AP Chemistry 5.2 Introduction to Rate Law Study Notes - New Syllabus Effective fall 2024

AP Chemistry 5.2 Introduction to Rate Law Study Notes- New syllabus

AP Chemistry 5.2 Introduction to Rate Law Study Notes – AP Chemistry – per latest AP Chemistry Syllabus.

LEARNING OBJECTIVE

Represent experimental data with a consistent rate law expression.

Key Concepts:

Introduction to Rate Law

AP Chemistry-Concise Summary Notes- All Topics

5.2.A.1 Experimental Methods for Monitoring Reaction Rates:

1. Reaction Rate and Influencing Factors:

The reaction rate indicates how quickly a chemical reaction takes place. It can be measured by the change in concentration of either reactants or products over a specific time period. This can be mathematically represented as:

$Reaction rate = \frac{Change in concentration of reactants or products}{Time}$

The rate can vary significantly; it can be rapid, like in a violent explosion, or slow, such as the rusting of iron.

i. Factors Affecting Reaction Rate:

a. Temperature:
Effect: An increase in temperature causes molecules to move more rapidly, leading to more frequent and energetic collisions among reactants. This enhances the chances of a reaction taking place.
Explanation: Higher temperatures supply more energy to the reactants, increasing the number of particles that have sufficient energy to surpass the activation energy barrier.

b. Concentration:
Effect: Raising the concentration of reactants typically boosts the reaction rate. With a greater number of molecules or ions, the likelihood of collisions between reactant particles increases.
Explanation: A higher number of reactant particles in a specific volume results in more frequent collisions, which accelerates the reaction rate.

c. Surface Area:
Effect: A greater surface area of a solid reactant results in a faster reaction rate.
Explanation: When the surface area of a solid is enlarged (for instance, using powdered solid instead of larger chunks), more particles are available to react, leading to increased collisions and quicker reactions.

d. Catalysts:
Effect: Catalysts enhance the reaction speed without being consumed in the process. They reduce the activation energy needed for a reaction to occur.
Explanation: A catalyst offers an alternative pathway for the reaction that has a lower activation energy, facilitating the conversion of reactants into products more easily.

2. Experimental Methods:

i. Spectrophotometry:
a. This technique measures how much light a solution absorbs, allowing us to monitor changes in the concentration of reactants or products.
b. It is particularly useful for reactions that involve colored compounds.

ii. Gas Volume Measurement:
a. This method involves measuring the volume of gas that is either produced or consumed during a reaction.
b. It is applicable in reactions that generate gases, such as acid-carbonate reactions.

iii. Mass Loss:
a. This approach tracks the decrease in mass that occurs due to gas production or evaporation.
b. It is relevant for reactions where products are released as gas, like decomposition reactions.

iv. Conductivity Measurement:
a. This technique measures changes in electrical conductivity that result from variations in ion concentration.
b. It is commonly used in reactions that involve ions, such as acid-base or precipitation reactions.

v. Titration:
a.This method determines the concentration of a reactant by gradually adding a solution of known concentration until a reaction endpoint is reached.
b. It is frequently used in acid-base and redox reactions.

vi. Temperature Measurement:
a. This technique monitors changes in temperature to identify whether a reaction is exothermic or endothermic.
b. It is particularly useful for reactions that involve significant heat release or absorption.

vii. Chromatography:
a. This method separates and analyzes the components of a reaction over time.
b. It is especially useful for complex reactions that produce multiple products or intermediates.

