031102

Chemical Kinetics:

11. The thermal decomposition of HCO2H is a first order reaction with a rate constant of 2.4 × 10-3 s-1 at a certain temperature. Calculate how long will it take for three-fourths of initial quantity of HCO2H to decompose. (log 0.25 = -0.6021). (Chiref 11)

14.(a) For a reaction

A + B → P

the rate law is given by, r = k[A]1/2 [B]2. What is the order of this reaction? (b) A first order reaction is found to have a rate constant k = 5.5 × 10-14 s-1. Find the half life of the reaction. (Chiref 14)

15. Rate constant k for a first order reaction has been found to be 2.54 × 10-3 sec-1. Calculate its 3/4th life, (log 4 = 0.6020). (Chiref 15)

16. A first order gas phase reaction :

A2B2(g) → 2A(g) + 2B(g)

at the temperature 400°C has the rate constantk = 2.0 × 10-4 sec-1. What percentage of A2B2 is decomposed on heating for 900 seconds? (Antilog 0.0781 = 1.197) (Chiref 16)

27. A first order reaction has a rate constant of 0.0051 min-1. If we begin with 0.10 M concentration of the reactant, what concentration of reactant will remain in solution after 3 hours? (Chiref 27)

28. For a decomposition reaction the values of rate constant k at two different temperatures are given below : k1 = 2.15 × 10-8 L mol-1 s-1 at 650 K

k2 = 2.39 × 10-7 L mol-1 s-1

at 700 K Calculate the value of activation energy for this reaction. R = 8.314 J K-1 -mol1

30. The rate of a reaction becomes four times when the temperature changes from 293 K to 313 K. Calculate the energy of activation (Ea) of the reaction assuming that it does not change with temperature. R = 8.314 J K-1 -mol-1

(Chiref 30)

33. Hydrogen peroxide, H2O 2(aq) decomposes to H2O(l) and O2(g) in a reaction that is first order in H2O2 and has a rate constant k = 1.06 × 10-3min-1. (i) How long will it take for 15% of a sample of H2O(l) and O2 to decompose? (ii) How long will it take for 85% of the sample to decompose? (Chiref 33)

34. For a decomposition reaction, the values of k at two different temperatures are given below: k1 = 2.15 × 10-8 L mol-1 s-12 = 2.39 × 10-7 L mol-1 s-1 at 700 K Calculate the value of activation energy for this reaction. (Log 11.11 = 1.046) (R = 8.314 J K-1 -mol-1)

(Chiref 34)

SVOENB Sec
Instructional Video Sec
Chemical Kinetics:
Chemical kinetics it is branch of chemistry that deals with the study of rates of chemical reactions the factors affecting it and the mechanism by which reactions proceeds rate of reaction it is the change in the concentration of reactants or products per unit time

Rate of chemical reaction : The change in concentration of any reactant or product per unit time is called rate of reaction.

Types of Rate of Reaction :

1. Average rate of reaction : The rate of reaction measured over the long time interval is called average rate of reaction.
2. Instantaneous rate of reaction : The rate of reaction measured at a particular time is called instantaneous rate of reaction.

Factors affecting Rate of Reaction
1. Concentration of reactant
2. Surface area
3. Temperature
4. Nature of reactant
5. Presence of catalyst
6. Radiation in photochemical reaction

Rate constant (k) : It is equal to the rate of reaction when molecular concentration of reactant is at unity.

Rate law : The rate of reaction is directly proportional to the product of concentration of reactant and each concentration is raised to some power which may or may not be equal to stereochemistry experimentally.
For a reaction,

aA + bB → cC + dD


Molecularity : The total number of reactants taking part in elementary chemical reaction is called molecularity.

Order of reaction : The sum of powers to which the concentration terms are raised in a rate law expression is called order of reaction.

For above case, Order = P + Q
Orders of reaction is determined experimentally.

Half-life period :
The time during which the concentration of the reactant is reduced to half of its initial concentration is called half-life period.

Activation energy :
The minimum extra amount of energy absorbed by reactant molecules so that their energy becomes equal to the threshold energy is called activation energy.

