The document discusses reaction kinetics and reaction rates. It defines reaction rate as the change in concentration of a reactant or product with time. Reaction rates can be determined from graphs of concentration versus time or from differential rate equations. Differential rate equations relate the rates of changes of concentrations of reactants and products. Several examples show how to write differential rate equations for reactions and calculate reaction rates from given information. Common student mistakes in working with differential rate equations are also discussed.

1. REACTION KINETICS
8.1 REACTION RATE
LEARNING OUTCOMES:
• Define reaction rate
• Explain the graph of concentration against time in
relation to reaction rate
• Write differential rate equation
• Determine the reaction rate based on a differential
equation

2. What does rate of reaction mean?
The speed of different chemical reactions . Some reactions
are very fast and others are very slow.
The speed of a reaction is called the rate of the reaction.
What is the rate of these reactions?
rusting
slow
baking
fast
explosion
very fast

3. A
B
?
rate = -
?
rate = +
?
[A]
t
[B]
t
?

4. Reaction rate is speed of chemical reaction which is the
change in the concentration of a reactant or a product
with time.
What is the unit for reaction rate?
kg
mol
nm
dm-3
L-1
Ms-1
mol L-1s-1
oC
molal
mol
s-1
mol dm-3 s-1
Newton
Kelvin
meter
kJ mol-1
mol L-1min-1
gram

5. Differential rate equation / Rate expressions
aA+bB
rate =
cC+dD
-1 d[A] = -1 d[B] = +1 d[C]
a dt
b dt
c dt
= +1 d[D]
d dt
Differential Rate Equation Example1:
O3(g) + NO(g)
NO2(g) + O2(g)
d O3
d[NO]
d[ NO 2 ]
d[ O 2 ]
rate = ==+
=+
dt
dt
dt
dt

6. Differential Rate Equation Example2:
2 NOCl (g)
2 NO + Cl2 (g)
1 d NOCl
1 d[NO]
d[Cl2 ]
rate = =
=+
2
dt
2 dt
dt
2 moles of NOCl disappear for every 1 mole Cl2
formed.
Rate of disappearance of NOCl is twice as fast
as the rate of formation of Cl2

7. Differential Rate Equation Question 1:
Write the differential rate equation for the following reactions:
(a) I-(aq) + OCl-(aq)
(b) 3O2(g)
(c) 4NH3(g)
Cl-(aq)
+ OI-(aq)
2O3(g)
+ 5O2(g)
4NO(g)
+
6H2O(g)

8. Differential Rate Equation Challenging Question 1:
Write the rate expression for the following reaction:
(a) N2O5(g)
(b) 2H2O2(aq)
(c) 4NH3 (g) + 5O2 (g)
2NO2(g)
+
2H2O(l) +
½ O2(g)
O2(g)
4NO (g) + 6H2O (l)
Write the differential rate equation in the term of changes in pressure with time
(d) 2NOBr (g)
2NO (g) + Br2 (g)

9. Differential Rate Equation Example 3:
C2H6(g) + 7O2(g)
4CO2(g) + 6H2O(g)
If the ethane, C2H6 is burning at the rate of 0.20 mol dm-3s-1. Calculate the rate of
formation of CO2
STEP 1: Write the differential rate equation for the
substances that related to the question
d [C 2 H 6]
dt
?
1 d [CO 2]
4
dt
STEP 2: Substitute the given information into the
differential equation
d [CO 2]
dt
d [CO 2]
dt
4(0.20moldm 3s 1 )
0.80moldm 3s
1
Rate of formation
of CO2 is
0.80 moldm-3s-1

10. C2H6(g) + 7O2(g)
4CO2(g) + 6H2O(g)
If the ethane, C2H6 is burning at the rate of 0.20 mol dm-3s-1. Calculate the rate of
formation of CO2
Student common mistakes:
d [C 2 H 6]
dt
1 d [CO 2]
4
dt
d [CO 2]
dt
d [CO 2]
dt
d [CO 2]
dt
1 d [CO 2]
4
dt
d [C 2 H 6]
dt
d [C 2 H 6]
4
dt
4(0.20moldm 3s 1 )
0.80moldm 3s
1

