AP Chem Integrated Rate Law

Summary

In this video, Mrs. Oliver introduces integrated rate laws, a key concept in AP Chemistry. Unlike differential rate laws, which relate the concentration of reactants to reaction rates, integrated rate laws focus on the relationship between concentration and time. The video covers three types of integrated rate laws—zero, first, and second order—explaining how to identify them using graphs. Mrs. Oliver emphasizes recognizing linear relationships in these graphs to determine reaction order and calculating rate constants (K) from slope values. Practical graphing techniques and calculations are also demonstrated.

Takeaways

• 📚 Integrated rate laws relate concentration to time, unlike differential rate laws which relate concentration to reaction rate.
• 📊 There are three integrated rate laws to know: zero-order, first-order, and second-order.
• 📉 For a zero-order reaction, plotting concentration versus time gives a linear relationship, where the slope is negative K (the rate constant).
• 📝 Zero-order reactions follow the equation: [A] = -Kt + [A]₀, which is in slope-intercept form (Y = MX + B).
• 🔢 For a first-order reaction, a linear graph is obtained by plotting the natural log (ln) of concentration versus time.
• 📈 The first-order integrated rate law is: ln[A] = -Kt + ln[A]₀, also in slope-intercept form.
• 🧮 Second-order reactions give a linear plot when time is graphed versus the inverse of concentration (1/[A]).
• 🔍 To determine the reaction order, graph the data three ways: concentration versus time, ln(concentration) versus time, and 1/concentration versus time, and see which graph is linear.
• 🧠 For a first-order reaction, the slope of the ln(concentration) vs. time graph equals -K, and calculating this slope gives the rate constant.
• 💡 Use the slope of the linear graph to find K, with the rate constant being positive even if the slope is negative in the calculation.

Q & A

What is the difference between differential rate laws and integrated rate laws?

Differential rate laws show the relationship between the concentration of reactants and the rate of reaction, while integrated rate laws focus on the relationship between concentration and time.

How do you identify a zero-order reaction using a graph?

For a zero-order reaction, if you graph concentration versus time and get a straight line with a constant slope, the reaction is zero-order.

What is the significance of the slope in an integrated rate law graph?

The slope of the line in an integrated rate law graph represents the rate constant (K). In a zero-order reaction, the slope is the rate constant, while in a first-order or second-order reaction, it corresponds to the natural log or the inverse of the concentration.

How can you identify a first-order reaction from a graph?

A first-order reaction can be identified if the graph of time versus the natural log of the concentration gives a straight line.

What do the variables in the zero-order integrated rate law equation represent?

In the zero-order integrated rate law equation [A] = -Kt + [A]₀, [A] is the concentration at time t, K is the rate constant, and [A]₀ is the initial concentration.

What is the equation for the first-order integrated rate law?

The equation for the first-order integrated rate law is ln[A] = -Kt + ln[A]₀, where [A] is the concentration at time t, K is the rate constant, and [A]₀ is the initial concentration.

How do you determine if a reaction is second-order from a graph?

For a second-order reaction, a graph of time versus 1/[A] should yield a straight line if the reaction follows second-order kinetics.

What steps do you follow to determine the order of a reaction using graphing techniques?

You graph time versus concentration, time versus the natural log of concentration, and time versus 1/concentration. The graph that results in a straight line indicates the order of the reaction.

How is the rate constant (K) calculated from a graph?

The rate constant (K) is calculated by finding the slope of the linear graph that corresponds to the correct order of the reaction (e.g., concentration, natural log of concentration, or 1/concentration).

Why is it important to double-check the graphs for first- and second-order reactions?

Double-checking ensures that the reaction order is correct. For example, if the natural log of concentration versus time gives a straight line, it suggests a first-order reaction. However, you should also verify that the second-order graph does not give a linear relationship.

Outlines

00:00

📚 Introduction to Integrated Rate Laws

Mrs. Oliver introduces the topic of integrated rate laws, contrasting them with differential rate laws. Differential rate laws show the relationship between the concentration of reactants and the reaction rate, typically expressed as Rate = k[Reactant]^n. Integrated rate laws, on the other hand, involve graphing concentration vs. time to determine reaction order. She explains the three types of integrated rate laws (zero, first, and second order) relevant for AP Chemistry, with an emphasis on recognizing these laws through graphical representations. A linear concentration vs. time graph indicates a zero-order reaction, while the slope of this line is the rate constant (k), following the slope-intercept form (y = mx + b).