Temperature coefficient : The ratio of rate constant at two temperatures having difference of 10ºC is called temperature coefcient.

Temperature coefcient = Rate constant at T + 10ºC/Rate constant at TºC

Integrated rate equation
Concentration dependence of rate is called differential equation. it is not always convenience to measure the instantaneous rate because it is measured by determination of slope of the tangent at point ‘t’ in the concentration versus time graph, there for it is difficult to determine the rate law and hence order of the reaction.

To solve this problem we can integrate the rate equation and obtain integrated rate equation which gives a relation between directly measured experiment quantities that is concentrations at different times.

Integrated rate equations are different for reactions of different orders. This is the most common method for studying the kinetics of chemical reactions.

The differential rate law equation
The differential rate law in chemical kinetics relates the instantaneous reaction rate to reactant concentrations, typically expressed as

Rate Law: Rate = k[A]m[B]n

Differential Form: −d[R]⁄dt = k[A]m[B]n

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The differential form of rate law is transformed to integrated form of rate law by simple mathematics calculus the integrated rate equations for different order reactions can be derived as follows-

Zero order reaction-
A reaction is said to be off zero order if its rate is independent of the concentration of the reactant.
Let [R] be the concentration of the reactant are and k0 is the rate constant for the zero order reaction.
For the zero order reaction the rate of the reaction is independent of the concentration of [R].
This form of rate law is known as differential rate equation.

Significance of differential rate equation
Differential rate laws are generally expressed as:

First Order: Rate = -d[A] / dt = k[A]

General Form: -d[R] / dt = k[R]n


The differential rate equation is significant because it directly relates the instantaneous rate of a chemical reaction to the concentration of its reactants at any given point in time.

Key Significance of Differential Rate Equations:

Determines Reaction Orders: It reveals the dependence of the reaction rate on reactant concentrations, defining the order (e.g., zero, first, or second order) for each reactant.

Identifies Reaction Mechanisms: By comparing experimental rate laws with theoretical models, it helps identify the specific pathways or elementary steps of a reaction.

Calculates Instantaneous Rate: It provides the precise, immediate rate of reaction at a specific moment, which corresponds to the slope of a concentration-time plot.

Identifies Rate-Controlling Steps: It indicates which reactants are involved in the slow, rate-determining step, which is crucial for chemical engineering and catalysis.

Distinguishes from Stoichiometry: It highlights that the rate dependence on concentration is often different from the stoichiometric coefficients in a balanced equation, providing deeper insight into chemical kinetics.

