LESSON 17.1
Tri-Valley AP Chemistry
C60
THE RATE LAW AND ORDERS
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There are actually TWO different rate laws.
This is the first, known simply as THE rate law.
Part 1: Meet the Rate Law
For the hypothetical reaction
A+BC
we can write a rate law (aka – the differential rate law) describing the rate of the reaction as a function
of reactant concentration. It looks like this:
Part 2: The Order of a Reactant
A reactant’s order is how the rate depends on the concentration of that reactant. In this class, we will
see three different orders: 1st, 2nd, and 0th.
We will learn two different ways to determine a reactant’s order:
1. Calculating with THE rate law using initial rates of many experiments (trials)
2. Graphing with integrated rate laws using concentrations of a single trial over time
But first, let’s play around with them a bit.
Discussion Questions #5 and 9, pg. 601
1st Order Reaction
AB
The hypothetical reaction above is first-order in A.
1) What is the rate law for this reaction?
2) When the concentration of A is 2.0 mols/L, the rate of the reaction is 6 mol/L∙min. What is the
value of k, the rate constant? Include units.
3) The concentration of A is now doubled to 4.0 mol/L. What is the new rate of the reaction?
2nd Order Reaction
CD
The hypothetical reaction above is second-order in C.
4) What is the rate law for this reaction?
5) The value of the rate constant, k¸ is 0.25 L/mol∙sec. If the concentration of C is 1.2 M, what is the
rate of the reaction?
6) The concentration of C is now doubled to 2.4 M. What is the new rate of the reaction?
0th Order Reaction
EF
The hypothetical reaction above is zeroth-order in E.
7) What is the rate law for this reaction?
8) The rate of the reaction is 1200 molecules/min when the concentration of E is 2.4 × 10 6
molecules/L. What is the value of k, the rate constant? Include units.
9) The concentration of E is now doubled to 4.8 × 106 molecules/L. What is the new rate of the
reaction?
A Combo!
G+HI
The hypothetical reaction above is first-order in G and second-order in H.
10) What is the rate law for this reaction?
11) When the concentration of G is 0.100 M and the concentration of H is 0.350 M, the rate of the
reaction is 0.812 M/min. What is the value of the rate constant, k? Include units.
12) If the concentration of G is 1.2 M and the concentration of H is 0.90 M, what is the rate of the
reaction?
LESSON 17.2
Tri-Valley AP Chemistry
C60
DETERMINING THE RATE LAW OF A REACTION
Opportunity + Dedication  Success
Example 1. Consider the following reaction:
A→ P
The reaction was repeated three times using different concentrations of A and the initial rate
was measured each time. The results are tabulated below.
Trial
1
2
3
Initial Rate (mol L-1 s-1)
7.20 * 10-4
1.44 * 10-3
2.24 * 10-3
[A]0
0.35
0.70
1.05
1) Find the order of the reaction and write the rate law.
2) Calculate the value (including units) of the rate constant, k.
Example 2. The decomposition of nitrosyl chloride, NOCl, was studied:
2 NOCl(g) ↔ 2 NO(g) + Cl2(g)
The following data were obtained, where Rate = - Δ[NOCl]/Δt.
Trial
1
2
3
4
[NOCl]0
0.30
0.20
0.10
0.40
Initial Rate (mol L-1 s-1)
0.00598
0.00266
0.000664
0.0106
1) What is the rate law for this reaction?
2) Calculate the rate constant at this temperature (include units).
Example 3. Consider the following reaction:
A+B→P
The reaction was repeated five times using different concentrations of A and B and the initial
rate was measured each time. The results are tabulated below.
Trial
[A]0
[B]0
1
2
3
4
5
0.100
0.100
0.200
0.100
0.300
0.100
0.300
0.100
0.200
0.600
Initial Rate
(M s-1)
1.53 * 10-4
4.59 * 10-4
6.12 * 10-4
3.06 * 10-4
8.26 * 10-3
Write the rate law and find the rate constant (including units).
Example 4. The reaction
2 I-(aq) + S2O82-(aq) → I2(aq) + 2 SO42-(aq)
was studied at 25oC. The following results were obtained where Rate = -Δ[S2O82-]/Δt.
[I-]0
[S2O82-]0
0.080
0.040
0.080
0.032
0.060
0.040
0.040
0.020
0.040
?
1) Determine the rate law.
2) Calculate a value for the rate constant (including units).
3) Calculate the initial [S2O82-] for the last trial.
Initial Rate
(mol/L∙s)
12.5 * 10-6
6.25 * 10-6
6.25 * 10-6
5.00 * 10-6
7.00 * 10-6
C60
Tri-Valley AP Chemistry
LESSON 17.3
Opportunity + Dedication  Success
THE INTEGRATED RATE LAW AND HALF-LIVES
We can also write a rate law for the reaction describing the reactant concentrations as a function of time. This form of the rate law
is known as the integrated rate law (Recall that the other rate law is known simply as THE rate law).
Consider the reaction of R → P:
If it’s ___Order in
R:
THE Rate Law
The Integrated Rate Law
(as given on Free Response)
Graph of [R] vs. Time
How to “Fix” the Graph
[R]
0
th
Time
[R]
1st
Time
[R]
2nd
Time
Thus graphing gives us a second way to determine the order of a reactant. In this case (which we’ll practice tomorrow), you perform
only one trial but you measure the concentrations for the entire time. You then make various graphs to see which gives you a
straight line.
If you plot…
 ln[A] vs. t and get a straight line, the reactant is 1st order and slope = -k.
 1/[A] vs. t and get a straight line, the reactant is 2nd order and slope = +k.
 [A] vs. t and get a straight line, the reactant is 0th order and slope = -k.
It can be confusing when to do each rate law. Test your skills on the following:

