Chapter: Chemical Kinetics
Rate of Chemical Reaction
Question 1
Nitrogen pentaoxide decomposes according to equation:
This first order reaction was allowed to proceed at 40 oC and the data below were
collected:
[N2O5] (M)
Time (min)
0.400
0.00
0.289
20.0
0.209
40.0
0.151
60.0
0.109
80.0
(a) Calculate the rate constant. Include units with your answer.
(b) What will be the concentration of N2O5 after 100 minutes?
(c) Calculate the initial rate of reaction.
Ans.
(a)The plot of [N2O5] v/s t is as follows
[N2O5] (M)
0.400
0.289
0.209
0.151
0.109
Time (min)
0.00
20.0
40.0
60.0
80.0
log[N2O5]
-.03979
-0.5391
-0.6798
-0.8210
-0.9625
From the plot, log [N2O5] v/s t, we obtain
Also, slope of the line of the plot =
(b) After 100 min
(c) The initial rate of reaction
Question 2
Distinguish between 'rate expression' and 'rate constant' of a reaction.
Ans.
The rate expression can be defined as an expression in which the rate of reaction is
given as the product of the molar concentration of the reactants, with each term raised
to some power, which may or may not be the stoichiometric coefficients of the reacting
species in a balanced chemical equation.
The rate constant can be defined as the rate of reaction when the concentration of each
of the reactant is taken as unity.
Example:
The rate expression for the above reaction can be written as follows:
(Experimentally determined)
Now, if the concentration of NO and O2 is taken to be unity, then the rate constant is
found to be equal to the rate of the reaction.
Question 3
Ans.
Question 4
The oxidation of iodide ion by peroxydisulphate ion is given as:
3I- +S2 O82i)
I3 + 2SO42-
If
given interval than what is the value
of
ii)
Also calculate the average rate of formation of SO4
2-
for the same interval.
Ans.
According to the given equation
i)Therefore
ii)
Question 5
If the rate of formation of Oxygen gas is 48 g mm-1
i) Find the rate of disappearance of N2O5
ii) Find the rate of appearance of NO2
Ans.
The rate of a reaction is always expressed in mol L-1, therefore,
The rate of formation of O2
i)
rate of disappearance of N2O5,
ii)
rate of appearance of NO2,
Question 6
The rate of formation of nitric oxide (NO) in the following reaction is 3.6 x 10-3 mol L-1 s-1.
4NH3 (g) + 5O2 (g)
4NO (g) + 6H2O (g)
Find the rate of disappearance of Oxygen.
Ans.
The rate of above reaction in terms of Oxygen and NO are
Therefore rate of disappearance of Oxygen =
Question 7
The reaction, 2N2O (g) + O2 (g)
i)
NO + O2
2NO2(g) proceeds through the following steps:
NO3 (fast)
ii)
NO3 +NO
NO2 + NO3 (slow)
Predict the rate law expression for the reaction.
Ans.
In the above reaction, the slowest step also called the rate determining step is
NO3 + NO
NO2 + NO3
Rate of the reaction = k [NO]2 [O2]
Question 8
The following reaction was carried out in water:
Cl2 + 2I2Cl- + I2
The initial concentration of I - was 0.50mol L-1 and concentration after 10 minutes was
0.46 mol L-1. Calculate the rate of disappearance of I- and rate of appearance of iodine.
Ans.
[ I-] = 0.46 – 0.50 = - 0.04 mol L-1 t = 10.0 -0.0 = 10 min
Rate of disappearance of I- =
Rate of appearance of iodine =
=
(Rate of disappearance of I-)
Question 9
Ans.
Question 10
For a chemical reaction 2A + B
C, the rate of formation of C is 0.25 mol L-1hr-1. What
is the rate of disappearance of A and B?
Ans.
According to the equation, the rate of disappearance of A is twice the rate of formation
of C. So rate of disappearance of A = - 0.5 mol L-1 h-1 and that of B is -0.25 mol L-1hr -1
Question 11
In what respect specific reaction rate differs from rate of the reaction?
