It tells how fast or slow a certain chemical reaction occur. There are two factors that can be used to determine reaction rates: concentration and rate constant. It can simply be determined by measuring the changes in the concentrations of the reactants or products within a particular time frame. Generally, a chemical reaction is represented in the following format. As the chemical reaction takes place, the amount of reactants decrease as the amount of the products increase. Δ[A], Δ[B], Δ[C], and Δ[D] are the measures of the change in respective concentrations over a period of time, Δt. Reaction rates are always positive. In terms of appearance of a product in a reaction, the expression is positive since the change in concentration is positive. In term of disappearance of a reactant, the case is opposite; hence the expression is appended by a negative sign. The rate law expresses the relationship of the rate of reaction to the rate constant and the concentration of the reactants raised to certain exponents. The rate constant, k, is a constant of proportionality between the reaction rate and the concentration of the reactants. Rate laws are always determined experimentally.

1. Lesson 9.2
Measurement of Reaction
Rates

2. Objective
understand how fast a
chemical reaction takes
place.
1
At the end
of the
lesson, you
should be
able to:

3. Learn about It!
• It tells how fast or slow a certain chemical reaction occur.
• There are two factors that can be used to determine
reaction rates: concentration and rate constant.
• It can simply be determined by measuring the changes in
the concentrations of the reactants or products within a
particular time frame.
Reaction Rate

4. Learn about It!
• Generally, a chemical reaction is represented in the
following format.
• As the chemical reaction takes place, the amount of
reactants decrease as the amount of the products increase.
Reaction Rate

5. Learn about It!
Consider the conversion of substance A to substance B.
Reaction Rate
The progress of the reaction A ⟶ B every 10-second interval.

6. Learn about It!
• The speed of a chemical
reaction = reaction rate
• It is defined as the change in
the amount (or concentration)
of the reactants or products
over a range of time.
• It is often expressed in the units
of molarity per second (M/s).
Reaction Rate
The rate of reaction A ⟶ B shows that
as time passes, the amount of A
decreases while the amount of B
increases.

7. Learn about It!
For the following general equation,
The rate expression can be written as:
where a, b, c and d are coefficients of molecules A, B, C, and D.
Rate Expression

8. Learn about It!
• Δ[A], Δ[B], Δ[C], and Δ[D] are the measures of the change in
respective concentrations over a period of time, Δt.
• Reaction rates are always positive.
• In terms of appearance of a product in a reaction, the
expression is positive since the change in concentration
is positive.
• In term of disappearance of a reactant, the case is
opposite; hence the expression is appended by a
negative sign.
Rate Expression

9. Learn about It!
• The rate law expresses the relationship of the rate of
reaction to the rate constant and the concentration of the
reactants raised to certain exponents.
• The rate constant, k, is a constant of proportionality
between the reaction rate and the concentration of the
reactants.
• Rate laws are always determined experimentally.
The Rate Law

10. Learn about It!
In general, for the reaction
The rate law can be expressed as
where k is the rate constant, [A] and [B] are initial
concentrations of A and B, respectively, and m and n are the
reaction order.
The Rate Law

11. Learn about It!
• The higher the rate constant is, the faster is the reaction.
• The reaction order specifies how do the concentrations of
each reactant correspond with reaction rate.
• The overall reaction order is defined as the sum of the
exponents of the reactants in the rate law expression.
• Note that the stoichiometric values of the reactants in the
balanced chemical equation has nothing to do with the
order of the reaction.
The Rate Law

12. Learn about It!
A first-order reaction is a reaction whose rate is directly
proportional to the concentration of the reactant. Consider
the reaction,
The reaction is considered to be first order if the rate law can
be expressed as
Reaction Orders and Half-Lifes: First-Order

13. Learn about It!
• The unit for k of first-order reactions is s-1.
• Reaction half-life, t1/2 : the time required for the
concentration of the reactant to decrease to half of its
initial concentration.
where [A] is the new concentration and [A]o is the original
concentration of the substance A.
Reaction Orders and Half-Lifes: First-Order

14. Learn about It!
• For first-order reactions, the half-life can be expressed as
where k is the rate constant, in s-1.
• For first-order reactions, the t1/2 is a constant and does not
depend on the initial concentration of the reactant.
Reaction Orders and Half-Lifes: First-Order

15. Learn about It!
A second-order reaction is a reaction whose rate is
dependent on one of two possibilities:
• the rate is dependent on the square of the concentration of
a single reactant
• the rate is dependent on two reactants that are first order
for each.
Reaction Orders and Half-Lifes: Second-Order

16. Learn about It!
• Consider the reaction,
• The reaction is considered second order if the rate law can
be expressed as
• The unit for k of second order reactions is M-1 s-1.
Reaction Orders and Half-Lifes: Second-Order

