Overview
This lecture covers solving chemical equilibrium problems using ICE tables and quadratic equations, focusing on setting up, solving, and validating equilibrium concentrations.
ICE Tables for Equilibrium
- ICE stands for Initial, Change, Equilibrium; it's used to organize data for equilibrium calculations.
- Assume the change in concentration is x (or ±nx for stoichiometry), then solve for x.
- Equilibrium concentrations (E) are calculated as Initial (I) plus Change (C): E = I + C.
- Use stoichiometry to assign the coefficients for the changes in reactant and product concentrations.
Solving Quadratic Equations in Equilibrium
- Set up the equilibrium expression K = (products/reactants), substitute ICE values, and solve for x.
- Most problems lead to a quadratic equation: ax² + bx + c = 0.
- There are always two mathematical solutions for x, but only one yields all positive equilibrium concentrations (required in chemistry).
Validating Solutions & Significant Figures
- After solving for x, verify which solution gives positive concentrations for all species.
- Substitute equilibrium concentrations back into the K expression to check if calculated K matches the given K.
- Keep extra significant figures in intermediate steps; round final answers to match the precision of the given data.
Common Algebraic Techniques
- Expand expressions like (a + x)² = a² + 2ax + x².
- Be familiar with distributing and combining like terms when manipulating the quadratic.
Example Problem Walkthrough
- Demonstrated the full process: set up an ICE table, construct and solve a quadratic equation, check both solutions, and validate with K.
- Emphasis on early vs. late rounding and its effect on final answers.
Tips for Success
- Always show your ICE table and the resulting quadratic equation in your work.
- Ensure all calculated concentrations are positive at equilibrium.
- Verification is essential: recalculate K from your concentrations to confirm accuracy.
Key Terms & Definitions
- ICE Table — Tool for tracking Initial, Change, and Equilibrium concentrations in a reaction.
- Equilibrium Constant (K) — Ratio of product concentrations to reactant concentrations at equilibrium, each raised to the power of their coefficients.
- Quadratic Equation — An equation of the form ax² + bx + c = 0, which may yield two solutions.
- Stoichiometry — The numerical relationships between reactants and products in a balanced chemical equation.
Action Items / Next Steps
- Practice setting up and solving ICE table problems with quadratic equations.
- Complete homework problems and review online quizzes on equilibrium calculations.
- Show all steps in your work, including ICE tables, equations, and final verification of K.