#AP Chemistry: Kinetics - Rate Laws Study Guide

Hey there! Let's break down rate laws and get you feeling confident for the exam. Remember, you've got this! 💪

#Reaction Rates and Rate Laws

#What is a Rate Law?

A rate law is an equation that shows how the rate of a chemical reaction depends on the concentrations of the reactants. It's all about figuring out how much faster a reaction goes when you add more stuff. Think of it as the recipe for speed! 🏎️

The general form of a rate law is:

$R = k[A]^n[B]^m...$

Where:

R = Reaction Rate (often Δ[]/Δt)
k = Rate Constant (temperature-specific)
[A], [B] = Concentrations of reactants
n, m = Reaction Orders (experimentally determined)

Key Concept

Rate laws can only be determined by experiments, not by looking at the balanced equation.

Exam Tip

Remember that the rate law is determined experimentally, not by the stoichiometric coefficients of the reaction.

Memory Aid

Think of 'R = k[A]^n[B]^m' as the Rate = k times the concentration of reactants to their orders.

Collisions are key for reactions!

#Reaction Order Explained

Reaction order tells us how the rate changes when we change the concentration of a reactant. It's the exponent in our rate law equation. 📈

If the reaction is first order with respect to a reactant (e.g., [A]¹), doubling the concentration doubles the rate.
If it's second order (e.g., [A]²), doubling the concentration quadruples the rate.
And so on... (tripling concentration for 2nd order increases rate by 9 times, for 3rd order by 27 times)

The overall reaction order is the sum of all individual reactant orders. For example, if R = k[A]²[B]¹, the overall order is 2 + 1 = 3.

Quick Fact

The overall reaction order is the sum of the exponents in the rate law.

Visualizing linear vs. quadratic relationships.

#Experimental Determination of Rate Laws

Rate laws are determined by analyzing experimental data. Here’s how it’s done:

Run multiple experiments with varying reactant concentrations.
Measure the initial rates for each experiment.
Compare how the rate changes as you change the concentration of each reactant, keeping others constant.

Let's look at an example:

Reaction: 2NO + 2H₂ → N₂ + 2H₂O

To find the order for NO: Compare experiments 1 and 2 (where [H₂] is constant). [NO] doubles, and the rate quadruples. Therefore, the reaction is second order in [NO].
To find the order for H₂: Compare experiments 2 and 3 (where [NO] is constant). [H₂] doubles, and the rate doubles. Therefore, the reaction is first order in [H₂].

Common Mistake

Don't assume reaction orders from the balanced equation! Always use experimental data.

So, the rate law is: R = k[NO]²[H₂]

Exam Tip

When comparing experiments, always pick two trials where only one reactant concentration changes.

#The Rate Constant (k)

The rate constant (k) is a proportionality constant that relates the rate of a reaction to the concentrations of reactants. It's unique for each reaction and is temperature-dependent. 🌡️

A larger k means a faster reaction.
k changes with temperature (Arrhenius equation).

The units of k depend on the overall reaction order:

#Zeroth Order

Rate Law: R = k
Units of k: M/s

#First Order

Rate Law: R = k[A]
Units of k: s⁻¹

#Second Order

Rate Law: R = k[A]² or R = k[A][B]
Units of k: M⁻¹s⁻¹

Memory Aid

Remember the units of k by thinking: 'Rate (M/s) divided by concentration terms'.

#Final Exam Focus

High-Priority Topics: Rate laws, reaction orders, experimental determination of rate laws, and the rate constant (k).
Common Question Types:
- Determining rate laws from experimental data.
- Calculating reaction rates given a rate law and concentrations.
- Finding the units of k based on overall reaction order.
- Understanding how changes in concentration affect reaction rates.
Time Management: Practice setting up rate law problems quickly. Focus on identifying the experiments needed to find each order.
Common Pitfalls:
- Confusing reaction orders with stoichiometric coefficients.
- Forgetting that k is temperature-dependent.
- Incorrectly calculating the units of k.

#Practice Questions

Practice Question

#Multiple Choice Questions

The rate law for the reaction 2A + B → C is given by rate = k[A][B]². If the concentration of A is doubled and the concentration of B is halved, the rate of the reaction will: (A) remain the same (B) be halved (C) be doubled (D) be quadrupled
For the reaction A + 2B → C, the following data were obtained:

Experiment	[A] (M)	[B] (M)	Initial Rate (M/s)
1	0.1	0.1	0.02
2	0.2	0.1	0.08
3	0.1	0.2	0.04

The rate law for the reaction is: (A) rate = k[A][B] (B) rate = k[A]²[B] (C) rate = k[A][B]² (D) rate = k[A]²[B]²

#Free Response Question

The decomposition of dinitrogen pentoxide (N₂O₅) in the gas phase is represented by the equation:

2N₂O₅(g) → 4NO₂(g) + O₂(g)

The following data were obtained at a certain temperature:

Time (s)	[N₂O₅] (M)
0	0.500
100	0.352
200	0.248
300	0.175

(a) Calculate the average rate of disappearance of N₂O₅ between 100 and 200 seconds. (b) Determine the rate law for the decomposition of N₂O₅. Provide reasoning based on the data. (c) Calculate the rate constant, k, including units. (d) What is the concentration of N₂O₅ at 400 seconds?

#FRQ Scoring Breakdown

(a) Average Rate = -Δ[N₂O₅]/Δt Average Rate = -(0.248 M - 0.352 M) / (200 s - 100 s) = 0.00104 M/s (1 point for calculation, 1 point for units)

(b) The rate law will be first order, as the rate of decay is proportional to the concentration of N2O5. (1 point for first order, 1 point for justification)

(c) Using the first data point: rate = k[N₂O₅] 0.00148 = k(0.500) k = 0.00296 s⁻¹ (1 point for calculation, 1 point for units)

(d) Using the integrated rate law for first-order reactions: ln[A]t - ln[A]0 = -kt ln[A]400 - ln(0.500) = -(0.00296)(400) ln[A]400 = -1.184 + ln(0.500) [A]400 = 0.127 M (1 point for calculation)

You've got this! Keep practicing and you'll ace the exam. 🚀

Introduction to Rate Law

Caleb Thomas