Significance of Integrated rate equation
Half life period method. The order of a reaction can also be determined by another method known as half life period method. This is discussed below. Half life period of a reaction is defined as the time during which the concentration of a reactant is reduced to half of its initial concentration Half life period of a first order reaction is independent of the initial concentration of the reactant. For zero order reaction, integrated rate equation is Go back - Top
E1. From the concentrations of C4H9Cl (butyl chloride) at different times given below, calculate the average rate of the reaction: C4H9Cl + H2O ® C4H9OH + HCl during different intervals of time. t/s 0 50 100 150 200 300 400 700 800 [C4H9Cl]/mol L–1 0.100 0.0905 0.0820 0.0741 0.0671 0.0549 0.0439 0.0210 0.017 E2. The decomposition of N2O5 in CCl4 at 318K has been studied by monitoring the concentration of N2O5 in the solution. Initially the concentration of N2O5 is 2.33 mol L–1 and after 184 minutes, it is reduced to 2.08 mol L–1. The reaction takes place according to the equation 2 N2O5 (g) ® 4 NO2 (g) + O2 (g) Calculate the average rate of this reaction in terms of hours, minutes and seconds. What is the rate of production of NO2 during this period? E3. Calculate the overall order of a reaction which has the rate expression (a) Rate = k [A]1/2 [B]3/2 (b) Rate = k [A]3/2 [B]–1 E4. Identify the reaction order from each of the following rate constants. (i) k = 2.3 × 10–5 L mol–1 s–1 (ii) k = 3 × 10–4 s–1 E5. The initial concentration of N2O5 in the following first order reaction N2O5(g) ® 2 NO2(g) + 1/2O2 (g) was 1.24 × 10–2 mol L–1 at 318 K. The concentration of N2O5 after 60 minutes was 0.20 × 10–2 mol L–1. Calculate the rate constant of the reaction at 318 K. E6. The following data were obtained during the first order thermal decomposition of N2O5 (g) at constant volume: ( ) ( ) ( ) 2 5 2 4 2 2N O g ® 2N O g + O g S.No. Time/s Total Pressure/(atm) 1. 0 0.5 2. 100 0.512 Calculate the rate constant. E7. A first order reaction is found to have a rate constant, k = 5.5 × 10-14 s-1. Find the half-life of the reaction. E8. Show that in a first order reaction, time required for completion of 99.9% is 10 times of half-life (t1/2) of the reaction. E9. The rate constants of a reaction at 500K and 700K are 0.02s–1 and 0.07s–1 respectively. Calculate the values of Ea and A. N1.1 For the reaction R ® P, the concentration of a reactant changes from 0.03M to 0.02M in 25 minutes. Calculate the average rate of reaction using units of time both in minutes and seconds. N2. In a reaction, 2A  Products, the concentration of A decreases from 0.5 mol L–1 to 0.4 mol L–1 in 10 minutes. Calculate the rate during this interval? N3. For a reaction, A + B ® Product; the rate law is given by, r = k [ A]1/2 [B]2. What is the order of the reaction? N4. The conversion of molecules X to Y follows second order kinetics. If concentration of X is increased to three times how will it affect the rate of formation of Y ? N5. A first order reaction has a rate constant 1.15 × 10-3 s-1. How long will 5 g of this reactant take to reduce to 3 g? N6. Time required to decompose SO2Cl2 to half of its initial amount is 60 minutes. If the decomposition is a first order reaction, calculate the rate constant of the reaction. N7. What will be the effect of temperature on rate constant ? N8. The rate of the chemical reaction doubles for an increase of 10K in absolute temperature from 298K. Calculate Ea. N9. The activation energy for the reaction 2 HI(g) ® H2 + I2 (g) is 209.5 kJ mol–1 at 581K.Calculate the fraction of molecules of reactants having energy equal to or greater than activation energy? B B1. From the rate expression for the following reactions, determine their order of reaction and the dimensions of the rate constants. (i) 3NO(g) ® N2O (g) Rate = k[NO]2 (ii) H2O2 (aq) + 3I– (aq) + 2H+ ® 2H2O (l) + 3 I Rate = k[H2O2][I-] (iii) CH3CHO (g) ® CH4 (g) + CO(g) Rate = k [CH3CHO]3/2 (iv) C2H5Cl (g) ® C2H4 (g) + HCl (g) Rate = k [C2H5Cl] B2. 3.2 For the reaction: 2A + B ® A2B the rate = k[A][B]2 with k = 2.0 × 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. B3. The decomposition of NH3 on platinum surface is zero order reaction. What are the rates of production of N2 and H2 if k = 2.5 × 10–4 mol–1 L s–1? B4. 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, so the rate can also be expressed in terms of the partial pressure of dimethyl ether, i.e., ( ) 3 3 3/2 Rate = k pCH OCH If the pressure is measured in bar and time in minutes, then what are the units of rate and rate constants? B5. Mention the factors that affect the rate of a chemical reaction. B6. 