05:01

📊 Finding the Integrated Rate Law and Rate Constant

Mrs. Oliver outlines the procedure for determining the integrated rate law and the rate constant (k) using a set of experimental data. The process involves graphing the data three ways: concentration vs. time, natural log of concentration vs. time, and 1/concentration vs. time. By comparing the graphs, students can determine the reaction order based on which graph shows a linear relationship. She also mentions tools like Google Classroom resources and spreadsheet programs to assist with the graphing process. The key is to find the graph that yields a straight line, which will indicate whether the reaction is zero, first, or second order.

10:01

📈 Analyzing the Graphs: Identifying Reaction Order

In this paragraph, Mrs. Oliver walks through an example using hydrogen peroxide. The concentration vs. time graph is curved, ruling out a zero-order reaction. After plotting the natural log of concentration vs. time, the resulting straight line indicates that the reaction is first-order. To double-check, she suggests plotting 1/concentration vs. time, but this graph is non-linear, confirming that the reaction is not second-order. Therefore, the reaction is determined to be first-order because the natural log vs. time graph gives a linear relationship.

🧮 Calculating the Rate Constant (k) from Graph Data

Mrs. Oliver explains how to calculate the rate constant (k) from the slope of the linear natural log vs. time graph. Using specific data points, she demonstrates the calculation of the slope (change in y over change in x) to find k. For a first-order reaction, the slope is negative, and the absolute value of this slope gives the rate constant k. In this example, the calculated slope is -8.32, meaning the rate constant k is 8.32.

Keywords

💡Differential Rate Law

The differential rate law describes how the rate of a reaction depends on the concentration of reactants. In the video, it's mentioned that the rate is proportional to the concentration of each reactant raised to a specific power, known as the reaction order. This concept is contrasted with integrated rate laws, where the relationship between concentration and time is explored.

💡Integrated Rate Law

Integrated rate laws express the relationship between the concentration of reactants and time, rather than just the reaction rate. In the video, it's explained that these laws allow chemists to determine the order of a reaction by analyzing concentration data over time and looking for linear relationships in specific types of graphs.

💡Reaction Order

Reaction order refers to the exponent to which the concentration of a reactant is raised in the rate law. The video discusses how the reaction order can be determined by analyzing graphs of concentration versus time. For example, a zero-order reaction shows a linear relationship between concentration and time, while first-order and second-order reactions show different linear relationships with transformed concentration values.

💡Zero-order Reaction

In a zero-order reaction, the rate of the reaction is independent of the concentration of the reactant. The video explains that when a graph of concentration versus time is linear, the reaction is zero-order. The corresponding integrated rate law is described as concentration being equal to the initial concentration minus a term involving the rate constant and time.

💡First-order Reaction

A first-order reaction is one where the rate of reaction is directly proportional to the concentration of one reactant. In the video, it is explained that a graph of the natural log of concentration versus time will be linear for a first-order reaction. The integrated rate law for this type of reaction involves the natural log of concentration.

💡Second-order Reaction

A second-order reaction is one where the rate depends on either the concentration of one reactant squared or on the concentrations of two different reactants. In the video, a graph of 1/concentration versus time is used to identify second-order reactions. The slope of this graph gives the rate constant for second-order reactions.

💡Rate Constant (K)

The rate constant (K) is a proportionality constant in the rate law that relates the rate of reaction to the concentrations of the reactants. In the video, it is explained that the value of K can be determined from the slope of a graph, depending on the reaction order. For example, in a first-order reaction, K is equal to the negative of the slope of the linear graph of the natural log of concentration versus time.

💡Slope-Intercept Form

Slope-intercept form is a linear equation format (y = mx + b) used to describe straight lines. The video emphasizes that integrated rate laws are expressed in this form, where the y-value corresponds to concentration or a transformation of concentration, the x-value corresponds to time, the slope is related to the rate constant, and the intercept is related to the initial concentration.

