Overview
This lecture covers integrated rate laws for zero, first, and second-order reactions, how to use graphs to determine reaction order, apply rate laws to solve problems, and introduces the concept of half-life in kinetics.
Integrated Rate Laws
- First-order rate law: rate = k[A], integrated form is ln[A]ₜ = ln[A]₀ - kt.
- Second-order rate law: rate = k[A]², integrated form is 1/[A]ₜ = 1/[A]₀ + kt.
- Zero-order rate law: rate = k, integrated form is [A]ₜ = [A]₀ - kt.
- Each order produces a characteristic graph: natural log for first-order, inverse concentration for second-order, and concentration vs. time for zero-order.
Using Graphs to Determine Reaction Order
- Plotting ln[A] vs. time: straight line indicates first-order (slope = -k).
- Plotting 1/[A] vs. time: straight line indicates second-order (slope = +k).
- Plotting [A] vs. time: straight line indicates zero-order (slope = -k).
- The graph that is linear reveals the reaction order.
Solving Integrated Rate Law Problems
- Use the appropriate integrated rate law and plug in known values for calculations.
- To find concentration at a certain time, use the exponential or logarithmic form as needed.
- Fraction decomposed = 1 - ([A]ₜ/[A]₀); fraction remaining = [A]ₜ/[A]₀.
- For first-order, the ratio of concentrations (not absolute values) is important.
Calculating Rate Constant and Fraction Decomposed
- For first-order: k = (ln([A]₀/[A]ₜ))/t; units of k are s⁻¹.
- To determine how much has decomposed, calculate [A]ₜ using the rate law and solve for the fraction lost.
Half-Life (T₁/₂)
- Half-life is the time for the concentration to fall to half its initial value.
- For first-order: T₁/₂ = ln(2)/k; half-life is constant regardless of initial concentration.
- Each additional half-life cuts the remaining reactant by half (½, ¼, ⅛, etc.).
Key Terms & Definitions
- Integrated Rate Law — equation relating reactant concentration to time for a given reaction order.
- First-order Reaction — reaction whose rate depends linearly on one reactant’s concentration.
- Second-order Reaction — reaction rate depends on the square of one reactant's concentration.
- Zero-order Reaction — reaction rate is independent of reactant concentration.
- Half-life (T₁/₂) — time required for half of the reactant to be consumed.
Action Items / Next Steps
- Memorize the three integrated rate laws.
- Practice using graphs to determine reaction order.
- Complete homework problems on first-order rate law applications.
- Prepare for a lab exercise on plotting kinetics data.
- Review use of Excel for graphing reaction rates.