14.3.Integrated Laws & Half-life
Introduction to Chemical Kinetics
Kinetics focuses on the rate or speed of chemical reactions.
Factors Affecting Reaction Rate
Various factors influence the rate at which reactions occur.
Identified key experimental methods for measuring these rates.
Rate Laws
General Rate Law: Depend on the number of reactants involved in the reaction.
Each reactant has a specific order, contributing to the total order of the reaction.
Total order is the sum of the individual orders for each reactant.
Finding Orders (m, n):
Determined through experimental data from trials.
Calculate the rate constant (k) using the experimental data.
Units of k:
To find the unit of k, use the formula:
\text{Units of k}=\frac{1}{\text{Molarity}^{\text{total order}-1}s}
The total order defines the exponent for molarity in the units of k.
Differential Rate Laws (Initial Rates)
This method may lead to errors due to empirical limitations.
Graphical Approach Preferred
Utilizes concentration and time for a more accurate analysis.
Integrated rate laws created for the graphical representation.
Integrated Rate Laws
Concentration is plotted against time to determine the order of reaction:
Different forms of concentration on the y-axis based on the order of reaction.
Graph Types for Reactions:
Concentration vs. Time
ln(Concentration) vs. Time
1/Concentration vs. Time
Only one graph among these will show a linear relationship, indicating the reaction order.
Reactions by Order
First Order Reactions
Differential Rate Law:
Rate = k [A]
Change in Concentration over Time: \frac{d[A]}{dt} .
Integrated Rate Law Formula:
\ln[A] = -kt + \ln[A]_0
A_0 represents initial concentration.
Graph Characteristics:
Linear graph results in a negative slope of -k.
y-axis: ln(Concentration), x-axis: Time.
Second Order Reactions
Differential Rate Law:
Rate = k [A]^2
Change in Concentration over Time: \frac{d[A]}{dt} .
Integrated Rate Law Formula:
\frac{1}{[A]} = kt + \frac{1}{[A]_0}
Graph Characteristics:
Plotting 1/[A] vs Time yields a linear graph.
The slope is equal to k.
Zero Order Reactions
Differential Rate Law:
Rate = k
Changes in Concentration yield:
[A] = -kt + [A]_0
Graph Characteristics:
Plotting Concentration vs. Time will be linear with a negative slope.
Examples of Rate Laws in Action
Example #1: First Order Reaction
Decomposition of an insecticide follows first order kinetics with k = 1.45 per year.
Initial concentration: 5 x 10^(-7) g/cm^3.
Given time: 1 year.
Final concentration is calculated using: \ln[A] = -kt + \ln[A]_0 .
Resulting final concentration: ~ 1.2 x 10^(-7) g/cm^3.
Example #2: Second Order Reaction
L A concentration drops from 0.657 to 0.0981 in 17 seconds.
Using the second order formula for calculations.
Resulting k value determined to be 0.510 1/(Molarity*seconds).
Half-Life Concept
Definition of Half-Life: Time required for a quantity to reduce to half its initial value.
Common Applications: Radiometric dating with carbon-14 for organic materials.
Carbon-14 half-life: 5730 years.
Half-Life Formulas by Reaction Order:
First Order:
t_{1/2} = \frac{\ln{2}}{k}ln(2) = 0.693, indicating half-life is independent of concentration.
First-order reactions have a constant half-life (it does not depend on concentration)
Second Order:
t1/2 =
DependenceI <[ao] on initial concentration.
Zero Order:
t{1/2} = \frac{[A]0}{2k}
Comparative Summary of Rate Laws and Half-Life
A comprehensive table summarizing rate laws, integrated rates, graphs, and half-life equations per reaction order is essential for solving problems effectively.
It's crucial to understand each type well by practicing various problems and examples.
Final Remarks
Students are encouraged to ask questions for clarification as there are no dumb questions.
Emphasis on rigorous practice building towards quizzes and exams, utilizing provided worksheets and examples.