Chapter: Chemical Kinetics Rate of Chemical Reaction Question 1 Nitrogen pentaoxide decomposes according to equation:

This first order reaction was allowed to proceed at 40oC 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) Time (min) log[N2O5]

0.400 0.00 -.03979

0.289 20.0 -0.5391

0.209 40.0 -0.6798

0.151 60.0 -0.8210

0.109 80.0 -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 O82- I3 + 2SO4

2-

i) If given interval than what is the value

of

ii) Also calculate the average rate of formation of SO42-

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) 2NO2(g) proceeds through the following steps:

i) NO + O2 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 + 2I- 2Cl- + 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 CH4, 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 CH3

OCH3

)3/2

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 undergoing simultaneous collision in the reaction.

i) It is the sum of the powers of the concentration terms in the rate law expression.

ii) It is a theoretical concept. ii) It is determined experimentally.

iii) It does not tell us anything about the mechanism of the reaction.

iii) It tells us about the slowest step and hence gives some clues about the mechanism of the reaction.

iv) It does not change with change in temperature and pressure.

iv) It changes with change in temperature 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] 2

4HBr +O2 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 the reactants are converted into the products at any moment of time.

i) It is constant of proportionality in the rate law expression.

ii) It depends upon the concentration of reactant species at that moment of time.

ii) It refers to the rate of reaction at the specific point when concentration of every reacting species is unity.

iii) It generally decreases as the reaction proceeds.

iii) It is constant and does not depend on 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 C is zero. Write its rate equation? Ans. Rate = k [A] 0 [B] 0 Question 13

Ans.

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 mol-

2 s-1. 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 Ea 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 = …(i) According to Arrhenius equation k = Ae-Ea/RT

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) 2HI (g) Ans.

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. @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@