Chemical Kinetics Exercises

CHEMICAL KINETICS EXERCISE – I UNSOLVED PROBLEMS Q.1 The rate of decomposition of substance A becomes eight times when its concentration is doubled. What is the order of the reaction? Q.2 The following rate data were obtained at 300 K for the reaction 2A + B  C + D Exp.No. Amol/L  Bmol/L  1 0.1 0.1 2 0.3 0.2 7.2  10 2 3 0.3 0.4 2.40  10 1 4 0.4 0.1 2.40  10 2 Rate of formation of Dmol/L/min  6  10 3 Determine the rate law and rate constant for reaction. Q.3 Define collision frequency, threshold energy and activation energy. Q.4 The rate of a particular reaction triples when temperature changes from 50ºC to 100ºC. Calculate the activation energy of reaction. Q.5 What is the catalyst? How does it effects the rate of reaction? Q.6 From the rate expression for the following reactions determine the order of reaction and the dimensions of the rate constants. (i) 3NO(g) N2O(g) + NO2(g) ; Q.7 Rate = k[NO]2 (ii) H2O2(aq) + 3I–(aq) + 2H+(aq) 2H2O(I) + I3– ; 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] For the reaction 2A + B  A2B the rate = k[A] [B]2 with k = 2.0 ×106 mol–2 L2s–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. Q.8 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 Q.9 Sucrose decomposes in acid solution into glucose and fructose according to the first order rate law, with t1/2 = 3.00 hours. What fraction of sample of sucrose remains after 8 hours. Q.10 Show that in case of a first order reaction, the time required for 99.9% of the reaction take place is ten times that required for half of the reaction. Q.11 The half life of a reaction A  B is 8 minutes. How long it takes [A] to reach 25% of the initial concentration? Q.12 For a first order reaction, calculate the ratio between the time to complete three fourth of the reaction and the time taken to complete half of the reaction. CHEMICAL KINETICS EXERCISE – II BOARD PROBLEMS Q.1 A first order decomposition reaction takes 40 minutes for 30% decomposition. Calculate its t1/2 value. Q.2 The decomposition of phosphine, 4 PH3(g)  P4(g) + 6 H2(g) has the rate law, rate = k [PH3]. The rate contant is 6.0 × 10–4 s–1 at 300 K and activation energy is 3.05 ×105 J mol–1. Calculate the value of rate contant at 310 K. (Give, R = 8.314 JK–mol–) Q.3 Define the following : (i) Elementary step in a reaction Q.4 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 mol–1) Q.5 Define the following :(i) Order of a reaction (ii) Activation energy of a reaction Q.6 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 the reactant will be left after 3 hours ? Q.7 (a) Explain the following terms: (i) Order of a reaction (ii) Molecularity of a reaction (b) The rate of a reaction increases four times when the temperature changes from 300 K to 320 K. Calculate the energy of activation of the reaction, assuming that it does not change with temperature. (R = 8314 JK–1 mol–1) Q.8 (a) Explain the following terms: (i) Rate of a reaction (ii) Activation energy of a reaction (b) The decomposition of phosphine, PH3, proceeds according to the following equation: 4 PHa(g)  P4(g) + 6 H2(g) It is found that the reaction follows the following rate equation: Rate = k [PH3]. The half-life of PH3 is 37.9 s at 120ºC. (i) How much time is required for 3/4th of PH3 to decompose? (ii) What fraction of the original sample of PH3 remains behind after 1 minute? Q.9 Define 'activation energy' of a reaction. Q.10 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) Q.11 What do you understand by the rate law and rate constant of a reaction? Identify the order of a reaction if the units of its rate constant are : (i) L–1 mol s–1 (ii) L mol–1 s–1 The rate of a reaction increases four times when the temperature changes from 300 K to 320 K. Calculate the energy of activation of the reaction, assuming that it does not change with temperature. (R = 8.314 JK–1 mol–1) Q.12 Q.13 Q.14 Q.1 Q.4 Q.8 Q.10 (ii) Rate of a reaction (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 × 1–14 s–1 . Find the half life of the reaction. 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 , log 4 = 0.6021] n=3 22.012 kJ/mole (i) 4 times, (ii) 1/4 times t99.9% = 10 × t50% Answers Q.2 Q.9 Q.11 Rate = k[A][B]2, 6 mol–2 L2 S–1 Q.7 3.89 × 10–9 mole litre–1 s–1 0.158 M. 16 min Q.12 2