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5.2 Introduction to Rate Law

5 min readjanuary 8, 2023

Dylan Black

Dylan Black

Dalia Savy

Dalia Savy

Dylan Black

Dylan Black

Dalia Savy

Dalia Savy

In chemistry, when discussing , we know that when the concentration of a reactant rises, the rate of the reaction similarly increases. This makes sense since it logically follows that if we have more in the same volume compared to a lesser amount of reactant, there will be a quicker reaction. However, how do we quantitatively determine how much faster the rate will be? Well, this is where a comes into play.

👉Be sure to review reaction rates and factors that influence it, such as concentration as we spoke about here.

What is a Rate Law?

In chemistry, a is an equation that describes the relationship between the rate of a chemical reaction and the concentrations of the . A is defined by saying: R = k[A]^n[B]^m... where:

  • R is the rate of the reaction (sometimes also notated as Δ[]/Δt, which we will delve more in-depth into in the next section),

  • k is the ,

  • [A] and [B] represent the concentrations of , and

  • n and m are for each reactant (A, B, etc).

This is generalized, which is why there is a ... following. A reaction could hypothetically have 3, 4, or 5 , though for the AP exam you often won't see more than 2. It's actually quite rare for a reaction with 3+ since it would require three atoms/molecules to bump into each other just right for a reaction to take place. It occurs, but not often and not quickly.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-YhQkosgMIqHK.gif?alt=media&token=8247b409-41d7-4bc0-8e5e-c71d68be57d3

Animation Courtesy of GIPHY; We'll delve deeper into collisions later in this unit.

What Does Reaction Order Mean?

n and m define what is called each reactant's reaction order. Reaction order brings us back to the initial question we asked: how do we determine quantitatively how the ? The reaction order is the answer! It describes how the rate of the reaction changes as the concentration of each reactant changes.

For example, let's say the imaginary for the reaction A + B → C is R = k[A]²[B]¹. This can tell us that as we increase the concentration of A (assuming a constant [B]), the rate will increase quadratically. For example, if we double the concentration of A, the rate will quadruple. Similarly, if we double the concentration of B, the rate will double, since the order of B is 1. The same applies for orders of 3, 4, etc. (if we double [], R goes up by 8 times and 16 times respectively).

The overall reaction order for the full reaction is the sum of the orders for each reactant. In our imaginary example, the overall reaction order would be 3, since the reaction order of reactant A is 2 and the reaction order of reactant B is 1.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F5c446a0dbe17643a5341e1305925d455.png?alt=media&token=0c3e486c-071f-4cfd-b377-c7d72266f365

Quadratic vs. Linear Relationships (x2 vs x)

Using Experiments to Determine a Rate Law

There's one important thing to note about rate laws: they can only be determined experimentally. What a chemist will do is run a ton of tests at different concentrations and then find the corresponding rates for each test. With this data, they can determine the rate of the reaction. Let's take a look at an example to find out how we mathematically figure this out:

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F7f1b824a255cb409a8d07a77551fb6b8.png?alt=media&token=f5546abf-387d-4932-92fc-bf5e7352e80f

Example Courtesy of Khan Academy

Here we have a reaction: 2NO + 2H₂ → N₂ + 2H₂O. We can see three experiments done with different concentrations for each reactant. Let's take a look at the first two experiments where [NO] changes. We see the concentration of [NO] double from the first experiment to the second, and then we see the rate increase from 1.25 * 10⁻⁵ to 5.00 * 10⁻⁵. This is a change by a factor of 4 (5 * 10⁻⁵/1.25 * 10⁻⁵ = 4). Therefore, since doubling concentration makes the rate quadruple, the reaction is 2nd order with regard to NO. Note that in order to find the reaction order with respect to NO, we had to choose two experiments where the [NO] changed, but [H₂] was constant.

Let's take a look at H₂ now. For experiments 2 and 3, the concentration of H₂ doubles like it did for NO, but the rate increases from 5 * 10⁻⁵ to 1 * 10⁻⁴, by a factor of 2 (1 * 10⁻⁴/⁵ * 10⁻⁵ = 2). Therefore, the reaction is first order in H₂. Now, we can put together the by putting all of this together: R = k[NO]²[H₂]. As an exercise, pick one of the experiments and plug in the correct numbers to figure out the value of k, and then read the next section and figure out the right units for k. (You should get k = 250 M⁻²s⁻¹).

Understanding k, the Rate Constant

The , k, is a tricky thing to understand. Essentially, it serves as a proportionality constant for the reaction to take place. It makes a bit more sense if you understand the calculus behind (which we will describe in the next section, though it is by no means required for the AP exam), but essentially all you need to know is that k is a constant that quantifies the rate of each reaction and that it is temperature specific. This means that for the same reaction at different temperatures, the is different!

