Chemical Kinetics and Nuclear Chemistry Exercise # 5

CHEMICAL KINETICS AND NUCLEAR CHEMISTRY Exercise # 5 Part # I [Previous Year Questions] 1. In a first order reaction, the concentration of the reactant, decreases from 0.8 M to 0.4 M in 15 minutes. The time taken for the concentration to change from 0.1 M to 0.025 M is : (A) 30 minutes (B) 15 minutes (C) 7.5 minutes (D) 60 minutes 2. The rate equation for the reaction 2A + B  C is found to be : rate = k[A] [B]. The correct statement in relation to this reaction is that the : (A) unit of k must be sec–1 (B) t1/2 is a constant (C) rate of formation of C is twice the rate of disappearance of A (D) value of k is independent of initial concentrations of A and B. 3. The half - life of a radioisotope is four hours. If the initial mass of the isotope was 200 g, the mass remaining after 24 hours undecayed is : (A) 1.042 g (B) 2.084 g (C) 3.125 g (D) 4.167 g. 4. Consider an endothermic reaction X  Y with the activation energies Eb and Ef for the backward and forward 5. reaction, respectively. In general (A) Eb < Ef (B) H = U (C) H < U A reaction involving two different reactants can never be : (A) unimolecular reaction (B) first order reaction (C) second order reaction (D) bimolecular reaction (D) H > U 6. A reaction was found to be second order with respect to the concentration of carbon monoxide. If the concentration of carbon monoxide is doubled, with everything else kept the same, the rate of reaction will be (A) remain unchanged (B) tripled (C) increased by a factor of 4 (D) doubled 7. The following mechanism has been proposed for the reaction of NO with Br2 to form NOBr. NO (g) + Br2 (g) NOBr2 (g) ; NOBr2 (g) + NO (g)  2NOBr (g) (slow step) If the second step is the rate determining step, the order of the reaction with respect to NO(g) is (A) 1 (B) 0 (C) 3 (D) 2 8. The energies of activation for forward and reverse reactions for A2 + B2 2AB are 180 kJ mol–1 and 200 kJ mol– 1 respectively. The presence of a catalyst lowers the activation energy of both (forward and reverse) reactions by 100 kJ mol–1. The enthalpy change of the reaction (A2 + B2 2AB) in the presence of catalyst will be (in kJ mol–1). (A) 280 9. (B) 20 (C) 300 (D) 120 A radioactive element gets spilled over the floor of a room. Its half-life period is 30days. If the initial activity is ten times the permissible value, after how many days will it be safe to enter the room : (A) 10 days (B) 100 days (C) 1000 days (D) 300 days 10. For a reaction (A)  1 A  2B, rate of disappearance of 'A' related to the rate of appearance of 'B' by the expression. 2 d [ A ] 1 d [B]  dt 4 dt (B)  d [ A ] d [B]  dt dt (C)  d[A] d [B] 4 dt dt (D)  d [ A ] 1 d [B]  dt 2 dt 11. The half life period of a first order chemical reaction is 6.93 minutes. Time required for the completion of 99% of the chemical reaction will be (log 2 = 0.301) : (A) 23.03 minutes (B) 46.06 minutes (C) 460.6 minutes (D) 230.3 minutes 12. The time for half life period of a certain reaction A  Products is 1 hour. When the initial concentration of the reactant ‘A’, is 2.0 mol L–1 , how much time does it take for its concentration to come from 0.50 to 0.25 mol L–1. If it is a zero order reaction? (A) 4 h (B) 0.5 h (C) 0.25 h (D) 1 h 13. Consider the reaction Cl2 (aq) + H2S(aq)  S(s) + 2H+ (aq) + 2Cl– (aq) The rate equation for this reaction is, rate = k [Cl2][H2S] Which of these mechanisms is/are consistent with this rate equation? A. Cl2 + H2S  H+ + Cl– + Cl+ + HS– (slow) ; Cl+ + HS–  H+ + Cl– + S (fast) B. H2S  H+ + HS– (fast equilibrium) Cl2 + HS–  2Cl– + H+ + S (slow) (A) B only 14. 15. (B) Both A and B ; (C) Neither A nor B (D) A only The rate of a chemical reaction doubles for every 10ºC rise of temperature. If the temperature is raised by 50ºC, the rate of the reaction increases by about : (A) 10 times (B) 24 times (C) 32 times (D) 64 times A reactant (A) forms two products : A k1 B, Activation Energy Ea1 A k2 C, Activation Energy Ea2 ; If Ea2 = 2 Ea1, then k1 and k2 are related as : (A) k 2  k 1eEa1 / RT 16. 17. 19. (C) k 1  Ak 2 eEa1 / RT (D) k 1  2k 2 eEa 2 / RT For a first order reaction (A)  products the concentration of A changes from 0.1 M to 0.025 M in 40 minutes. The rate of reaction when the concentration of A is 0.01 M is : (A) 1.73 × 10–5 M/min (B) 3.47 × 10–4 M/min (C) 3.47 × 10–5 M/min (D) 1.73 × 10–4 M/min The rate of a reaction doubles when its temperature changes from 300 K to 310 K. Activation energy of such a reaction will be : (R = 8.314 JK–1 mol–1 and log 2 = 0.301) (A) 53.6 kJ mol–1 18. (B) k 2  k 1eEa 2 / RT (B) 48.6 kJ mol–1 (C) 58.5 kJ mol–1 (D) 60.5 kJ mol–1 Decomposition of H2O2 follows a first order reaction. In fifty minutes the concentration of H2O2 decreases from 0.5 to 0.125 M in one such decomposition. When the concentration of H2O2 reaches 0.05 