💡Natural Log (ln)

The natural logarithm (ln) is used in the analysis of first-order reactions in the video. By plotting the natural log of concentration versus time, a linear relationship can reveal a first-order reaction. The natural log allows the non-linear concentration data to be transformed into a linear format for easier analysis.

💡Graphing Techniques

Graphing techniques are essential in identifying the order of a reaction. The video describes how to create different types of graphs (concentration vs. time, ln(concentration) vs. time, and 1/concentration vs. time) to find linear relationships, which indicate the reaction order. This technique helps in determining the appropriate integrated rate law and rate constant for the reaction.

Highlights

Introduction to integrated rate laws and their differences from differential rate laws.

Differential rate laws reveal the relationship between the concentration of reactants and the rate of reaction.

Integrated rate laws focus on the relationship between concentration and time using graphs.

Three types of integrated rate laws to know: zero-order, first-order, and second-order reactions.

In zero-order reactions, concentration versus time produces a linear graph.

Zero-order rate law equation: [A] = -kt + [A]₀, where k is the slope, and [A]₀ is the initial concentration.

First-order reactions are identified by a linear relationship between the natural log of concentration and time.

First-order rate law equation: ln[A] = -kt + ln[A]₀, with k representing the rate constant.

Second-order reactions exhibit linearity when plotting 1/[A] versus time.

Second-order rate law equation: 1/[A] = kt + 1/[A]₀, where [A]₀ is the initial concentration.

Graphing techniques include plotting concentration, natural log of concentration, and inverse of concentration versus time.

Use graphs to determine the order of the reaction by finding which plot gives a straight line.

Google Classroom tools are available for plotting rate laws and generating graphs.

Example problem: Graph concentration of hydrogen peroxide to determine reaction order using three different methods.

For first-order reactions, the slope of the natural log plot can be used to calculate the rate constant (k).