Ans.
Specific reaction rate is the rate of a reaction at unit concentration of each of reactant.
It is always constant for a particular reaction at a given temperature.
Question 12
The instantaneous rate of reaction A
B is
. What is the significance of
plus and minus sign?
Ans.
In the above equation the negative sign indicates the decrease in concentration of the
reactant and a positive sign indicates the increase in concentration of the product.
Question 13
How is the rapid change in concentration of reactants or products monitored for fast
reactions?
Ans.
The rapid change in concentration of reactants or products of fast reactions is
determined by flow methods, relaxation method or spectrophotometric techniques.
Order and Molecularity of reaction
Question 1
A reaction is of first order in reactant A and of second order in reactant B. How is the
rate of this reaction affected when (i) the concentration of B alone is increased to
three times (ii) the concentrations of A as well as B are doubled?
Ans.
Question 2
Define 'order of a reaction'.
Ans.
The sum of the exponents (powers) of the concentration of reactants in the rate law
expression is termed as order of that chemical reaction.
Question 3
Ans
Question 4
The decomposition of dimethyl ether leads to the formation of CH 4, H2 and CO and the
reaction rate is given by
Rate = k[CH3OCH3]3/2
The rate of reaction is followed by increase in pressure in a closed vessel and the rate can also be
expressed in terms of partial pressure of dimethyl ether i.e.
Rate = k(p CH OCH )3/2
3
3
If pressure is measured in bar and time in minutes, then what are the units of rate and rate
constants?
Ans.
CH3OCH3
CH4 + H2 + CO
Rate of reaction,
= k(pCH3OCH3)3/2
K=
= bar-1/2. time -1
Question 5
Differentiate between the order of a reaction and its molecularity
Ans.
Molecularity
Order of a reaction
i) It is the number of reacting species
i) It is the sum of the powers of the
undergoing simultaneous collision in the
concentration terms in the rate law
reaction.
expression.
ii) It is a theoretical concept.
ii) It is determined experimentally.
iii) It does not tell us anything about the
iii) It tells us about the slowest step and
mechanism of the reaction.
hence gives some clues about the
mechanism of the reaction.
iv) It does not change with change in
iv) It changes with change in temperature
temperature and pressure.
And pressure.
Question 6
Name the factors that influence the rate of a chemical reaction.
Ans.
The rate of a chemical reaction is influenced by the following factors
i)
Concentration of the reactants
ii)
Temperature of the reactants
iii)
Nature of the reacting substances
iv)
Presence of catalyst
v)
Exposure to radiations
Question 7
The rate expression for a chemical reaction
4HBr(g) + O2(g)
2H2O(g) + 2Br2(g) is
Rate = k [HBr] [O2].
Write the probable mechanism of this reaction?
Ans.
The mechanism of this reaction is:
Step I: HBr + O2
HOOBr
Step II: HOOBr + HBr
2HOBr
Step III: [HOBr + HBr
H2O + Br2]
4HBr +O2
2
2H2O + 2Br2
Question 8
In what respect does the rate law differ from the law of mass action? Explain with an
example
Ans.
The rate law of the reaction gives the mathematical expression which gives the actual
rate of reaction where as the law of mass action gives the rate on the basis of
stoichiometry of the balanced equation. For example
aA +bB
cC + dD
The rate law for this equation can be written as
Rate = k [A]m [B]n
In the rate law expression, the numerical values of m and n are determined
experimentally and cannot be deduced from the balanced equation. The values of m
and n may or may not be the same as a and b.
Question 9
Distinguish between the rate of a reaction and rate constant of a reaction
Ans.
