Barker
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6.1 - Expressing & Measuring Reaction Rates
• Reaction Rate: the change in the amount of reactants or products over time. Chemists
typically measure amount in concentration (mol/L, M) and time in seconds (s). Therefore,
reaction rate is often mathematically computed as follows:
Rate of reaction = Δ[A] = [A]final - [A]initial
Δt
tfinal - tinitial
Where ∆ represents “change in.”
Where [A] represents the concentration of a compound, A, in mol/L or molars (M).
Where t represents time in seconds, s.
Where “final” represents the final measurement (could be abbreviated f or 2).
Where “initial” represents the initial measurement (could be abbreviated i or 1).
*Note: Placing square brackets around a chemical, [ ], means “concentration of” the chemical.
• By convention, a reaction rate is always positive since it considers the overall rate of
production of products. However, rates of products and reactants depend on the direction of
the reaction and the stoichiometry of the reaction.
Consider the reaction:
bB(g) → cC(g) + dD(g)
If this reaction is going forward, then:
Rate of reaction = - 1 Δ[B] = + 1 Δ[C] = + 1 Δ[D]
b Δt
c Δt
d Δt
“-” means disappearing; “+” means producing.
• Reaction rates can be obtained by graphing concentrations as a function of time.
- The average reaction rate is the average change is concentration over a given time
interval. It can be found by taking a secant slope from the graph.
- Secant lines touch the graph’s curve at two points.
- This tells you overall how the reaction is progressing, but it does not tell you
much about how the reaction is progressing at a specific time.
- The instantaneous reaction rate is the reaction rate at a specific time in the reaction. It
can be found by taking a tangent slope from the specific time of interest.
- Tangent lines, unlike secant lines, are lines that touch the graph’s curve at one
point.
6.1 - Expressing & Measuring Reaction Rates
forward
to following
find reaction
rates. You would just need the initial and final
Consider
the
reaction.
Barker
concentrations and the time interval. Reaction rates, however, are not
A(g) →with
C(g)time.
+ D(g)
usually constant. They change
How does this affect the way
that chemists
determine
reaction
Now examine
the graph
in Figure
6.2.rates?
The blue line on the graph shows
Consider the following reaction.
the concentration of product C as the reaction progresses, based on the
A(g) → C(g) + D(g)
data in Table 6.1.
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2
Now examine
the→
graph
blue
line on theover
graph
shows time and was
Ex. 1 Consider the reaction
2B(g)
C(g)in+Figure
D(g).6.2.
[C]The
was
monitored
a given
the
concentration
of
product
C
as
the
reaction
progresses,
based
on
recorded inTable
the table
below.
6.1 Concentration
of C During a Reaction at Constant Temperaturethe
data in Table 6.1.
(a) Find the average
0.0 s and 5.0 s.
Time rate
(s) of generation of C between
[C] (mol/L)
(b) Find the Table
instantaneous
rate ofof generation
of C 0.00
at
s. Temperature
6.10.0
Concentration
C During a Reaction
at 10.0
Constant
5.0
Time (s)
10.0
[C] (mol/L)
3.12 × 10−3
0.0
0.00
4.41 × 10−3−3
3.12 × 10
5.0
15.0
10.0
−3
5.40
4.41× ×10
10−3
20.0
15.0
−3
6.24
5.40× ×10
10−3
20.0
6.24 × 10−3
The average rate of a reaction is the average change in the concentration
The average
rate ofper
a reaction
is the
average
change
in the
concentration
of a reactant
or product
unit time
over
a given
time
interval.
For
of
a
reactant
or
product
per
unit
time
over
a
given
time
interval.
For rate
example,
using
the
data
in
Table
6.1,
you
can
determine
the
average
Solution:
(a) average rate of generation of C between 0.0 s and 5.0 s can be calculated as
example, using the data in Table 6.1, you can determine the average rate
of the
reaction from t = 0.0 s to t = 5.0 s.
follows:
of the reaction from t = 0.0 s to t = 5.0 s.
∆[C]
Average
rate =rate = ∆[C]
Average
∆t
∆t
The slope
of the tangent is the instantaneous rate of the reaction.
−3
(3.12
0.00at
mol/L
(3.12
10×−310mol/L)
− −0.00
mol/L
t = 10.0 s. As shown on the graph,
themol/L)
tangent
line
= 6.2×shows
=Figure
5.0
0.0s s
s −s −0.0
the slope of the5.0
tangent
(therefore
the instantaneous rate) at t = 10.0 s
−4
×−4mol/(L
10−4 mol/(L
• s)
2.3=××6.2
10
• s).• s)
=is 6.2
10
mol/(L
Notice
that near
of the reaction,
when the concentration
You can see this calculation
in Figure
6.2.the
Onbeginning
a concentration-time
graph,
HR • Unit 3 Energy Changes and Rates of Reaction
[C] (mol/L × 103 )
268 MHR • Unit 3
You can the
seeaverage
this calculation
6.2.
On by
a concentration-time
of in
the Figure
reactants
is relatively
high,
theofslope
of that
the graph,
tangent
is greater
rate of a reaction
is represented
the
slope
a line
is
(steeper).
This
indicates
a
faster
reaction
rate.
