AP Chem Integrated Rate Law
Summary
TLDRIn 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
📚 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).
📊 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.
📈 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.
Mindmap
Keywords
💡Differential Rate Law
💡Integrated Rate Law
💡Reaction Order
💡Zero-order Reaction
💡First-order Reaction
💡Second-order Reaction
💡Rate Constant (K)
💡Slope-Intercept Form
💡Natural Log (ln)
💡Graphing Techniques
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
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