4.1 From the rate expression for the following reactions determine their order of reaction and the dimensions of the rate constants:
4.2 For the reaction, 2A + B ————> A2 B, the rate = k [AJ[B]2 with k = 2.0 x 10-6 mol-2 L2 s-1. Calculate the initial rate of the reaction when [A] = 0.1 mol L-1, [B] = 0.2 mol L-1. Calculate the rate of reaction after [A] is reduced to 0.06 mol L-1.
Sol. Initial rate of reaction = k [A] [B]2
= (20 x 10-6 mol-2 s-1) (0.1 mol L-1) (0.2 mol L-1)2 = 8 x 10-9molL-1 s-1.
When [A] is reduced from 010 mol L-1 to 0.06 molL-1, i.e., 0.04 mol L-1 of A has reacted, the concentration of B reacted, is = 1/2 x 0.04 mol L-1 = 0.02 mol L-1
Concentration of B, remained after reaction with A = 0.2 – 0-02=0.18 mol L-1
Now, rate=(20 x 10-6 mol-2 L2 s-1) (0.06 mol L-1) (0.18 molL-1)2
= 3-89 x 10-9mol L-1 s-1
4.3 The decomposition of NH3 on platinum surface is zero order reaction. What are the rates of production of N2 and H2 if Ar=2.5 x 10-4 mol-1 Ls-1.
4.4 The decomposition of dimethyl ether leads to the formation of CH4, H2 and CO and die reaction, rate is given by Rate=k [CH3OCH3]3/2 The rate of reaction is followed by increase in pressure in a closed vessel, so the rate can also, be expressed in terms of the partial pressure of dimethyl ether, i.e., Rate= k (PCH3OCH3)3/2
If the pressure is measured in bar and time in minutes, then what are the units of rate and rate constants?
Sol. As the concentration in the rate law equation is given in terms of pressure,
4.5 Mention the factors that affect the rate of a chemical reaction.
Sol. Factors affecting the rate 6f chemical reaction are following:
(i) Natpre of reactants
(ii) Concentration of reactants
(iii) Surface area of reactants
(iv) Effect of temperature
(v) Presence of catalyst
(vi) Presence of light
4.6 A reaction is second order with respect to a reactant How is the rate of reaction affected if the concentration of the reactant is (i) doubled (ii) reduced to half?
4.7 What is the effect of temperature on the rate constant of a reaction? How can this effect of temperature on rate constant be represented quantitatively?
Sol. The rate constant of a reaction increases with increase of temperature and becomes nearly double for every 10 °C rise of temperature. Quantitatively, this temperature effect on the rate constant is represented as, k = Ae-Ea/RT
where Ea is the activation energy of the reaction, and A represents the frequency factor.
4.8 In a pseudo first order hydrolysis of ester in water, the following results were obtained:
t/s 0 30 60 90
[Ester] mol L-1 0-55 0-31 0 17 0 085
(i) Calculate the average rate of reaction between the time interval 30 to 60 seconds.
(ii) Calculate the pseudo first order rate constant for the hydrolysis of ester.
4.9 A reaction is first order in A and second order in B.
(i) Write the differential rate equation.
(ii) How is the rate affected on increasing the concentration of B three times?
(iii) How is the rate affected when the concentrations of both A and B is doubled?
4.10 In a reaction between A and B, the initial rate of reaction (r0 ) was measured for different initial concentrations of A and B as given below:
What is the order of the reaction with respect to A and B?
4.11 The following results have been obtained during the kinetic studies of the reaction.
2A+B ——–> C + D
Determine the rate law and the rate constant for the reaction.
4.12 The reaction between A and B is first order with respect to A and zero order with respect to B. Fill in the blanks in the following table:
4.13 Calculate the half-life of a first order reaction from their rate constants given below:
(i) 200 s-1 (ii) 2 min-1
(iii) 4 years-1
4.14 The half-life for radioactive decay of 14C is 5730 years. An archaeological artifact containing wood had only 80% of the 14C found in a living tree. Estimate the age of the sample.
Sol. Radioactive decay follows first order kinetics.
4.15 The experimental data for decomposition of N2O5