To learn how to write out rate laws, let's refresh ourselves on what exactly a rate law is. Given a reaction A --> B, the rate law for this reaction is R = k[A]^n, where R is the reaction rate, k is the rate constant, and n is the order of the reaction in A. The rate law shows us that rate is directly proportional to the concentration of the reactants, or in this case just reactant.
Rate laws are simply what they look like: mathematical expressions to find the rate of a reaction. However, given any reaction, is there a way to find exactly what the rate law is? Let's find out!
Unfortunately, the only true way that rate laws can be found are through an experiment. It's a common mistake of chemistry students to look at the stoichiometric coefficients of the reactants and use those as reaction orders, but you CANNOT DO THAT! The reaction 2A --> B is not necessarily second order, it could be, but we won't know until we run an experiment. The experiment run to find a rate law is quite simple. All it involves is running multiple trials of a reaction with different concentrations of each reactant, typically doubling one and then seeing how the rate reacts to this change in concentration. One important stipulation is that these reactions MUST and I mean MUST be run at the same temperature. If the temperature fluctuates, the rate can change dramatically, giving incorrect results. This is because k, the rate constant, is temperature dependent. Once you find the orders of a reaction, you can plug in values from an experiment to find k.
You might be wondering, how does doubling the concentration change the rate? Well, let's take a look at a general example. Let's say at 1M, the rate of a reaction is 1 mol/Ls and at 2M, the same reaction at the same temperature is 4 mol/Ls. This means that by doubling the concentration, the rate quadrupled. This is a quadratic effect. Essentially, if R = k[A]^n and doubling [A] leads to a quadrupling in rate, n must be two. We can see this through some simple algebra:
1 = k[A]^n and 4 = k(2[A])^n ==> 4 = k(4[A]^2) ==> 1 = k[A]^2
As a general rule of thumb: if doubling  leads to rate doubling, it's first order, quadrupling rate means second order, octupling rate means 3rd order, etc., though it's rare to see more than 2nd order reactions.
Find the rate law for the reaction 2NO + 2H2 --> N2 + 2H2O given the reaction data below at 1280C.
Between experiments 1 and 2, [NO] doubles and [H2] remains constant, so we can use these to find the order of the reaction in NO. When [NO] is doubled, rate increases by a factor of 5.0/1.25 = 4 (we can cancel out the 10^-5 here). Therefore, the reaction is second order in NO.
Similarly, between experiments 2 and 3, [NO] remains constant and [H2] doubles. Therefore, we can do the same as before: [H2] doubles, and rate increases by a factor of 1 * 10^-4/5 * 10^-5 = 2. Thus, the reaction is first order in H2.
We now know the rate law is in the form R = k[NO]^2[H2]. Now, by plugging in values you can find k and write out the full rate law. Give it a try! The first two steps really are the hard parts.
✍️ Free Response Questions
AP Chemistry Free Response Questions
⚛️ Unit 1: Atomic Structure and Properties
1.1Moles and Molar Mass
1.2Mass Spectroscopy of Elements
1.3Elemental Composition of Pure Substances
1.4Composition of Mixtures
1.5Atomic Structure and Electron Configurations
1.6Photoelectron Spectroscopy & Graph Interp.
🤓 Unit 2: Molecular and Ionic Compound Structures and Properties
2.0Unit 2 Overview: Molecular and Ionic Bonding
2.1Types of Chemical Bonds
2.2Intramolecular Force and Potential Energy
2.3Ionic Bonding and Ionic Solids
2.4Metallic Bonding and Alloys
2.5Lewis Dot Diagrams
2.6Resonance and Formal Charge
🌀 Unit 3: Intermolecular Forces and Properties
3.0Unit 3 Overview: Intermolecular Forces and Properties
3.2Properties of Solids
3.3Solids, Liquids, and Gases
3.4The Ideal Gas Law
3.5The Kinetic Molecular Theory of Gases
3.6Deviations from the Ideal Gas Law
3.7Mixtures and Solutions
3.8Representations of Solutions
3.9Separation of Solids/Mixtures
3.10Solubility and Solubility Rules
3.11Spectroscopy and the Electromagnetic Spectrum
3.12Quantum Mechanics and the Photoelectric Effect
🧪 Unit 4: Chemical Reactions
4.0Unit 4 Overview: Chemical Reactions
4.1Recognizing Chemical Reactions
4.2Net Ionic Equations
4.4Physical vs. Chemical Changes
4.5Stoichiometry & Calculations
4.6Titrations - Intro and Calculations
4.8Intro to Acid-Base Neutralization Reactions
👟 Unit 5: Kinetics
5.0Unit 5 Overview: Kinetics
5.1Defining Rate of Reaction
5.2Introduction to Rate Laws
5.3Rate and Concentration Change
5.4Writing Rate Laws
5.5Collision Model of Kinetics
5.6Reaction Energy and Graphs w/ Energy
5.7Reaction Mechanisms and Elementary Steps
5.8Writing Rate Laws Using Mechanisms
🔥 Unit 6: Thermodynamics
6.0 Unit 6 Overview: Thermochemistry and Reaction Thermodynamics
6.1Endothermic Processes vs. Exothermic Processes
6.2Energy Diagrams of Reactions
6.3Kinetic Energy, Heat Transfer, and Thermal Equilibrium
6.4Heat Capacity and Coffee-Cup Calorimetry
6.5Phase Changes and Energy
6.6Introduction to Enthalpy of Reaction
6.7Bond Enthalpy and Bond Dissociation Energy
6.8Enthalpies of Formation
⚖️ Unit 7: Equilibrium
🍊 Unit 8: Acids and Bases
8.0Unit 8 Overview: Acids and Bases
8.1Introduction to Acids and Bases
Unit 9: Applications of Thermodynamics
🤺 AP Chemistry Essentials
🧐 Multiple Choice Questions
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