3. Rate Laws and Kinetics:

Rate laws illustrate the connection between the speed of a reaction and the concentrations of its reactants. They are generally expressed as follows:

$Rate = k [A]^{m} [B]^{n}$

Where:

( k ) represents the rate constant,
( A ) and ( B ) denote the concentrations of the reactants,
( m ) and ( n ) indicate the orders of the reaction concerning ( A ) and ( B ).

i. Steps to Determine Rate Laws and Reaction Order:

a. Gather Experimental Data: Record the reaction rate at various concentrations of the reactants.
b. Initial Rate Method: In each trial, alter the concentration of one reactant while keeping the others constant, and note the initial rate.
c. Identify Reaction Order:
– Analyze how the rate varies with concentration.
– If doubling a reactant’s concentration results in a doubled rate, the order for that reactant is 1.
– If the rate quadruples with a doubled concentration, the order is 2.
– If the rate remains unchanged with varying concentration, the order is 0.

d. Formulate the Rate Law: After determining the orders for each reactant, the rate law can be expressed using the known values of ( m ), ( n ), and the rate constant ( k ).

ii. Application of Integrated Rate Laws:

Once the rate law is defined, integrated rate laws can be used to express the concentration of reactants over time.

a. For Zero-Order Reactions:
– Rate = ( k )
– Integrated form: ( [A] = [A0] – kt )

b. For First-Order Reactions:
– Rate = ( k[A] )
– Integrated form: ( ln[A] = ln[A0] – kt )

c. For Second-Order Reactions:
– Rate =

$k[A]^2$

-Integrated form:

$\frac{1}{[A]} = \frac{1}{[A_0]} + kt$

5.2.A.2 Rate Law: Reaction Rate Proportional to Reactant Concentrations:

1. Reaction Rate:

The reaction rate is the speed at which a reaction takes place, usually by measurement of change in concentration of product or reactant with time.

i. How it’s Measured:
– By measuring change in concentration, volume of gases, temperature, or light absorption over time.

ii. Factors that affect Rate:
a. Concentration: Higher concentration of reactants increases the rate with more collisions occurring.
b. Surface Area: Increased surface area increases the rate by having more reactant molecules in contact with each other.
c. Temperature: Increased temperature speeds up the energy of the molecules and therefore there are more collisions, in addition to quicker reactions.
d. Catalysts: Catalysts lower the activation energy and the reaction occurs faster but the catalyst is not consumed.
c. Pressure (for gases): Increased pressure squeezes gas molecule concentration together and therefore makes the reaction quicker.

2. Rate Law:

The rate law is an equation-formula in the form of reactants. It takes the form:

$Rate = k [A]^{m} [B]^{n}$

representing the rate of the chemical reaction in terms of the reactant concentrations. It is:

Where:
– Rate refers to the reaction rate.
– k represents the rate constant, and it is based on the reaction and temperature.
– [A] and [B] represent the reactant A and B concentrations.
– m and n are the orders of reaction with respect to A and B (experimentally determined).

3. Reaction Order:

Order of reaction is an alternative definition for how rate of reaction depends upon concentration of the reactant.

i. Types of Orders:
– First-order: Rate as a linear function of concentration (doubling of concentration doubles rate).
– Second-order: Rate as square of concentration (doubling the concentration quadruples rate).
– Zero-order: Rate remains independent of concentration.

ii. Determining Reaction Order:
–Method of Initial Rates: Observe how the rate changes at changing concentrations.
–Integrated Rate Laws: Examine concentration vs. time data for trends (e.g., linear plots for first and second orders).

iii. Overall Order:
The sum of the individual orders. For example, if the rate law is

$\text{Rate} = k[A]^2[B]^1$

, the overall order is 3.

4. Rate Constant (k):

The rate constant (k) is a key factor in the rate law that connects the reaction rate to the concentrations of the reactants. It is unique to each reaction at a specific temperature and does not depend on the concentrations of the reactants.

i. Role of the Rate Constant (k):
a. Determines the speed of the reaction: A higher k signifies a quicker reaction, while a lower k indicates a slower one.
b. Depends on the reaction mechanism: The value of k is affected by the type of reaction and its transition states.

ii. Dependence on Temperature:
– The rate constant tends to rise with temperature because of increased molecular collisions and energy, resulting in more effective collisions.
– The relationship between k and temperature is expressed by the Arrhenius equation:

$k = A e^{- \frac{E_{a}}{R T}}$

Where:
– (A) is the pre-exponential factor (related to how often collisions occur),
– (Ea) is the activation energy,
– (R) is the gas constant,
– (T) is the temperature in Kelvin.