11. Differential Rate Equation Example 4:
C2H6(g) + 7O2(g)
4CO2(g) + 6H2O(g)
If the ethane, C2H6 is burning at the rate of 0.20 mol dm-3s-1. Calculate the rate of
disappearance of O2
STEP 1: Write the differential rate equation for the
substances that related to the question
d [C 2 H 6]
dt
?
1 d [O 2]
7 dt
STEP 2: Substitute the given information into the
differential equation
d [O 2]
7(0.20moldm 3s 1 )
dt
d [O 2]
1.40moldm 3s 1
dt
Rate of
disappearance of O2
is 1.40 moldm-3s-1

12. C2H6(g) + 7O2(g)
4CO2(g) + 6H2O(g)
If the ethane, C2H6 is burning at the rate of 0.20 mol dm-3s-1. Calculate the rate of
disappearance of O2
Student common mistakes:
d [C 2 H 6]
1 d [O 2]
dt
7 dt
1 d [O 2]
d [C 2 H 6]
7 dt
dt
d [O 2]
d [C 2 H 6]
7
dt
dt
d [O 2]
7(0.20moldm 3s 1 )
dt
d [O 2]
dt
1.40moldm 3s
1

13. Differential Rate Equation Question 2:
N2(g) + 3H2(g)
2NH3(g)
Suppose that at a particular moment during the reaction, molecule of hydrogen is
reacting at the rate of 0.074 Ms-1. Calculate the rate of
(a) formation of ammonia
(b) depletion of nitrogen

14. Differential Rate Equation Question 3:
4NH3(g)
+ 5O2(g)
4NO(g)
+
6H2O(g)
The rate of disappearance of oxygen is 0.020 moldm-3s-1.
Determine the rate of formation of NO and H2O and also the
rate of disappearance of NH3

15. Differential Rate Equation Challenging Question 2:
For the reaction,
4NH3(g) + 3O2(g)→ 2N2(g) + 6H2O(g)
the nitrogen gas was produced at a rate of 0.72 mol L-1 s-1.
a) Write the differential rate equation for the above reaction.
b) Calculate the rate of
(i) formation of water
(ii) depletion of oxygen
(iii) depletion of ammonia

16. Differential Rate Equation Challenging Question 3:
5Br-(aq) + BrO3-(aq) + 6H+(aq)
3Br2(aq)
+
3H2O(g)
It was found that at a particular instant bromine was being formed at the rate of 0.039
moldm-3s-1. At the instant, at what rate is
(a) Water being formed
ANS: 0.039 mol dm-3 s-1
(b) Bromide ion being oxidized
ANS: 0.065 mol dm-3 s-1
(c) H+ being consumed
ANS: 0.078 mol dm-3 s-1

17. Differential Rate Equation Challenging Question 4:
2A + B
C
+
3D
It was found that at a particular instant reactant A was being disappear at the rate of
6.0 x 10-5 Ms-1. Calculate
(a) The rate of reaction
ANS: 3.0 x 10-5 Ms-1
(b) Rate of formation of D
ANS: 9.0 x 10-5 Ms-1
(c) Rate of disapperance of B
ANS: 3.0 x 10-5 Ms-1

18. Differential Rate Equation Brain Teasers 1:
4NH3(g) + 5O2(g)→ 4NO(g) + 6H2O(g)
What is the value of the k and m in the following sequence:
k,0.016,0.020,0.016,m
ANSWER:
k = 0.004 , m = 0.024

19. Differential Rate Equation Revision 1:
Complete the rate expression for the following reaction:
Differential Rate Equation Revision 2:
Write the rate expressions for the following reactions in terms of the
disappearance of the reactants and the appearance of the products.

20. Differential Rate Equation Revision 3:
For the reaction A + B → 3C +D the initial rate of formation of C is 0.24 mol L-1 hr-1
a) What is the rate of disappearance of B?
b) What is the rate of formation of D?

21. Differential Rate Equation Revision 4:
For the reaction choose the correct phrase:
R
P
(R-reagents, P-products)
The rate of a chemical reaction is the measure of the rate at which
P _________, which is equal to the rate at which the R _________.
The rate of the reaction is the change in concentration over the
change of time and has units of __________. For the reaction,
reactant R gives product P, the rate is ________ divided by Δ of
_________, where Δ means change.The rate is always___________.
Answers:
is formed
is consumed
mol L-1 s-1
-Δ *R]
time
positive.