17. Learn about It!
• Provided that the reaction is 2nd order with respect to a
single component (A for example), the half-life for second
order reactions is expressed as
where k is the rate constant, in M-1 s-1 and [A]O is the initial
concentration in M.
• t1/2 depends inversely on its initial concnetration.
Reaction Orders and Half-Lifes: Second-Order

18. Learn about It!
A zero-order reaction is a reaction whose rate is independent
of the concentration of reactants and is simply defined by the
rate constant, k. Consider the reaction,
The reaction is considered zero order if the rate law can be
expressed as
Reaction Orders and Half-Lifes: Zero-Order

19. Learn about It!
• The unit of k for zero order reactions is M/s since the rate
constant is directly equal to the reaction rate.
• The half-life expression for the zero order reaction is given
by:
Reaction Orders and Half-Lifes: Zero-Order

20. Try it!
The reaction of the alkyl halide C5H11Cl with water is known to
be a first-order reaction. Calculate the half-life of the reaction
if the rate constant has a value of 2.0 x 10-3 s-1.

21. Try it! Solution
The reaction of the alkyl halide C5H11Cl with water is known to
be a first-order reaction. Calculate the half-life of the reaction
if the rate constant has a value of 2.0 x 10-3 s-1.
Step 1: Identify what is required to find in the problem.
You are asked to calculate the half-life of the reaction.
Step 2: Identify the given in the problem.
The value of the rate constant and the order of the r
reaction are given.
k = 2.0 x 10-3 s-1
rate order = 1

22. Try it! Solution
The reaction of the alkyl halide C5H11Cl with water is known to
be a first-order reaction. Calculate the half-life of the reaction
if the rate constant has a value of 2.0 x 10-3 s-1.
Step 3: Write the working equation.
For a first-order reaction, the half-life can be expressed
as
Step 4: Substitute the given values and find the answer.

23. Key Points
Reaction rates tell how fast or slow certain chemical
reactions occur. There are two factors that can be used to
determine reaction rates: concentration and rate
constant.
1
The reaction rate is defined as the change in the amount
(or concentration) of the reactants or products over a
range of time. It is often expressed in the units of molarity
per second (M/s).
2

24. Key Points
The rate law expresses the relationship of the rate of
reaction to the rate constant and the concentration of the
reactant raised to certain exponents.
3
The rate constant, k, is a constant of proportionality
between the reaction rate and the concentration of the
reactants.
4
The reaction order specifies how do concentrations of
each reactant correspond with reaction rate.
5

25. Key Points
The overall reaction order is defined as the sum of the
exponents of the reactants (i.e. their respective orders
with respect to each reactant) in the rate law expression.
6
The reaction half-life, t1/2, is the time required for the
concentration of the reactant to decrease to half of its
initial concentration.
7
A first-order reaction is a reaction whose rate is directly
proportional to the concentration of the reactant.
8

26. Key Points
A second-order reaction is a reaction whose rate is
dependent on the square of the concentration of the
reactants.
9
A zero-order reaction is a reaction whose rate is
independent on the concentration of reactants.
10

27. Check Your Understanding
1. The reaction rate is defined as the change in the amount of the
reactants or products over a range of time and is often
expressed in units of M/s.
2. The rate constant, k, is a constant of proportionality between
the reaction rate and the concentration of the reactants.
3. Fast chemical reactions have high values of rate constants.
4. A zero-order reaction has a rate constant with a unit of s-1.
5. The reaction half-life is the time it takes for the reaction to
decrease the reactants concentration by a factor of ½.
Write True if the following statement is correct. Otherwise, write
False.

28. Challenge Yourself
Prove that the unit for the rate constant of second
order reactions is M-1 s-1.

29. Bibliography
Atkins, P and De Paula, J. Atkins’ Physical Chemistry. 2006. Oxford: Oxford University Press.
Brown, T. L., et al. Chemistry: The Central Science. 2012. New York: Pearson.
Burton, George. Chemical Ideas, Vol.4. 2000. London : Heinemann.
Chang, R and Goldsby K.A. Chemistry. 2013. New York: McGraw-Hill, Inc.
Clark, J. Types of Catalysis. Chemguide: Helping you to understand chemistry. Accessed June 15, 2017.
http://www.chemguide.co.uk/physical/catalysis/introduction.html
McMurry, J., Fay R.C., Robinson, J.K. Chemistry. 2016. Harlow: Pearson.
Murzin, Dmitry. Chemical Reaction Technology. 2015. Berlin: Walter de Gruyter GmbH & Co KG.
Silberberg, M. Chemistry: The Molecular Nature of Matter and Change. 2006. New York: Mcgraw-Hill, Inc.