Rates of Reaction

Rates of Reaction
The rate of chemical reactions is the speed at which a chemical reaction takes place. It is usually
expressed as the change in concentration of a reactant or product per unit of time.
There are six factors that modify the rate of a chemical reaction:
#1 The Nature of the Reactant(s)
Reactions will proceed differently depending on which substances are reacting. Ions in solution tend to
react quickly and almost instantaneously in precipitate reactions. Reaction rates tend to decrease in
molecules with strong covalent bonds, especially if the molecules are large. Thus, methane will react
quicker than octane although the latter is a liquid and thus the preferred hydrocarbon fraction in gasoline.
Example: Consider the following reactions:
These two equations are very similar. The only difference is the nature of the reactants. It is clear that the
difference in the rates of reaction must be due to the properties of NO and CO.
#2 The Concentration of the Reactant(s)
According to the particle theory of matter, two particles must approach each other to react together. So,
chemical reactions must depend on the collisions between the particles of reactants. The collision theory
relies on this to explain the rate of chemical reaction. As the concentration of reactants increases, the
number of particles of reactants, per unit of volume, increases; the number of collisions per second also
increases. Thus, the rate of reaction will increase. The opposite is also true; a decrease in concentration
will cause a decrease in reaction rate.
#3 The Surface Area of the Reactants
All chemical reactions occur on the surface of the reactants. If one of the reactants is broken down into
smaller pieces, the total surface area which can react with the other reactant(s) increases. The number of
collisions between the particles of reactant increases and the rate of reaction also increases.
Example: Consider the following reaction:
If chunks of zinc are used, the reaction proceeds slowly.
If powdered zinc is used, the reaction occurs very quickly.
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#4 Temperature
High temperatures increase the speed of the reactants. This causes particles to collide with more force (or
higher kinetic energies), causing increased probabilities of a chemical reaction occurring for that collision.
Thus, the rate of reaction is usually higher at higher temperatures, and the rate is reduced as temperature
decreases, which is why we use refrigerators—to slow down the chemical reactions which spoil food. This
is analogous to dissolving sugar in a glass of cold water, versus a cup of hot coffee; it will dissolve quicker
in the hot coffee. This also gives rise to the “photographers' rule”: rates double (or times halve) for every
10°C rise in temperature.
#5 Pressure
An increase in the overall pressure will cause an increase in the number of collisions between the particles
of reactant, accelerating the rate of chemical reaction, and vice-versa for a decrease of the overall
pressure on the system. This only applies to reactions in which the reactants are gases.
#6 Effect of a Catalyst
A catalyst is a substance that alters the rate of a chemical reaction without itself undergoing any
permanent chemical change.
There are two important limits regarding the actions of a catalyst:
a. A catalyst does not cause a chemical reaction.
b. A catalyst does not affect the quantity of substances produced during the reaction.
There are three mechanisms which help explain how catalysts work:
Adsorption: Adsorption is the accumulation of molecules or atoms of a substance on the surface of
another substance. Certain particles of reactant accumulate on the surface of the catalyst, increasing the
concentration of the reactants locally in that region. Thus, it is easier for the other particles of reactant to
react with them.
Intermediate products: Intermediate products are unstable compounds or ions formed by catalysts with
certain reactants, which later decompose to form the final products of the reaction. When the final
product is formed, the catalyst returns to its initial state, allowing it to begin the process all over again.
In this example, the H+ acts as the catalyst, and HCOOH2+ is the intermediate product. Notice that H+
returns to its initial state as one of the products of the reaction.
Activation energy: Activation energy is the minimum energy which is necessary to initiate a chemical
reaction between two particles. Often this is supplied with heat (a match) or increased pressure (inside a
diesel engine`s combustion chamber). When a catalyst is added, a lower activation energy is required in
order to initiate the reaction. Its symbol is Ea. The following diagram represents the progress of a reaction
in terms of energy and time:
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Below are graphs of the activation energy required to complete certain reactions:
Endothermic
reaction (without
catalyst)
Exothermic
reaction (with
catalyst)
Endothermic
reaction (with
catalyst)
Exothermic
reaction (without
catalyst)
Notice that endothermic reactions always have Hproduct > Hreactant and exothermic reactions always have
Hproduct < Hreactant. Also, reactions that involve a catalyst have a lower activation energy than if a catalyst
was not used.