Another important aspect of the is that its units change depending on the overall reaction order. Let's see if we can figure some of them out. Rate is always in M/s, and concentration is always in M (M = mol/L). Thus it follows that for certain reactions:

Zeroth Order

If the overall reaction order is 0:

  • The is R = k[A]⁰, which simplfies to R = k

  • k is in units M/s.

First Order

If the overall reaction order is 1:

  • R = k[A]¹, which you can think of as M/s = k * M

  • k is in s⁻¹ (per seconds)

Second Order

If the overall reaction order is 2:

  • R = k[A]², which you can think of as M/s = k * M²

  • k is in M⁻¹*s⁻¹ (1/Ms)

🎥 Watch AP Chemistry teacher Mónica Gracida review reaction rates and rate laws in unit five of AP Chemistry: Kinetics.

Key Terms to Review (14)

Concentration Changes

: Concentration changes refer to variations in the amount of substance per unit volume in a solution or mixture during a chemical process.

Experimental Determination

: Experimental determination involves using experimental methods to find out specific values or properties of substances involved in chemical reactions.

First Order Reaction

: A first order reaction is a type of chemical reaction where the rate of the reaction depends on the concentration of one reactant.

Kinetics

: Kinetics is branch of chemistry or biochemistry concerned with measuring and studying rates of reactions.

Linear Relationship

: A linear relationship in chemistry refers to a situation where any change in one quantity results in a proportional change in another quantity. This is often represented graphically as a straight line.

Quadratic Relationship

: A quadratic relationship between two variables means that one variable varies with square value other variable.

Rate Constant

: The rate constant (k) is a proportionality factor in kinetics equations that relates the rate of a reaction to the concentrations of reactants. Its value depends on temperature and other factors but not on concentration.

Rate Law

: The rate law is an equation that relates the reaction rate with concentrations or pressures of reactants and constant parameters.

Rate of Reaction

: The rate of reaction refers to how quickly reactants turn into products in a chemical reaction.

Reactants

: Reactants are substances that start a chemical reaction. They interact with each other to form new substances called products.

Reaction Orders

: Reaction orders describe how the rate of a chemical reaction changes as the concentration of its reactants change. It can be zero, first, or second order.

Reaction Rates

: Reaction rates refer to how fast reactants turn into products in a chemical reaction.

Second Order Reaction

: A second order reaction is another type of chemical reaction where the rate depends on either two different reactants' concentrations or square of concentration of single reactant.

Zeroth Order Reaction

: A zeroth order reaction is a chemical reaction whose rate does not depend on the concentration of the reactant. The rate remains constant over time.

5.2 Introduction to Rate Law

5 min readjanuary 8, 2023

Dylan Black

Dylan Black

Dalia Savy

Dalia Savy

Dylan Black

Dylan Black

Dalia Savy

Dalia Savy

In chemistry, when discussing , we know that when the concentration of a reactant rises, the rate of the reaction similarly increases. This makes sense since it logically follows that if we have more in the same volume compared to a lesser amount of reactant, there will be a quicker reaction. However, how do we quantitatively determine how much faster the rate will be? Well, this is where a comes into play.

👉Be sure to review reaction rates and factors that influence it, such as concentration as we spoke about here.

What is a Rate Law?

In chemistry, a is an equation that describes the relationship between the rate of a chemical reaction and the concentrations of the . A is defined by saying: R = k[A]^n[B]^m... where:

  • R is the rate of the reaction (sometimes also notated as Δ[]/Δt, which we will delve more in-depth into in the next section),

  • k is the ,

  • [A] and [B] represent the concentrations of , and

  • n and m are for each reactant (A, B, etc).

This is generalized, which is why there is a ... following. A reaction could hypothetically have 3, 4, or 5 , though for the AP exam you often won't see more than 2. It's actually quite rare for a reaction with 3+ since it would require three atoms/molecules to bump into each other just right for a reaction to take place. It occurs, but not often and not quickly.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-YhQkosgMIqHK.gif?alt=media&token=8247b409-41d7-4bc0-8e5e-c71d68be57d3

Animation Courtesy of GIPHY; We'll delve deeper into collisions later in this unit.

What Does Reaction Order Mean?

n and m define what is called each reactant's reaction order. Reaction order brings us back to the initial question we asked: how do we determine quantitatively how the ? The reaction order is the answer! It describes how the rate of the reaction changes as the concentration of each reactant changes.

For example, let's say the imaginary for the reaction A + B → C is R = k[A]²[B]¹. This can tell us that as we increase the concentration of A (assuming a constant [B]), the rate will increase quadratically. For example, if we double the concentration of A, the rate will quadruple. Similarly, if we double the concentration of B, the rate will double, since the order of B is 1. The same applies for orders of 3, 4, etc. (if we double [], R goes up by 8 times and 16 times respectively).