As
the
reaction
the average
rate
of
a
reaction
is
represented
by
the
slope
of
a
line
that
is
(b) instantaneous
generation
of CThis
at 10.0
be calculated by proceeds,
taking
drawn betweenrate
two of
points
on the curve.
line sisneeds
called to
a secant.
the
reactants
are
used
up
and
the
slope
of
the
tangent
The of
average
rate ofon
an overall
idea
of how
quickly
thedecreases.
drawn
two
the curve.
line is
called
a secant.
the between
tangent
thepoints
curve
ata reaction
10.0
s: givesThis
progressing.
not, however,
tell idea
you how
fast the
reaction
The reaction
averageisrate
of a reaction
an overall
of how
quickly
the
9.00 It doesgives
is
progressing
at
a
specific
time.
For
example,
suppose
that
someone
of C the
Versus
Time
reaction is progressing. It does not, however, The
tellConcentration
you how fast
reaction
asked you how fast the reaction in Figure 6.2 was progressing over 20.0 s.
is progressing at a specific time. For example, suppose that someone
You would probably calculate the average rate from t = 0.0 s to t = 20.0 s.
8.00
asked you
fastcome
the up
reaction
Figure3.12
6.2× was
over
10−3 progressing
mol/(L • s). (Try
Youhow
would
with theinanswer
this 20.0 s.
0.0 were
t = 20.0 s.
You would
probably
calculate
average
rate
from t if= you
s to asked
calculation
yourself.)
Whatthe
would
you do,
however,
t = 10.0•s?
howcome
fast the
wasanswer
progressing
3.12at ×exactly
10−3 mol/(L
s).
You would
upreaction
with the
(Try
∆[C] = 5.4 ×this
10−3 mol/L − 3.1 × 10−3 mol/L
7.00 rate of a reaction is the rate of the reaction at a−3
The
instantaneous
calculation yourself.) What would you do, however, if you were
= 2.3 asked
× 10 mol/L
time. To find the instantaneous rate of a reaction using a
= 10.0 s?
how fastparticular
the reaction
was progressing at exactly t ∆[C]
concentration-time graph, draw Instantaneous
a tangent line =to the curve and find the
The slope
instantaneous
rateA of
a reaction is
the rate∆tof
the reaction at a
of the tangent.6.00
tangent line is rate
like a secant
line, but it touches the
2.3reaction
× 10−3 mol/L
particular
time.
To
find
the
instantaneous
rate
of
a
using a
=
curve at only one point. It does not intersect the curve.
10.0 s
−4
concentration-time graph, draw a tangent line to= 2.3
the× curve
and• s)find the
10 mol/(L
slope
of the
tangent.
A tangent
line
is
like
a
secant
line,
but
it touches the
Energy
Changes
and Rates
of Reaction
5.00
curve at only one point. It does not intersect the curve.
Tangent Line
4.00
∆t = 15.0 s − 5.0 s
= 10.0 s
3.00
∆[C] = 3.1 × 10−3 mol/L − 0.0 mol/L
= 3.1 × 10−3 mol/L
Secant Line
2.00
∆[C]
∆t
3.1 × 10−3 mol/L
=
5.0 s
= 6.2 × 10−4 mol/(L • s)
Average rate =
1.00
6.1 - Expressing & Measuring Reaction Rates
0.00
∆t = 5.0 s − 0.0 s
= 5.0 s
0
5.0
10.0
15.0
Time (s)
Figure 6.2
The slope of a tangent drawn to a concentration-time curve represents the
20.0
Physic
In your pr
in science
you proba
difference
aneous ve
velocity. H
displacem
determine
velocity an
Write a m
instantane
average ra
by compa
with veloc
Barker
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3
Ex. 2 In the previous question, you determined that, at 10.0 s, C was being generated at 2.3 ×
10-4 M/s. What is the corresponding rate of disappearance of B at 10.0 s?
Solution:
As seen earlier,
- 1 Δ[B] = + 1 Δ[C]
b Δt
c Δt
Therefore,
- 1 Δ[B] = + 1 Δ[C]
b Δt
c Δt
- 1 Δ[B] = + 1 (2.3 x 10-4 M/s)
2 Δt
1
Δ[B] = -2(2.3 x 10-4 M/s)
Δt
Δ[B] = -4.6 x 10-4 M/s
Δt
This answer makes sense since twice the amount of B disappears for every C
generated!
• Reaction rates can be monitored by scientists in many different ways:
1) Monitoring the change in mass (ex. if a gas is emitted during the reaction, one can
monitor the change in mass of the reaction mixture).
2) Monitoring the change in pH (when an acid or base is a reactant or product).
3) Monitoring conductivity (when an ionic compound reacts to form a precipitate).
4) Monitoring pressure or volume (when dealing with gases, since pressure and volume
are proportional to number of moles of a gas).
5) Monitoring colour change by measuring the amount of light absorption via a
spectrophotometer (if one of the reactants or products are coloured). The amount of
light absorbed is proportional to the concentration of the coloured chemical species.
• As you have seen in previous chemistry courses, reaction rates are affected by different
environmental conditions. Rate of reaction are increased by...
- Increasing temperature.
- Increasing reactant concentrations.
- Adding a catalyst (a substance that speeds up a reaction but does not get used up by the
reaction).
- Increasing surface area.
- Enhancing the nature of the reactants and products.
6.1 - Expressing & Measuring Reaction Rates