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Reaction Mechanisms
Reactions happen invisibly and any intermediate products which may have formed, and then undergo a
secondary reaction, must be deduced from the Experimental Rate Law (to be considered later) and the
observed products. Thus, many reaction mechanisms have been proposed with more than one step.
Given that chemical reactions can occur in a series of steps, with intermediate products, care must be take
in determining reaction rates from the overall reaction equation.
Rate-Determining Step
The rate-determining step is the slowest reaction in a reaction mechanism. For instance, the reaction of
nitrogen dioxide and carbon monoxide is thought to occur in 2 steps:
Overall reaction: NO2(g) + CO(g) → NO(g) + CO2(g)
1. NO2 + NO2 → NO + NO3 (slow step)
2. NO3 + CO → NO2 + CO2 (fast step)
The second reaction happens almost immediately but the production of carbon dioxide is limited by the
slow process of the first step which creates a “bottleneck” in the conversion of carbon monoxide to
carbon dioxide. This rate-determining step would be reflected in the rate law for the reaction.
Rate Law
Most chemical reaction rates vary with reactant, and sometimes product, concentrations. This relation
between concentration and reaction rate is experimental (it cannot be reliably determined from the
balanced chemical equation since the actual reaction mechanism is not apparent from the chemical
reaction describing the overall reaction). The same experiment is performed several times with varying
initial concentrations of reactants and the initial reaction rate is measured carefully. Analyzing this data
will allow the Rate Law or rate equation to be determined.
Such analysis of data from actual experiments could be applied to the reaction of nitrogen monoxide and
hydrogen:
2NO(g) + 2H2(g) → N2(g) + 2H2O(g)
Data reveals that doubling nitrogen monoxide concentration results in a fourfold rate increase, whereas
doubling the hydrogen concentration only doubles the reaction rate. Combining both effects we can relate
the rate to concentration:
rate α *NO+2[H2]
And this proportion statement can be converted to an equation with the simple addition of a rate
constant:
rate = k [NO]2[H2]
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The rate constant, k, depends on the nature of the reactants and temperature, but it does not vary with
concentration. This is consistent with our earlier observation that temperature increases reactant rates
which was logically but not quantitatively based on collision theory (increased temperature results in
increased speed which increases the portion of molecules in a sample that could climb over the activation
energy threshold).
Using our nitrogen monoxide and hydrogen reaction, we can see how this k value can be experimentally
determined. We would just substitute our experimental data (which we would also use to plot the
concentration versus time graph) into the rate equation derived.
Data from graph: slope of tangent = 0.25 M/s, [H] = 0.04 M, [NO] = 0.1 M
rate = k [NO]2[H2]
0.25 = k (0.1)2 (0.04)
k = 625 M-2/s (or L2/mol2)/s
So, we can now write the full rate equation:
rate = 625 [NO]2[H2] (with appropriate units in terms of M and s)
Reaction Order
The order of the reaction is just the sum of the exponents in its Rate Law and the Rate Law worked out in
detail above is third order (2 + 1). You could also say this reaction is first order with respect to hydrogen
and second order with respect to nitrogen monoxide. Keep in mind that reactants in some chemical
reactions have no effect on rate so that reactant would be zero order with respect to that reactant (or
product). Furthermore, some rate equations contain the concentration of substances not in the reaction
such as an effective catalyst which speeds up the reaction.
General Form of the Rate Law
For the following reaction:
We can write the general form of the Rate Law Equation.
rate = kAB x [A]a x [B]b
where: A, B = the reactants
AB = the product
x, y, m = the number of moles of each reactant in the balanced equation
[A], [B] = the molarities of A and B
rate = the rate of reaction to form AB
a, b = the order of each reactant determined experimentally
kAB = the rate constant (in appropriate units of M and s), which corresponds to the rate of
reaction when the reactants have a concentration of 1 M
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Please note that the coefficients in the balanced chemical equation are not helpful in determining the
reaction order. Only experimentation and subsequent analysis can uncover the reaction order, and
thereby attempt to outline the unseen reaction mechanism and any intermediate steps.
