Ch.13 - Chemical KineticsWorksheetSee all chapters
All Chapters
Ch.1 - Intro to General Chemistry
Ch.2 - Atoms & Elements
Ch.3 - Chemical Reactions
BONUS: Lab Techniques and Procedures
BONUS: Mathematical Operations and Functions
Ch.4 - Chemical Quantities & Aqueous Reactions
Ch.5 - Gases
Ch.6 - Thermochemistry
Ch.7 - Quantum Mechanics
Ch.8 - Periodic Properties of the Elements
Ch.9 - Bonding & Molecular Structure
Ch.10 - Molecular Shapes & Valence Bond Theory
Ch.11 - Liquids, Solids & Intermolecular Forces
Ch.12 - Solutions
Ch.13 - Chemical Kinetics
Ch.14 - Chemical Equilibrium
Ch.15 - Acid and Base Equilibrium
Ch.16 - Aqueous Equilibrium
Ch. 17 - Chemical Thermodynamics
Ch.18 - Electrochemistry
Ch.19 - Nuclear Chemistry
Ch.20 - Organic Chemistry
Ch.22 - Chemistry of the Nonmetals
Ch.23 - Transition Metals and Coordination Compounds

Solution: The first-order integrated rate law for a reaction A is derived from the rate law using calculus as follows:large{egin{array}{l} { m{Rate}} = k[{ m{A}}]quad quad ({ m{first - order;rate;law)}} { m{Rat

Problem
The first-order integrated rate law for a reaction is derived from the rate law using calculus as follows:

The above equation is a first-order, separable differential equation that can be solved by separating the variables and integrating:

In the above integral, [A]0 is the initial concentration of A. We then evaluate the integral:

Use a procedure similar to the one above to derive an integrated rate law for a reaction A →products which is one-half order in the concentration of A (that is, Rate = k[A]1/2).