As the temperature goes up, (k) also increases, which means the reaction rate accelerates.

In conclusion, the rate constant (k) indicates how fast a reaction occurs and increases with temperature due to greater molecular activity and energy.

5.2.A.3 Reaction Order and Rate Law:

1. Rate Law and Reaction Order:

i. Rate Law: The rate law gives the relationship of the reaction rate to the reactant concentration. It is normally expressed as:

$Rate = k [A]^{m} [B]^{n}$

where k is the rate constant, and m and n are the orders of the reaction with respect to reactants A and B.

Reaction Order: The reaction order is the exponent of the concentration term in the rate law. It indicates how the rate changes with the concentration of a reactant:
Zero-order: Rate is independent of the concentration of the reactant.
First-order: Rate is directly proportional to the concentration.
Second-order: Rate is proportional to the square of the concentration.

2. Overall Reaction Order:

The total reaction order is represented by the sum of the orders for each of the reactants in the rate equation.

For an example rate law:

$Rate = k [A]^{m} [B]^{n} [C]^{p}$

– m, n, and p are reaction orders relative to reactants A, B, and C, respectively.
– The total reaction order is the addition of these exponents:

$Overall Order = m + n + p$

Example:

If the rate law is:

Rate = k [A]^{2} [B]^{1}

The individual orders are 2 (for A) and 1 (for B), so the overall reaction order is:

2 + 1 = 3

Thus, the overall order of the reaction is 3.

3. Experimental Methods:

To experimentally determine the order of reaction, the following methods are typically used:

i. Method of Initial Rates:
a. Procedure: Measure the initial rate of reaction at different concentrations of reactants with all other variables constant.
b. How it Works* By studying how the rate changes with a change in reactant concentrations, you can determine the order for each reactant.
c. Example: If doubling the concentration of reactant A doubles the rate, the reaction is **first-order** with respect to A. If the rate quadruples, it is **second-order** with respect to A.

ii. Integrated Rate Laws:
a. Procedure: Measure the concentration of a reactant over time during the reaction.
b. How it Works: The concentration vs. time data will show some patterns depending on the reaction order. You can analyze the data in different forms (e.g., ln[A], 1/[A], or [A]) to determine the reaction order.

iii. Half-Life Method:
a. Procedure: See how the half-life (time required for half of a reactant to be consumed) changes with concentration.
b. How it Works:
first-order reactions, the half-life is independent of concentration and constant.
second-order reactions, the half-life depends on the variation in concentration.
zero-order reactions, the half-life is directly proportional to the initial concentration.

iv.Method of Isolation:
Procedure: If there is more than one reactant, isolate one reactant by maintaining its concentration far in excess of the others.
How it Works: Isolating a reactant makes its concentration effectively remain constant over the course of the reaction, allowing for easier determination of the order with respect to other reactants.

5.2.A.4 Rate Constant and Its Dependence on Temperature:

1. Rate Constant (k):

i. Definition:
The rate constant (symbolized as k) is a proportionality factor in the rate law equation that connects the rate of a chemical reaction to the concentrations of reactants. It is unique to a specific reaction at a specific temperature and usually depends on temperature.

In a rate law, it is expressed as follows:

$Rate = k [A]^{m} [B]^{n}$

where:
Rate is the reaction rate.
[A] and [B] are the concentrations of reactants.
m and n are the reaction orders with respect to each reactant.

ii. Role in the Rate Law:
The rate constant determines how fast a reaction occurs for given concentrations of reactants.
It is independent of the concentration of reactants, but it depends on factors like temperature and the nature of the reaction.
The magnitude of k assists in measuring the correlation between the reaction rate and the concentrations of reacting substances. Increasing values of k point towards faster reactions, whereas decreasing values point towards slower reactions.

iii. Temperature Dependence:
The rate constant k usually rises with an increase in temperature because of higher collision frequency and energy among reactant particles. This is expressed by the Arrhenius equation:

$k = A e^{- \frac{E_{a}}{R T}}$

where
A is the pre-exponential factor (frequency factor),
Ea is the activation energy,
R is the universal gas constant,
T is temperature in Kelvin.

