Welcome to s2i!
Wednesday, February 6th
Katie Seehusen
Kseehusen09@winona.edu
Agenda:
1. New Material:
a. Radioactive Decay
b. Equilibrium Constants
2. Review Older Material
a. Differential Rate Laws
b. Integrated Rate Laws
c. Arrhenius Equation
Radioactive Decay Practice:
Fill in the blank: Radioactive decay obeys __first__ order kinetics.
51
23𝑉
→ 42𝐻𝑒 + _ 47
21 𝑆𝑐____
210
85𝐴𝑡
→
108
47𝐴𝑔
→ 01𝑒 +
0
−1𝛽
+
210
86𝑅𝑛
108
46𝑃𝑑
Write out the reaction for Mn undergoing beta decay.
55
25𝑀𝑛
→
0
−1𝛽
+
55
26𝐹𝑒
Equilibrium Constants
For the generic reaction aA + bB  cC + dD, the equilibrium constant is:
Kc=
[𝐶]𝑐 [𝐷]𝑑
[𝐴]𝑎 [𝐵]𝑏
True or False? If false, write a correct statement in the line below.
T / F Pure liquids and solids are included in the equilibrium constant.
__Pure liquids and solids are NOT included in the equilibrium constant_
T / F The top of the fraction contains the reactants and the bottom contains the products.
___The products are on top and the reactants are on bottom____
Write the equilibrium expression for the generic reaction:
3A + 2B  4C + 6D
[𝐶]4 [𝐷]6
Kc =
[𝐴]3 [𝐵]2
What would the constant be if we specified the states like this:
3A (g) + 2B (l)  4C (s) + 6D (g)
[𝐷]6
Kc=
[𝐴]3
Here’s a tricky one: Write the equilibrium constant for the combustion of C4H10?
Hints: a) Combustion= add O2 and get CO2 and H2O.
b) Write the balanced reaction first
c) Assume all of the states are gas when writing the constant.
2 C4H10 (g) + 13 O2 (g)  8 CO2 (g) + 10 H2O (g)
[𝐶]4 [𝐷]6
Kc=
[𝐴]3 [𝐵]2
Differential Rate Law Practice
Experiment
1
2
3
[ClO2] (M)
0.060
0.020
0.020
Write the rate law for the reaction:
Rate=k[ClO2]2[OH]
[OH-] (M)
0.030
0.030
0.090
Rate (M/s)
0.0248
0.00276
0.00828
What is the value of the rate constant? Remember your units!!
k= 230 M-2s-1
What would the rate be if [ClO2] was 0.040 M and [OH-] was 0.050 M?
Rate= (230)(.04)2(.05)
Rate= 0.0184
Integrated Rate Law Practice:
Helpful Chart: I RECOMMEND PUTTING THIS ON YOUR NOTECARD IN
SOME FORM!!!
Order
zero
1st
2nd
Rate law
rate = k
rate = k[A]
rate = k[A]2
Integrated
rate law
[A]t=−kt+[A]0
ln[A]t=−kt+ln[A]0
1/[A]t=kt+1/[A]0
Straight-line
plot
[A] vs. t
ln[A] vs. t
1/[A] vs. t
Slope
−k
−k
k
Half-life (t1/2)
[A]o/2k
0.693/k
1/k[A]0
Time (s)
0
50
100
150
200
[C5H6]
0.040
0.030
0.024
0.020
0.0174
1/[C5H6]
Given the following data, use Excel to determine if the reaction is 0, 1st or 2nd order for [C5H6].
70y = 0.1632x + 25.172
60
R² = 0.9996
50
40
30
20
10
0
0
100
200
Time (s)
300
What is the value of the rate constant?
Because the most linear graph has 1/[C5H6] on the y axis, the reaction is second order. Looking
at the chart above, for second order the slope= k so the rate constant is 0.1632 M-1s-1
What is the half-life of the reaction?
t1/2= 1/k[A]0
= 1/(0.1632*0.04)
= 153 seconds
Given the following graphs, what is the order of the reaction?