Example:
If kHI is 1.8 x 10 -4 M-1s-1, [I2] is 4.0 M and [H2] is 2.0 M, find the reaction rate for the following reaction.
Assume it is first order with respect to both reactants.
First, you must balance the reaction:
rate = kHI x [H2] x [I2]
= 1.8 x 10-4 M-1s-1 x 2.0 M x 4.0 M
= 1.4 x 10-3 M/s
The reaction rate is 1.4 x 10-3 M/s.
It is important to remember that the Rate Law Equation finds the rate of reaction for a specific point in the
reaction. The concentrations of the reactants are decreasing as the reaction occurs. Therefore, there is
obviously a higher concentration of reactants at the start of the reaction than at the midway point, and
even less at the end.
Back on page one, the concentration of reactants was listed as a factor that modified the rate of reaction.
The higher the concentration, the faster the reaction. Therefore, a reaction is fastest at the start, and
begins to slow as the reactants are used up.
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Worksheet #4 – Rates of Reaction
1. A catalyst increases the speed of a reaction by:
a. lowering the ΔH of the reaction
b. lowering the activation energy
c. increasing the kinetic energy of the particles
d. increasing the enthalpy of the reactants
2. What happens to the reaction rate if a catalyst is added?
a. the rate remains unchanged
b. more products are produced
c. more reactants are used
d. the reaction either speeds up or slows down
e. the reaction stops
3. What happens to the reaction rate if more reactants are added?
a. the rate remains unchanged
b. the rate usually increases
c. the rate always increases
d. more products are produced
e. the reaction stops
4. If the rate-determining step of a reaction is A + 2B
C , the reaction rate is represented by
(assume it is third order overall and the concentration of B is a bigger rate determinant than concentration
of A):
a. k[A] 2[B]
b. k[A][B]2
c. k[B]2
d. k[A][B]2[C]
5. At the beginning of a reaction, the reaction rate for the reactants is:
a. largest, then decreases
b. largest and remains constant
c. smallest then increases
d. smallest and remains constant
e. the same as the final rate
6. Catalysts may not:
a. speed up a reaction
b. be solids
c. form new substances in a reaction
d. be present in living tissues
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7. Which one of the following would not increase the reaction rate?
a. Increasing the temperature of the reactants.
b. Dissolving two solids in water before mixing them together.
c. Diluting a solution of HCl with water before adding magnesium.
d. Grinding a solid into fine particles.
e. Adding an enzyme catalyst.
8. What is the effect on the energy diagram of a certain reaction if a catalyst is added?
9. State what happens to the reaction rate if the following are done.
a. a catalyst is added?
b. more reactants are added?
c. the temperature decreases?
10. According to the general Rate Law Equation, when is the rate of reaction the fastest: at the beginning
of the reaction, when 50% of the reactants have been consumed, or at the end of the reaction? Explain
briefly.
11. The Rate Law equation allows you to calculate the instantaneous rate of a chemical reaction. What
difference is there between the instantaneous and average rate of reaction?
12. For the following chemical reaction:
Three students measure the initial reaction rate, but under different conditions (initial concentration of
substances A and B).
Student
1
2
3
[A]
0.20 M
0.20 M
0.40 M
[B]
0.20 M
0.40 M
0.40 M
The rate constant for this reaction, at a certain temperature, is 2.5 M-1s-1 (assume it is first order with
respect to both reactants):
a. Which student observed the reaction which proceeded the quickest?
b. What is the rate of the quickest reaction?
c. What is the rate of the slowest reaction?
d. Does the rate of reaction remain constant for the duration of the reaction? Briefly explain your
answer.
e. Give an explanation as to why each student would obtain different experimental results for the
initial reaction rate.
13. A student performed a chemical reaction which involved 3 reactants: A, B and C and measured the
initial reaction rate but varied initial concentrations. The results showed that doubling the concentration
of A doubled the reaction rate, doubling the concentration of B quadrupled the reaction rate and doubling
the concentration of C had no effect on the rate of reaction.
Find the overall reaction order and write the rate equation.
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14. A student performed a chemical reaction which involved each molecule of A reacting with 2 molecules
of B to form one molecule of product C.
This reaction is 0 order for A and first order for B. The rate of A being consumed is 1.2 M/s when both
initial concentrations are 0.2 M.
Determine k (include units).
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