2. Units of k:

The units of the rate constant k depend on the overall reaction order, which is the sum of the orders with respect to each reactant in the rate law. The general form of the rate law is:

$Rate = k [A]^{m} [B]^{n}$

The rate of the reaction typically has units of concentration/time (e.g., mol/L·s).

To determine the units of k, we can use the relationship between rate and concentration in the rate law. The rate equation has units:

$Rate = k \cdot [A]^{n} \cdot [B]^{m}$

The concentration terms have units of mol/L. The units of k depend on the reaction order as follows:

i. Zero-Order Reaction (Overall Order = 0):
Rate law: Rate = k[A]^0
The rate is independent of the concentration of reactants.
Units of k: Since rate = k, and rate = mol/L·s, the units of k are:

$k = \frac{mol}{L \cdot s} (Units of k : mol/L \. s)$

ii. First-Order Reaction (Overall Order = 1):
Rate law: Rate = k[A]^1
Units of k: For first-order reactions, the rate is directly proportional to the concentration of a single reactant. The units of k are:

$Units of k = \frac{mol/L \c. s}{mol/L} = s^{- 1}$

iii. Second-Order Reaction (Overall Order = 2):
Rate law: Rate = k[A]^2 or Rate = k[A]^1[B]^1
Units of k: For second-order reactions, the rate is proportional to the square of the concentration of a single reactant, or the product of the concentrations of two reactants. The units of k are:

$Units of k = \frac{mol/L \c. s}{{(mol/L)}^{2}} = \frac{mol/L \c. s}{{mol}^{2} / L^{2}}$

iv. Summary of Units for Different Overall Reaction Orders:

– Zero-order: mol/L·s
– First-order: s⁻¹
– Second-order: L/mol·s
– Third-order: L²/mol²·s

The units of k change depending on the overall reaction order, reflecting how the reaction rate depends on the concentrations of the reactants.

5.2.A.5 Determining Reaction Order by Comparing Initial Rates:

1. Initial Rate Method:

The Initial Rate Method is among the experimental techniques that are employed to determine the reaction order by comparing the initial rates of reaction at different concentrations of the reactants.

i. Steps to Determine Reaction Order Using the Initial Rate Method:

a. Determine Initial Rates: Set up experiments where the concentration of one or more reactants are varied, and measure the initial rate of the reaction for each set of concentrations. The initial rate is the rate of reaction at the very beginning, before a significant amount of product is formed or reactant concentrations have altered significantly.

b. Vary Reactant Concentrations: In each experiment, change the concentration of one reactant while keeping others constant. This isolates the effect of individual reactants on the rate of reaction.

c. Compare the Rates: Investigate how the initial rate changes when the concentration of a reactant is altered. This comparison is vital in determining the **reaction order** with regard to each reactant.

ii. How the Rate Law Relates to Initial Rates:
For a reaction like:

$Rate = k [A]^{m} [B]^{n}$

m and n are reaction orders with respect to reactants A and B.
The rate law shows how the rate changes as A and B concentrations change.

iii. Example of Using Initial Rate Method:

Suppose you perform two experiments with different concentrations of reactant A and observe the following initial rates:

Experiment	[A] (mol/L)	[B] (mol/L)	Initial Rate (mol/L·s)
1	0.10	0.10	0.020
2	0.20	0.10	0.080

Steps:

1. Compare the rates for [A]: In experiments 1 and 2, the concentration of B is kept constant, and only [A] is changed.

– The A concentration is doubled from 0.10 M to 0.20 M.
– The original rate is doubled from 0.020 mol/L·s to 0.080 mol/L·s (fourfold).