Most linear graph has axis of ln (A) so the reaction is first order.
600
500
1/ [A]
[A]
400
300
200
100
0
0
5000
10000
Time (s)
15000
0.03
0.025
0.02
0.015
0.01
0.005
0
0
5000
10000
Time (s)
15000
7
ln(A)
6
5
4
3
0
5000
10000
Time (s)
15000
If the equation of the linear trendline is y= -0.0002 + 6.2251, what is the value of the rate
constant?
Slope= -k so k= 0.0002 s-1
What is the half-life of the reaction?
t1/2= 0.693/k
=3465 seconds
What will the [A] be at t= 10,000 seconds if the original concentration is 500 M? (I forgot to add
this)
ln[A]10000=−(0.0002)(10000)+ln(500)
[A]10000= 67.67 M
Arrhenius Equation Practice
Remember, when we are looking at how the rate constant changes when we change temperature,
we will use this form:
𝒌𝟏
𝑬𝒂 𝟏
𝟏
𝐥𝐧 ( ) =
( − )
𝒌𝟐
𝑹 𝑻𝟐 𝑻𝟏
If a reaction has a rate constant of 6.67x 10-2 s-1 when the temperature is 250 K and a rate
constant of 8.89 x 10-1 s-1 when the temperature is raised to 320 K, what is the activation energy?
𝟔. 𝟔𝟕 𝒙 𝟏𝟎−𝟐
𝑬𝒂
𝟏
𝟏
𝐥𝐧 (
)
=
(
−
)
𝟖. 𝟖𝟗 𝒙 𝟏𝟎−𝟏
𝟖. 𝟑𝟏𝟒 𝟑𝟐𝟎 𝟐𝟓𝟎
Ea= 24.6 kJ/mol
If a reaction has an activation energy of 31 kJ/mol and has a rate constant of 20 s-1 when the
temperature is 300 K, what will the rate constant be when the temperature is lowered to 275 K?
𝟐𝟎
𝟑𝟏𝟎𝟎𝟎 𝟏
𝟏
𝐥𝐧 ( ) =
(
−
)
𝒌𝟐
𝟖. 𝟑𝟏𝟒 𝟐𝟕𝟓 𝟑𝟎𝟎
k2= 6.46
To wrap up, let’s review some concepts with some multiple-choice questions:
1. Which of the following is true when a reaction has reached its equilibrium?
a. Products are being formed faster than reactants
b. Reactants are being formed faster than products
c. Products and reactants are changing at the same rate
d. No reactant is being made into product and no product is being made into
reactant.
2. What “reaction” occurs fastest?
a. Solid + liquid
b. Solid+ gas
c. Liquid + gas
d. Gas + gas
3. Rank the following letters from lowest to highest on probability of reacting with each
other:
a. 0.002 M H2O and 0.002 M CO2
b. 1.0 M H2O and 1.0 M CO2
A, c, b, d
c. 0.03 M H2O and 0.03 M CO2
d. 5 M H2O and 5 M CO2
4. True or False? The units for the rate constant, k, for a 5th order reaction are M-5s-1?
i. They are M-4s-1
5. If something undergoes alpha decay, it’s mass number will change by:
a. -4
b. +4
c. -2
d. +2
6. If an element were to undergo radioactive decay, what equation would be used to solve
for the half life?
a. [A]o/2
b. 0.693/k
c. 1/k[A]0
d. [A]0/2k
7. Which of the following would NOT be included in the equilibrium constant given the
expression 4CH3 (l) + 7O2 (g)  4CO2 (g) + 6H2O (aq) ?
a. CH3 (l)
b. O2 (g)
c. CO2 (g)
d. H2O (aq)
8. What would the overall equilibrium constant be given the following steps of an equation:
A + B C + D equilibrium constant= K1
C + E  A + F equilibrium constant = K2
B + E  D + F overall constant= ?
a)
b)
c)
d)
K1 + K2
K1*K2
K2 / K1
A number unrelated to the individual Ks.