You’re given a set of initial concentrations and initial rates for several experiments. Which rate law do you use?

You’re given a set of concentrations and times for a single experiment. Which rate law do you use?
Part 2: Half-Lives - When will [R] = ½ [R]0?
Example 1. In 6 M HCl the complex ion Ru(NH3)63+ has a half-life of 14 h at 25oC. Under these conditions, how long will it take for
the [Ru(NH3)63+] to decrease to 12.5% of its initial value?
Deriving the Equations for Half-Lives: An Exercise of Sheer Joy
1st Order
2nd Order
0th Order
Example 2. A certain first-order process is 45.0% complete in 65 s. What are the rate constant and the half-life for this process?
AP CHEMISTRY
Lesson 18d: Using the Integrated Rate Law
Example 1. A certain reaction has the following general form:
aA → bB
At a particular temperature and [A]0=2.80 * 10-3 M, concentration versus time data were collected
for this reaction, and a plot of 1/[A] versus time resulted in a straight line with a slope value of
+3.60 * 10-2 L/mol∙s.
a) Determine the rate law, the integrated rate law, and the value of the rate constant for this
reaction.
b) Calculate the half-life for this reaction.
c) How much time is required for the concentration of A to decrease to 7.00 * 10 -4 M?
Example 2. The decomposition of hydrogen peroxide was studied and the following data were
obtained at a particular temperature:
Time (s)
[H2O2]
(mol/L)
a) Assuming that Rate = -Δ[H2O2]/Δt, determine the rate law, the
integrated rate law, and the value of the rate constant.
0
1.00
b) Calculate the [H2O2] at 4000. s after the start of the reaction.
120
0.91
300
0.78
600
0.59
1200
0.37
1800
0.22
2400
0.13
3000
0.082
3600
0.050
To do this, you will have to construct three graphs of the data and see
which gives you a straight line:



ln[A] vs. time,
1/[A] vs. time, or
[A] vs. time
Directions on using the spreadsheet and graphing program Graphical
Analysis are on the reverse; Excel works similarly if you would prefer
to use it instead.
Using Graphical Analysis to Determine a Rate Law
By making graphs of [A] vs. time, ln[A] vs. time, and 1/[A] vs. time, we will determine if the
reaction is 0th, 1st, or 2nd order, respectively.
1. Open up Graphical Analysis. You will see a spreadsheet on the left half of the screen and a
graph on the right half.
2. Name your x and y columns in the spreadsheet by double-clicking on the headers.
3. Enter the data from the problem into the respective columns. Note that a graph is formed as
you enter the data.
4. The graph created shows [A] vs. time, from which you can tell if the graph is 0th order. To
see how linear it is, calculate the regression line. To do this, highlight the graph and, under
the Analyze menu, choose Linear Fit. A black line should appear showing the equation of the
line of best fit for your curve. The closer your correlation is to 1, the better the line fits
your data and the more linear it is.
Now plot ln[A] vs. time to determine if the reaction is 1st order in A. Instead of calculating ln[A] by
hand, we’ll let the spreadsheet do it by setting up a new column.
5. Under Data, select New Calculated Column. Enter a name (such as ln[A]) and skip down to
the equation field.
6. Under Functions, scroll down and select ln( ). Under variables, select your [A] data. Click
OK. A third column should now appear in your data table.
7. To plot a ln[A] vs. time graph, click on the y-axis of the graph and select your ln[A] data. (if
you choose, you can deselect your [A] data)
8. Inspect your graph and then add a regression line as above. Is the reaction 1 st order in A?
Just for kicks, let’s see how well the 2nd order data jives with it. Add a fourth column, defining it
to give 1/[A]. Add a regression line and compare the correlation values for the three graphs.
Which graph gave the most linear line? That tells you the order of the reactant.
Note that you could also determine the order of the reactant without a graph by seeing if the data
were linear (if it changed by the same amount each time).