Transcripts

hi guys it's mrs. Oliver again

so hopefully you watched the review of

differential rate laws first if you

haven't stop this video and go back to

the first video so in this video we're

going to talk about integrated rate laws

this is going to be a new topic for us

and the difference between differential

rate laws so differential rate laws

reveal the relationship between

concentration of reactants and the rate

of reaction we usually call this the

rate law which is rate is equal to K

times the concentration of each reactant

raised to their order integrated rate

law and the other half we have to look

at graphs and when we look at the graphs

we're going to be looking at the

relationship of concentration versus

time so we're going to take a look at

those right now so there are going to be

three integrated rate laws that we need

to know zero first and second order

there are certainly others these are the

only ones that we need to know for ap

chemistry if you look on your green

sheet you will see that these laws are

all given to you you do not need to

memorize them whatsoever you do need to

be able to recognize which one is zero

order which ones first and which ones

second because that is not labeled for

you on the green sheet so zero order is

this time versus the concentration is

linear so again we will be able to

determine the order this time not by

comparing concentrations in a data table

like we were doing with differential

rate laws what we're going to do here is

we're literally going to look at graphs

and we're going to see which graph gives

us a linear relationship and that will

tell us what order it is so if we graph

our concentration versus time and we get

a straight line meaning linear constant

slope then we know the reaction is

zero-order and so therefore I this is

the rate law for it

concentration of our reactant a is equal

to negative K times time plus

concentration of a initially so AO means

initial concentration a and this is

going to be concentration at any given

time T and then K is going to be the

slope of that line

so hopefully you recognize that this is

in slope intercept form

right this would be y is equal to M Y or

slow X plus B so this is going to be

your your y-intercept right where we

have initial concentration so again

integrated rate laws are all in

slope-intercept form Y is equal to M X

plus B so our x value meaning I'm sorry

so our M values slope is going to give

you your rate constant looking at the

graph if we look at the slope of that

line that'll give you your your rate

constant K alright so if it's first

order time versus the natural log okay

so hey here's some precalc stuff coming

at you algebra two maybe a little but

high so time is equal to the natural log

not log base ten but natural log of the

concentration is linear if we get that

then we know that the reaction is

first-order and our rate law for that is

going to be natural log of the

concentration of a is going to equal

negative K times time plus natural log

of the initial concentration do you

notice that this so zero order and first

order is pretty much the same thing the

only difference is we've taken the

natural log of our concentrations at

each point okay and then finally second

order we're going to know that the

reaction is second order if we look at

the graph

and we have a linear constant slope when

we graph time versus one divided by the

concentration so here's our rate law for

that so one over and concentration that

should not be AO that should just be a

is equal to KT plus 1 over a Oh again

AO stands for initial so what is the

concentration at time zero and then this

right here is going to be the

concentration at time T not zero

all right so how would we do this here's

our problem find the integrated rate law

for the value for the sorry find Hana

created rate law and the value for the

rate constant K so you'll be given a set

of data kind of like this and you need

to graph it three different ways you're

gonna graph it as straight X versus Y

you're going to then graph it again by

taking the natural log of each of these

values first this time and then you will

also graph it a third time by taking

each of these values and doing 1 divided

by 1 1 divided by 0.9 1 divided by 0.7 8

and graph that again so you're going to

make three separate graphs and then what

you're going to want to do is compare

those three graphs of just the straight

time versus concentration time versus

natural log of each of these

concentrations and then time versus one

divided by the concentration so you're

gonna do this if you want I can post a

link where you can download a program

for a graphing calculator just totally

completely not necessary also on our

Google classroom I will give you the

rate law spreadsheet which all you have

to do is type in the numbers and it will

do the three different graphs for you so

let's take a look so we graph for this

first one right time versus the

concentration of hydrogen peroxide so

we're going to take these data points

we're gonna just straight graph them

right so these data points here in a

straight graph them and we see that it

gives us with our Google spreadsheet or

with our graphing calculator a curved

line so we did not get a linear

relationship between these so we know

that our reaction is not zero order so

not a zero order reaction so we're gonna

do to the graphing again but this time

we take the natural log of each of our

values so if you look at our previous

one right we had one point nine point

seven eight so we're taking all those

values and now we're taking the natural

log of each one of them and we're going

to recraft this so now this time my X is

still time but my Y values are now going

to be this natural log of each of my

concentrations and we can see that we

get a straight line right constant slope

no change in the slope same when we put

that into the Google generator so this

is a straight line which is going to let

me know that this is probably

first-order but we should double check

and make sure it's not second-order so

we're going to try that again so this

time we're going to take all of our

concentrations and we're going to say

one divided by the concentration so one

divided by one gave us one and so we

take each one of our our concentrations

and we say one divided by that

concentration we graph it again and we

can see that we definitely do not get a

linear relationship we see that it's

curving upward we have a change in rate

so therefore the one that gives us

linear tells us what order the reaction

is so natural log of the concentration

is linear therefore our reaction is

first-order because here it's definitely

not zero order we did not get a constant

slope here we do get a constant slope

which lets us know that it's first order

so if natural log or a time versus

natural log of concentration gives us

linear we know it's first order when we

double-checked and we know it's not

second-order because again we didn't get

a linear relationship so as a result the

reaction is first-order because we got a

your relationship when we graphed the

natural log of our concentration versus

time so our differential rate law for

this is going to be R is equal to the

concentration of hydrogen peroxide so

this is our differential rate law we

know that the concentration is

first-order because again we got a

linear relationship the integrated rate

law for this guy though is going to be

equal to natural log of the

concentration of hydrogen peroxide at a

given time is equal to negative K times

time and then natural log of h2o 2 at at

time 0 so to find that initial

concentration here we are going to look

at the y-intercept so our y-intercept is

going to tell us what that is this value

if we look happens to me 0 and then what

is the rate constant K so remember that

this guy this integrated rate law is in

slope intercept form so this is your Y

value so K would be M meaning slope so

if we take the slope of this line if we

calculate the slope of this linear line

that's going to give us our K value so

to calculate the slope from the time

versus natural log table what we'll do

is just take a pair of y's and x's and

get the slope so if we take the

difference in time right so if I'm

looking at at times starting with time 0

and taking the time at the end right

over 3600 seconds so it's y2 versus y1

and so it's just two point nine nine

minus zero over 3600 minus zero so this

is going to be my change in

concentration well natural log of

concentration and this is gonna be my

change in time I divide that out and so

this gives me my slope which also

happens to be my value for K

so here's our integrated rate law again

remember that it's in slope-intercept

form where K is going to equal our

negative slope so because it's negative

slope and our slope was negative eight

point three two then our K value is

going to be positive eight point three

two