Rate of reaction
Rate constant of reaction
i) It is the speed of the reaction at which
i) It is constant of proportionality in the
the reactants are converted into the
rate law expression.
products at any moment of time.
ii) It depends upon the concentration of
ii) It refers to the rate of reaction at the
reactant species at that moment of time.
specific point when concentration of every
reacting species is unity.
iii) It generally decreases as the reaction
iii) It is constant and does not depend on
proceeds.
the progress of the reaction.
Question 10
What are the units for the rate constant of first order reaction?
Ans.
The unit for the rate constant of first order reaction is s-1.
Question 11
The rate law for a reaction A + H2O
B is rate [A]. Find the molecularity and
order of the reaction.
Ans.
The molecularity of the reaction is 2 and order of the reaction is 1.
Question 12
The order of a reaction A + B
Ans.
Rate = k [A] 0 [B] 0
Question 13
Ans.
C is zero. Write its rate equation?
Integrated rate equation
Question 1
The rate constant for a reaction of zero order in A is 0.0030 mol L-1 s-1. How long will it
take for the initial concentration of A to fall from 0.10 M to 0.075 M?
Ans.
Question 2
Draw schematic graphs showing the following details of the first order reactions
i) Variation of the rate of reaction with change in the concentration of the reactant.
ii) Variation of In [R] Vs t and Log [Ro]/[R] vs t.
Ans.
Question 3
Derive an equation for calculating the half life of a first order reaction
Ans.
The rate equation for a first order reaction is:
K=
At t1/2 [R] =
Question 4
Calculate the rate of reaction from the rate law:
= k[A] [B]2, when the
concentration of A and B are 0.01 M and 0.02 M respectively and k = 5.1 x 10-3 L2 mol2 -1
s .
Ans.
Rate of reaction,
= 2.04 x 10-8 Ms-1
Question 5
The rate of reaction between A and B increases by a factor of 100. Calculate the order
of the reaction when the concentration of A is increased 10 times.
Ans.
Question 6
The half-life of a first order decomposition of nitramide is 2.1 hour at 25o C. Determine
the time taken for the compound to decompose 99% of its original amount, rate
constant = 0.2303 per hour.
Ans.
Here a = 100
a – x = 100 – 99 = 1
t=
Question 7
Ans.
Question 8
The reaction A + 3B
2C obeys the rate equation:
Rate = k[A]1/3 [B]3/2. Find out the order of this reaction?
Ans.
Rate = k [A]x[B]y
Overall order = x + y
So, Overall order = 1/3 + 3/2 = 11/6
Question 9
A gas phase decomposition of xy follows the rate law r = k[xy]n. what are the units of
its rate constant?
Ans.
The rate constant for decomposition of xy is atm (n-1) sec-1
Question 10
For a chemical reaction X
Y, The rate increases by the factor 2.25 when
concentration of X is increased by 1.5 derive suggest rate law equation and find the
order of reaction.
Ans.
(Rate)1 = k[X]m2
(Rate)2 = k [1.5X]m
Hence
Therefore order of the reaction is 2.
And rate law equation = k [X]2
Question 11
Explain why the rate of a chemical reaction does not remain uniform throughout the
reaction?
Ans.
The rate of a reaction does not remain uniform throughout the reaction because it
depends on concentration which changes with passage of time.
Temperature Dependence of reaction
Question 1
Derive an equation for calculating the value of activation energy E a by plotting a graph
between log k and 1/T
Ans.
Graph between In k and 1/T
A graph plotted between log k against 1/T gives a straight line having a slope equal to -
Ea = - 2.303 R x slope
Arrhenius equation = k = A e–Ea/RT
Taking logarithm of Arrhenius equation we get
log k = log A On differentiating equation (ia) w.r.t temperature we get
…(ib)
The value of Ea can be determined by measuring the rate constants of a reaction at two
different temperatures. If k1 and k2 are the rate constants for the reaction at
temperatures T1 and T2 then,
log k1 = logA log k2 = log A Subtracting Equation (ia) from (ib) we get
Question 2
The rate constant of a first order reaction becomes 6 times when the temperature is
increased from 350 K to 410 K. Calculate the energy of activation for the reaction.(R =
8.314 JK-1 mol-1)
Ans.