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 ? B7. 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? B8. In a pseudo first order reaction in water, the following results were obtained: t/s 0 30 60 90 [A]/ mol L–1 0.55 0.31 0.17 0.085 Calculate the average rate of reaction between the time interval 30 to 60 seconds. B9. 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 are doubled? B10. 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: A/ mol L–1 0.20 0.20 0.40 B/ mol L–1 0.30 0.10 0.05 r0/mol L–1s–1 5.07 × 10–5 5.07 × 10–5 1.43 × 10–4 What is the order of the reaction with respect to A and B? B11. The following results have been obtained during the kinetic studies of the reaction: 2A + B ® C + D Experiment [A]/mol L–1 [B]/mol L–1 Initial rate of formation of D/mol L–1 min–1 I 0.1 0.1 6.0 × 10–3 II 0.3 0.2 7.2 × 10–2 III 0.3 0.4 2.88 × 10–1 IV 0.4 0.1 2.40 × 10–2 Determine the rate law and the rate constant for the reaction. B12. 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: Experiment [A]/ mol L–1 [B]/ mol L–1 Initial rate/ mol L–1 min–1 I 0.1 0.1 2.0 × 10–2 II – 0.2 4.0 × 10–2 III 0.4 0.4 – IV – 0.2 2.0 × 10–2 B13. 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 B14. 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. B15. The experimental data for decomposition of N2O5 [2N2O5 ® 4NO2 + O2] in gas phase at 318K are given below: t/s 0 400 800 1200 1600 2000 2400 2800 3200 102 × [N2O5]/ 1.63 1.36 1.14 0.93 0.78 0.64 0.53 0.43 0.35 mol L–1 (i) Plot [N2O5] against t. (ii) Find the half-life period for the reaction. (iii) Draw a graph between log[N2O5] and t. (iv) What is the rate law ? (v) Calculate the rate constant. (vi) Calculate the half-life period from k and compare it with (ii). B16. The rate constant for a first order reaction is 60 s–1. How much time will it take to reduce the initial concentration of the reactant to its 1/16th value? B17. During nuclear explosion, one of the products is 90Sr with half-life of 28.1 years. If 1mg of 90Sr was absorbed in the bones of a newly born baby instead of calcium, how much of it will remain after 10 years and 60 years if it is not lost metabolically. B18. For a first order reaction, show that time required for 99% completion is twice the time required for the completion of 90% of reaction. B19. A first order reaction takes 40 min for 30% decomposition. Calculate t1/2. B20. For the decomposition of azoisopropane to hexane and nitrogen at 543 K, the following data are obtained. t (sec) P(mm of Hg) 0 35.0 360 54.0 720 63.0 Calculate the rate constant. B21. The following data were obtained during the first order thermal decomposition of SO2Cl2 at a constant volume.  SO2Cl2 g  SO2 g  Cl2 g Experiment Time/s–1 Total pressure/atm 1 0 0.5 2 100 0.6 Calculate the rate of the reaction when total pressure is 0.65 atm. B22. The rate constant for the decomposition of N2O5 at various temperatures is given below: T/°C 0 20 40 60 80 105 × k/s-1 0.0787 1.70 25.7 178 2140 Draw a graph between ln k and 1/T and calculate the values of A and E a. Predict the rate constant at 30° and 50°C. B23. The rate constant for the decomposition of hydrocarbons is 2.418 × 10–5s–1 at 546 K. If the energy of activation is 179.9 kJ/mol, what will be the value of pre-exponential factor. B24. Consider a certain reaction A ® Products with k = 2.0 × 10–2s–1. Calculate the concentration of A remaining after 100 s if the initial concentration of A is 1.0 mol L–1. B25. Sucrose decomposes in acid solution into glucose and fructose according to the first order rate law, with t 1/2 = 3.00 hours. What fraction of sample of sucrose remains after 8 hours ? B26. The decomposition of hydrocarbon follows the equation k = (4.5 × 1011s–1) e-28000K/T Calculate E a. Rationalised 2023-24 Chemistry 88 B27. The rate constant for the first order decomposition of H2O2 is given by the following equation: log k = 14.34 – 1.25 × 104K/T Calculate Ea for this reaction and at what temperature will its half-period be 256 minutes? B28. The decomposition of A into product has value of k as 4.5 × 103 s–1 at 10°C and energy of activation 60 kJ mol–1. At what temperature would k be 1.5 × 104s–1? B29. The time required for 10% completion of a first order reaction at 298K is equal to that required for its 25% completion at 308K. If the value of A is 4 × 1010s–1. Calculate k at 318K and Ea. B30. The rate of a reaction quadruples when the temperature changes from 293 K to 313 K. Calculate the energy of activation of the reaction assuming that it does not change with temperature. Answers to Some Intext Questions Go back - Top
Click Here 0 Chem kinetics
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