Solving Integrated Rate Law Problems

Introduction

• Discussion on rate law expressions for different reaction orders.
• Importance of understanding how reactant concentration affects reaction rate.

Rate Law Expression

Zero Order Reaction

• Rate = k[A]^0 = k
• Rate doesn't depend on reactant concentration.

First Order Reaction

• Rate = k[A]^1
• Rate is directly proportional to reactant concentration.

Second Order Reaction

• Rate = k[A]^2
• Rate increases with the square of reactant concentration.

Effect of Reactant Concentration on Rate

• Zero Order: Changing concentration has no effect.
• First Order: Doubling concentration doubles the rate.
• Second Order: Doubling concentration quadruples the rate.

Units of the Rate Constant (k)

Zero Order

• Units: M^1 T^-1

First Order

• Units: T^-1

Second Order

• Units: M^-1 T^-1

General Formula

• Units of k: M^(1-n) T^-1, where n = order of reaction.

Half-Life (t₁/₂)

• The time it takes for the reactant concentration to reduce by half.

Zero Order

• t₁/₂ = [A]0 / 2k

First Order

• t₁/₂ = ln(2) / k

Second Order

• t₁/₂ = 1 / (k[A]0)

Key Points

• First Order: Half-life is independent of initial concentration.
• Zero & Second Order: Half-life depends on initial concentration.

Integrated Rate Law Expressions

Zero Order

• [A]_t = -kt + [A]_0
• Slope = -k (straight line graph of concentration vs. time).

First Order

• ln[A]_t = -kt + ln[A]_0
• Slope = -k (straight line graph of ln[A] vs. time).

Second Order

• 1/[A]_t = kt + 1/[A]_0
• Slope = k (straight line graph of 1/[A] vs. time).

Graphical Representation

• Zero Order: [A] vs. time, negative slope.
• First Order: ln[A] vs. time, negative slope.
• Second Order: 1/[A] vs. time, positive slope.

Practice Problems

Problem 1

• Units of k for third-order reaction: M^-2 T^-1

Problem 2

• Straight line plot for first order: ln[A] vs. time, negative slope.

Problem 3

• Analyze statements to determine falsehood regarding half-life and reaction order.

Problem 4

• Calculate final concentration after a given time for a zero-order reaction.

Problem 5

• Determine initial concentration given final concentration, rate constant, and time.

Problem 6

• Calculate rate constant from concentration data for a zero-order reaction.

Problem 7

• Determine half-life for reaction with given k.

Problem 8

• Identify correct plot for first-order reaction based on given options.

Problem 9

• Determine the order of reaction from observed changes in rate with concentration changes.

Problem 10

• Calculate overall order of reaction given units of k.