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Rate Law Determination

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Chemical KineticsReaction Rate and Factors Affecting Reaction Speed→→Enzyme KineticsGlycolysis: Mechanism and Regulation+4 more
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Core Idea

The rate law expresses reaction rate as a function of reactant concentrations: rate = k[A]ᵐ[B]ⁿ, where k is the rate constant and m and n are the reaction orders with respect to each reactant. Reaction orders are determined experimentally, not from stoichiometric coefficients. The method of initial rates compares experiments where one reactant concentration is changed while others are held constant: if doubling [A] doubles the rate, the reaction is first order in A; if doubling [A] quadruples the rate, it is second order in A. The overall order is the sum of individual orders (m + n + ...).

How It's Best Learned

Set up ratio equations from pairs of experiments that isolate one variable at a time. Practice recognizing common patterns: rate unchanged when concentration doubles (zero order), rate doubles (first order), rate quadruples (second order). After finding orders, substitute back into any experiment to solve for k, paying attention to its units.

Common Misconceptions

Explainer

From chemical kinetics, you know that reactions happen at different speeds and that reaction rate measures how fast reactant concentrations decrease (or product concentrations increase) over time. The rate law takes this further by expressing the exact mathematical relationship between rate and reactant concentrations: rate = k[A]ᵐ[B]ⁿ. Here, k is the rate constant (a number specific to the reaction at a given temperature), [A] and [B] are reactant concentrations, and m and n are the reaction orders — exponents that tell you how sensitively the rate responds to each concentration.

The critical point that surprises many students is that reaction orders must be determined experimentally — you cannot simply read them off the balanced equation. A balanced equation tells you the stoichiometry (how much reacts), not the mechanism (how it reacts). The method of initial rates is the standard experimental approach. You run the reaction multiple times, each time changing the starting concentration of only one reactant while holding the others constant. By comparing how the initial rate changes, you deduce the order with respect to that reactant. If doubling [A] doubles the rate, the reaction is first order in A (m = 1). If doubling [A] quadruples the rate, it is second order (m = 2). If doubling [A] has no effect on the rate, it is zero order (m = 0).

The practical technique uses ratios. Take two experiments where only [A] changes. Divide one rate by the other: rate₂/rate₁ = ([A]₂/[A]₁)ᵐ. If [A] was doubled (ratio = 2) and the rate quadrupled (ratio = 4), then 2ᵐ = 4, so m = 2. Repeat this process for each reactant using a different pair of experiments. The overall reaction order is the sum of all individual orders (m + n + ...). Once you know all the orders, substitute the data from any single experiment into the rate law and solve for k. Pay attention to the units of k — they depend on the overall order. For a first-order reaction, k has units of s⁻¹; for second order, L mol⁻¹ s⁻¹. Getting the units right is a good check that your orders are correct.

Understanding the rate law unlocks the rest of kinetics. The orders tell you about the reaction mechanism — which species are involved in the rate-determining step. A reaction that is first order in A and first order in B suggests that one molecule of A and one of B collide in the slow step. Zero order in a reactant means it does not participate in the rate-determining step at all, even if it appears in the balanced equation. As you move on to integrated rate laws, you will use these same orders to derive equations that predict concentration as a function of time, determine half-lives, and distinguish reaction orders from graphical data.