The overall reaction order for the full reaction is the sum of the orders for each reactant. In our imaginary example, the overall reaction order would be 3, since the reaction order of reactant A is 2 and the reaction order of reactant B is 1.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F5c446a0dbe17643a5341e1305925d455.png?alt=media&token=0c3e486c-071f-4cfd-b377-c7d72266f365

Quadratic vs. Linear Relationships (x2 vs x)

Using Experiments to Determine a Rate Law

There's one important thing to note about rate laws: they can only be determined experimentally. What a chemist will do is run a ton of tests at different concentrations and then find the corresponding rates for each test. With this data, they can determine the rate of the reaction. Let's take a look at an example to find out how we mathematically figure this out:

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F7f1b824a255cb409a8d07a77551fb6b8.png?alt=media&token=f5546abf-387d-4932-92fc-bf5e7352e80f

Example Courtesy of Khan Academy

Here we have a reaction: 2NO + 2H₂ → N₂ + 2H₂O. We can see three experiments done with different concentrations for each reactant. Let's take a look at the first two experiments where [NO] changes. We see the concentration of [NO] double from the first experiment to the second, and then we see the rate increase from 1.25 * 10⁻⁵ to 5.00 * 10⁻⁵. This is a change by a factor of 4 (5 * 10⁻⁵/1.25 * 10⁻⁵ = 4). Therefore, since doubling concentration makes the rate quadruple, the reaction is 2nd order with regard to NO. Note that in order to find the reaction order with respect to NO, we had to choose two experiments where the [NO] changed, but [H₂] was constant.

Let's take a look at H₂ now. For experiments 2 and 3, the concentration of H₂ doubles like it did for NO, but the rate increases from 5 * 10⁻⁵ to 1 * 10⁻⁴, by a factor of 2 (1 * 10⁻⁴/⁵ * 10⁻⁵ = 2). Therefore, the reaction is first order in H₂. Now, we can put together the by putting all of this together: R = k[NO]²[H₂]. As an exercise, pick one of the experiments and plug in the correct numbers to figure out the value of k, and then read the next section and figure out the right units for k. (You should get k = 250 M⁻²s⁻¹).

Understanding k, the Rate Constant

The , k, is a tricky thing to understand. Essentially, it serves as a proportionality constant for the reaction to take place. It makes a bit more sense if you understand the calculus behind (which we will describe in the next section, though it is by no means required for the AP exam), but essentially all you need to know is that k is a constant that quantifies the rate of each reaction and that it is temperature specific. This means that for the same reaction at different temperatures, the is different!

Another important aspect of the is that its units change depending on the overall reaction order. Let's see if we can figure some of them out. Rate is always in M/s, and concentration is always in M (M = mol/L). Thus it follows that for certain reactions:

Zeroth Order

If the overall reaction order is 0:

  • The is R = k[A]⁰, which simplfies to R = k

  • k is in units M/s.

First Order

If the overall reaction order is 1:

  • R = k[A]¹, which you can think of as M/s = k * M

  • k is in s⁻¹ (per seconds)

Second Order

If the overall reaction order is 2:

  • R = k[A]², which you can think of as M/s = k * M²

  • k is in M⁻¹*s⁻¹ (1/Ms)

🎥 Watch AP Chemistry teacher Mónica Gracida review reaction rates and rate laws in unit five of AP Chemistry: Kinetics.

Key Terms to Review (14)

Concentration Changes

: Concentration changes refer to variations in the amount of substance per unit volume in a solution or mixture during a chemical process.

Experimental Determination

: Experimental determination involves using experimental methods to find out specific values or properties of substances involved in chemical reactions.

First Order Reaction

: A first order reaction is a type of chemical reaction where the rate of the reaction depends on the concentration of one reactant.

Kinetics

: Kinetics is branch of chemistry or biochemistry concerned with measuring and studying rates of reactions.

Linear Relationship

: A linear relationship in chemistry refers to a situation where any change in one quantity results in a proportional change in another quantity. This is often represented graphically as a straight line.

Quadratic Relationship

: A quadratic relationship between two variables means that one variable varies with square value other variable.

Rate Constant

: The rate constant (k) is a proportionality factor in kinetics equations that relates the rate of a reaction to the concentrations of reactants. Its value depends on temperature and other factors but not on concentration.

Rate Law

: The rate law is an equation that relates the reaction rate with concentrations or pressures of reactants and constant parameters.

Rate of Reaction

: The rate of reaction refers to how quickly reactants turn into products in a chemical reaction.

Reactants

: Reactants are substances that start a chemical reaction. They interact with each other to form new substances called products.

Reaction Orders

: Reaction orders describe how the rate of a chemical reaction changes as the concentration of its reactants change. It can be zero, first, or second order.

Reaction Rates

: Reaction rates refer to how fast reactants turn into products in a chemical reaction.

Second Order Reaction

: A second order reaction is another type of chemical reaction where the rate depends on either two different reactants' concentrations or square of concentration of single reactant.

Zeroth Order Reaction

: A zeroth order reaction is a chemical reaction whose rate does not depend on the concentration of the reactant. The rate remains constant over time.


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© 2024 Fiveable Inc. All rights reserved.

AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.