Question 3
The rate constant for the first order decomposition of certain reaction is described by
the equation log k (sec-1) =
Calculate the activation energy for this reaction.
Ans.
Given that log k =
According to Arrhenius equation
k = Ae-Ea/RT
…(i)
Comparing equation (i) and (ii), we have
Question 4
Explain why the activation energy of a reaction can never be zero.
Ans.
The Activation energy of a reaction can never be zero because if Ea = 0, then the
expression k = A.e -Ea/RT = A.eo = A
In other words the rate constant becomes equal to collision factor. This implies that
every collision results into a chemical product. This cannot be true.
Question 5
Draw a graph to show the various energy changes that take place in the following
reaction:
H2 (g) + I2 (g)
Ans.
2HI (g)
Question 6
The activation energy for a reaction is zero. Calculate the value of its rate constant at
300 K, if k = 1.6 x 106 s-1 at 280 K? (R = 8.31 JK-1 Mol-1)
Ans.
Question 7
Define transition state or activation complex.
Ans.
The arrangement of atoms corresponding to energy maxima (threshold energy) is called
transition state or activated complex.
Question 8
What is temperature coefficient? Explain
Ans.
Temperature coefficient is the ratio of rate constants of the reaction at two
temperatures differing by 10o.
Question 9
What is the effect of a catalyst on the equilibrium constant of a reaction?
Ans.
In a chemical reaction, a catalyst catalyses the forward and backward reaction to the
same extent, so the equilibrium constant remains the same.
Question 10
Define activation energy.
Ans.
The extra energy over and above the average potential energy of the reactants which
must be supplied to the reactants to enable them to cross the energy barrier between
reactants and products is called activation energy.
Collision theory
Question 1
Calculate the activation energy of a hydrogen carbon whose decomposition is given as
follows:
K= (4.5 x 1011 s-1) e-28000K/T
Ans.
According to Arrhenius equation k = A.e –Ea/RT
Comparing the given value of k = (4.5 x 1011 s-1) e-28000 K/T, we get
Question 2
The rate of a reaction becomes four times when the temperature changes from 293 K
to 313 K. Calculate the energy change of the reaction assuming that it does not change
with temperature.
Ans.
T1 = 293 K; T2 = 313 K
According to Arrhenius equation:
Question 3
Ans.
Question 4
State the main postulates of the collision theory.
Ans.
According to the collision theory:
i)
A reaction occurs on collision of two molecules only if they possess a certain
minimum amount of energy in excess of the normal energy of the molecules.
ii)
The minimum energy which molecules must possess before collision should
be equal to or greater than the activation energy.
Question 5
What are the two conditions that are necessary for effective collisions?
Ans.
The two conditions that are necessary for effective collisions are:
i)
The molecule should collide with sufficient kinetic energy also called the
threshold energy.
ii)
The molecules should have proper orientation.
Question 6
Hydrogen gas and iodine vapour combine to form hydrogen iodide gas, as shown in
the equation H2 + I2
2HI.
Using representations shown below draw a diagram to show an orientation for the
reactant molecules that can produce an effective collision capable of producing two
hydrogen iodide molecules.
Ans.
Question 7
Write down the modified form of Arrhenius equation on the basis of collision theory
Ans.
k = P ZAB.e-Ea/RT
Here P is called the stearic factor.
Question 8
What is the main drawback of the Collision theory?
Ans.
The main drawback of the Collision theory is that it considers atoms and molecules to be
hard spheres and ignores their structures.
Question 9
Define Collision frequency Z.
Ans.
The number of collisions per second per unit volume of the reaction mixture is known as
the collision frequency.
Question 10
Collision theory of chemical reactions is based on which theory?
Ans.
Collision theory of chemical reactions is based on the kinetic molecular theory of gases.
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