Integrated Rate Law Problems

In this lecture, we will explore how to solve integrated rate law problems, focusing on zero, first, and second-order reactions.

Rate Law Expressions

• Zero-order Reaction:
  • Rate = k
  • Reaction: A → B
  • Rate is independent of the concentration of reactant A.
• First-order Reaction:
  • Rate = k[A]^1
  • Doubling [A] doubles the rate.
• Second-order Reaction:
  • Rate = k[A]^2
  • Doubling [A] quadruples the rate (2^2 = 4).
• General Observation:
  • Higher order reactants have a greater impact on the rate.

Units of Rate Constant (k)

• Zero-order: M^1 T^-1
• First-order: M^0 T^-1 (or T^-1)
• Second-order: M^-1 T^-1
• General Formula: M^(1-n) T^-1

Integrated Rate Law Equations

Zero-order Reaction

• [A] = -kt + [A]₀
• Slope (m): -k

First-order Reaction

• ln([A]) = -kt + ln([A]₀)
• Slope (m): -k

Second-order Reaction

• 1/[A] = kt + 1/[A]₀
• Slope (m): +k

Graphs for Straight-Line Plots

• Zero-order: Plot [A] vs. time (straight line, negative slope)
• First-order: Plot ln[A] vs. time (straight line, negative slope)
• Second-order: Plot 1/[A] vs. time (straight line, positive slope)