2. Determine the reaction order with respect to A:
– Based on the rate and concentration relationship of A, the rate is directly proportional to [A]^m.
– If the rate increases by a factor of 4 when [A] doubles, the reaction is second-order with respect to A (since 2² = 4).

3. Determine the order with respect to B: If another experiment is performed, changing [B] while keeping [A] constant, similar analysis can be used to determine the order with respect to B.

iii. General Process:
1. Select experiments in which one reactant concentration is varied with the others remaining constant.
2. Compare initial rates for such experiments.
3. Use the rate law equation and rate comparison to solve for reaction order relative to each reactant.

2. Rate Law:

i. General Form:

$Rate = k [A]^{m} [B]^{n}$

Where:

– k: Rate constant, reaction and temperature dependent.
– [A], [B]: Concentrations of reactant A and B.
– m, n: Reaction orders, meaning how the rate changes with each reactant’s concentration.

ii. Key Concepts:
– Reaction Order (m, n): Tells us how the rate changes with concentration.
– First-order: Rate is linearly proportional to concentration.
– Second-order: Rate is proportional to square of concentration.
– Zero-order: Rate does not depend upon concentration.
– Rate Constant (k): It is a constant which relates rate to concentrations and depends upon the temperature.

iii. Example:
– First-order: Rate = k[A] (rate increases by two-fold if [A] is two-fold).
– Second-order: Rate = k[A]^2 (rate is four-fold if [A] is doubled).
– Zero-order: Rate = k (rate does not depend on [A]).

3. Calculating Reaction Order:

i. Collect Data: Record initial rates and reactant concentrations for various experiments.

ii. Express Rate Law: General equation:
(Rate = k[A]^m[B]^n), where m and n are the reaction orders.

iii. Choose Two Experiments: Choose two experiments in which concentration of one of the reactants varies while all other reactant concentrations are held constant.

iv. Compute Reaction Order:
– Compare the rates for each of the reactants:

$\frac{{Rate}_{1}}{{Rate}_{2}} = {(\frac{[A_{1}]}{[A_{2}]})}^{m}$

– Solve for m or n with logarithms.

v. Repeat for Other Reactants: Find orders for other reactants by holding one constant.

vi. Overall Order: Sum the individual orders (m + n) for the overall reaction order.

OLD Content

Rate Laws: An Introduction

Initial Rate Method: the “instantaneous rate” just after the reaction beings; Usually the fastest →
- K = rate constant; m and n = rate orders
Rate Constant (k): relates the rate of the reaction to the concentration of the reactants = slope
- Value of k is positive for slope of products and negative for the slope of reaction
- Value of this constant is dependent on temperature and units reflect the overall reaction order
- TRICK: units for k are always going to be molarity to the negative one number less than the reaction order / unit of time

2 Important Concepts (when writing a rate law)

The concentrations of the products are not in the rate law
The value of m/n can only be determined experimentally-not from the coefficients of the overall equation

- Except for elementary reactions

Types of Rate Laws

Differential Rate Law/the Rate Law: expresses how rate depends on concentration
Integrated rate law: expresses how the concentrations depend on time
- Use integrated rate law when asked to find how much of a reactant/product at certain time

Finding Rate Law Given Data Table

Find two experiments where the concentration of one reactant is changing and the other reactant remains the same
- Rate Formula 1 / Rate Formula 2 → solve for rate orders → plug in values in rate formula and solve for K

Overall Reaction Order

Find the overall reaction order → add up each rate order
- Ex: → Overall reaction order is 1 +2 + 3 = 6
Greater the order/exponent = the faster the reactant is being consumed

Determining the Form of the Rate Law (aA → products)

The reaction starts as a first-order reaction because the rate depends on the number of reactant molecules adsorbed by the catalyst. However, once all the surface sites of the catalyst are fully occupied, the rate is no longer affected by the concentration of the reactant and the reaction becomes zero-order

AP Chemistry 5.2 Introduction to Rate Law Study Notes

AP Chemistry 5.2 Introduction to Rate Law Study Notes - New Syllabus Effective fall 2024