 100 times greater than K, the change (x) can be considered negligible.

• Quadratic Formula: Used when the equilibrium equation reduces to a quadratic form: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Practice Problems and Applications

Practice problems involve calculating Q, predicting shifts, and determining equilibrium concentrations for various chemical systems. These skills are essential for understanding real-world chemical processes, such as blood pH regulation, industrial synthesis, and environmental chemistry.

Summary Table: Q vs. K Predictions

Condition	Prediction
Q < K	Shift right (toward products)
Q = K	At equilibrium (no shift)
Q > K	Shift left (toward reactants)

Key Takeaways

• The equilibrium constant (K) quantifies the extent of a reaction at equilibrium.

• The reaction quotient (Q) is used to determine if a system is at equilibrium and to predict the direction of shift.

• ICE tables and algebraic methods are essential tools for calculating equilibrium concentrations.

• Simplifying assumptions can be used for small K values, but must be justified using the hundred rule.