Practice Questions 5 questions

Prerequisite Chain

Understanding Zero → The Number Zero → Counting to Five → Counting to 10 → Counting to 20 → Counting a Set of Objects Up to 20 → Cardinality: The Last Number Counted → Matching Numerals to Quantities → Subitizing Small Quantities → Addition Within 10 → Number Bonds to 10 → Addition Within 20 → Doubles and Near Doubles → Doubles Facts Within 10 → Near Doubles Facts Within 20 → Mental Math Strategies for Addition → Mental Math: Adding and Subtracting Tens → Addition Within 100 → Repeated Addition as Multiplication → Multiplication as Equal Groups → Multiplication: Arrays → Basic Multiplication Facts (0s, 1s, 2s, 5s, 10s) → Multiplication Facts Within 100 → Division as Equal Sharing → Division as Grouping (Measurement Division) → Division: Grouping (Repeated Subtraction) Model → Division: Fair Sharing Model → Division as Equal Sharing → Division as Grouping → Basic Division Facts → Division Facts Within 100 → Multiplication and Division Fact Families → Relationship Between Multiplication and Division → Division Facts as Inverse of Multiplication → Remainders and Quotients in Division → Division Word Problems → Multi-Step Word Problems → Solving Multi-Step Word Problems → Multiplication Word Problems → Division Word Problems → Introduction to Long Division → Factors and Multiples → Prime and Composite Numbers → Equivalent Fractions → Relating Fractions and Decimals → Decimal Place Value → Integers and the Number Line → Comparing and Ordering Integers → Absolute Value → Adding Integers → Subtracting Integers → Multiplying Integers → Dividing Integers → Unit Rates → Proportions → Percent Concept → Converting Between Fractions, Decimals, and Percents → Operations with Rational Numbers → Two-Step Equations → Solving Multi-Step Equations → Equations with Variables on Both Sides → Angle Pairs: Complementary, Supplementary, and Vertical → Parallel Lines and Transversals → Corresponding Angles → Alternate Interior Angles → Triangle Angle Sum Theorem → Exterior Angle Theorem → Triangle Inequality Theorem → Similar Triangles: AA Similarity → Similar Triangles: SSS and SAS Similarity → Proportions in Similar Triangles → Right Triangle Trigonometry Introduction → Sine, Cosine, and Tangent Ratios → Trigonometric Ratios Review → Radian Measure → Converting Between Degrees and Radians → The Unit Circle → Graphing Sine and Cosine → Graphing Tangent and Reciprocal Trigonometric Functions → Derivatives of Trigonometric Functions → Antiderivatives → Indefinite Integrals → Basic Integration Rules → Riemann Sums → Definite Integral Definition → Double Integrals: Definition and Setup → Iterated Integrals and Fubini's Theorem → Double Integrals over Rectangular Regions → Double Integrals over General Regions → Applications of Double Integrals: Area, Mass, and Moments → Triple Integrals in Cartesian Coordinates → Triple Integrals in Cylindrical and Spherical Coordinates → Change of Variables and the Jacobian Determinant → Applications of Triple Integrals: Volume and Mass → Vector Fields and Their Representations → Line Integrals of Vector Fields → Work and Circulation → Line Integrals of Scalar and Vector Functions → Fundamental Theorem for Line Integrals → Conservative Vector Fields → Conservative Vector Fields and Potential Functions → Curl and Divergence of Vector Fields → Curl and Divergence → Divergence Theorem → Electric Flux and Divergence Theorem → Gauss's Law: Integral Form and Meaning → Solving Problems with Gauss's Law → Conductors in Electrostatic Equilibrium → Capacitance and Capacitors → Dielectrics → Dielectric Constant and Relative Permittivity → Electric Field Inside Dielectric Materials → Dielectric Materials and Polarization → Dielectric Susceptibility and Permittivity → Energy Density in Electric Fields → Electric Current and Current Density → Electrical Resistance and Resistivity → Ohm's Law and Circuit Elements → Electromotive Force (EMF) and Batteries → Kirchhoff's Circuit Laws: Voltage and Current → DC Circuit Network Analysis Methods → Transient Response in RC Circuits → RC Circuits → LC and RLC Circuits → AC Circuits: Fundamentals → Impedance and Reactance → AC Power and Resonance → Electromagnetic Waves → Postulates of Special Relativity → Time Dilation → Length Contraction → Lorentz Transformation → Relativistic Velocity Addition → Relativistic Momentum and Energy → Mass-Energy Equivalence and E=mc² → Photons as Particles with Energy and Momentum → Planck-Einstein Relation: Energy and Frequency → Photoelectric Effect → The Photon: Light as Quanta → Compton Scattering → Wave-Particle Duality → de Broglie Wavelength → The Schrödinger Equation → State Vectors and Wavefunctions → Quantum Superposition → Quantum Entanglement → Bell Theorem and Bell Inequalities → Postulates of Quantum Mechanics → Observables and Quantum Operators → Commutators and Commutation Relations → Quantum Angular Momentum → Quantum Mechanical Treatment of Hydrogen → Solving the Schrödinger Equation for Hydrogen Atom → Quantum Numbers → Electron Configuration → Periodic Trends → Covalent Bonding → Electronegativity and Bond Polarity → Ionic Bonding → Lewis Structures → VSEPR Theory and Molecular Geometry → Molecular Geometry and Electron Pair Geometry → Molecular Polarity and Dipole Moments → Intermolecular Forces → States of Matter and Phase Changes: Melting, Boiling, and Sublimation → Gas Laws and the Ideal Gas Equation → Gas Stoichiometry and Volume-Volume Calculations → Thermochemistry and Enthalpy → Heat Capacity and Calorimetry → Entropy and Molecular Disorder → Spontaneity and ΔG → Entropy and Gibbs Free Energy → Chemical Equilibrium → Chemical Kinetics → Reaction Rate and Factors Affecting Reaction Speed → Rate Law Determination

Longest path: 176 steps · 1005 total prerequisite topics

Prerequisites (2)

Leads To (6)