M, the rate of formation of O2 will be: (A) 6.93 × 10–4 mol min–1 (B) 2.66 L min–1 at STP (C) 1.34 × 10–2 mol min–1 (D) 6.93 × 10–2 mol min–1 Two reactions, R1 and R2 have identical pre-exponential factors. Activation energy of R1 exceeds that of R2 by 10 kJ mol–1. If k1 and k2 are rate constants for reactions R1 and R2 respectively at 300 K, then In (k2/k1) is equal to : (R = 8.314 J mol–1K–1) (A) 8 (B) 12 (C) 6 (D) 4 CHEMICAL KINETICS AND NUCLEAR CHEMISTRY 20. At 518° C, the rate of decomposition of a sample of gaseous acetaldehyde, initially at a pressure of 363 Torr, was 1.00 Torr s–1 when 5% had reacted and 0.5 Torr s–1 when 33% had reacted. The order of the reaction is : (A) 3 (B) 1 2. (D) 2 [Previous Year Questions] Part # II 1. (C) 0 Given X  product (Taking 1st order reaction) conc 0.01 0.0025 (mol/lit) time (min) 0 40 Initial rate of reaction is in mol //min. (A) 3.43 × 10–4 (B) 1.73 × 10–4 (C) 3.43 × 10–5 (D) 1.73 × 10–5 Initial rates, r0, of the A + B  P at different initial concentrations of A and B ([A]0 and [B]0) are given below: –––––––––––––––––––––––––––––––––––––––––––– [A]0 [B]0 r0 (A) (B) 3. (mol L–1)(mol L–1)(mol L–1 s–1) –––––––––––––––––––––––––––––––––––––––––––– 0.1 0.1 0.05 0.2 0.1 0.10 0.1 0.2 0.05 –––––––––––––––––––––––––––––––––––––––––––– Write the rate equation. Calculate the rate constant of the reaction. For a reaction 2X(g)  3Y(g) + 2Z(g) Time (min) 0 100 200 the following data is obtained. Px (mm of Hg) (Partial pressure of X) 800 400 200 Find order with respect to X, rate constant of the reaction, time taken for 75% completion and find the total pressure when partial pressure of X, Px = 700 mm of Hg. Comprehension Carbon–14 is used to determine the age of organic material. The procedure is based on the formation of 14C by neutron capture in the upper atmosphere. 14 1 14 1 7 N  0n  6 C  1p C is absorbed by living organisms during photosynthesis. The 14C content is constant in living organism, once the plant or animal dies, the uptake of carbon dioxide by it ceases and the level of 14C in the dead being, falls due to the decay which C14 undergoes 14 14 6C  14 7N   The half life period of 14C is 5770 years. The decay constant () can be calculated by using the following formula 0.693 = t 1/ 2 The comparison of the  – activity of the dead matter with that of the carbon still in circulation enables measurement of the period of the isolation of the material from the living cycle. The method however, ceases to be accurate over periods longer than 30,000 years. The proportion of 14C to 12C in living matter is 1 : 1012. 4. Which of the following option is correct? (A) Rate of exchange of carbon between atmosphere and living is slower than decay of 14C. (B) Carbon dating can be used to find out the age of earth crust and rocks (C) Rate of exchange of 14C between atmosphere and living organism is so fast that an equilibrium is set up between the intake of 14C by organism and its exponential decay. (D) Carbon dating can not be used to determine concentration of 14C in dead beings. 5. What should be the age of fossil for meaningful determination of its age? (A) 6 years (B) 6000 years (C) 60,000 years (D) It can be used to calculate any age 6. A nuclear explosion has taken place leading to increase in concentration of 14C in nearby areas. 14C concentration is C1 in nearby areas and C2 in areas far away. If the age of the fossil is determined to be T1 and T2 at the places respectively then (A) The age of the fossil will increase at the place where explosion has taken place and T1 – T2 = C1 1 ln C  2 (B) The age of the fossil will decrease at the place where explosion has taken place and T 1 – T2 = C1 1 ln C  2 (C) The age of fossil will be determined to be same T C 1 1 (D) T  C 2 2 7. Consider a reaction aG + bH  Products. When concentration of both the reactants G and H is doubled, the rate increases by eight times. However, when concentration of G is doubled keeping the concentration of H fixed, the rate is doubled. The overall order of the reaction is : (A) 0 (B) 1 (C) 2 (D) 3 8. Under the same reaction conditions, initial concentration of 1.386 mol dm–3 of a substance becomes half in 40  k1  seconds and 20 seconds through first order and zero order kinetics, respectively. Ratio  k  of the rate constant  0 for first order (k1) and zero order (k0) of the reaction is. (A) 0.5 mol–1 dm3 9. (B) 1.0 mol dm–3 (C) 1.5 mol dm–3 (D) 2.0 mol–1 dm3 For a first order reaction A  P, the temperature (T) dependent rate constant (k) was found to follow the equation log k = – (2000) 1 + 6.0. The pre-exponential factor A and the activation energy Ea, respectively, are : T (A) 1.0 × 106 s–1 and 9.2 kJ mol–1 (C) 1.0 × 106 s–1 and 16.6 kJ mol–1 (B) 6.0 s–1 and 16.6 kJ mol–1 (D) 1.0 × 106 s–1 and 38.3 kJ mol–1 CHEMICAL KINETICS AND NUCLEAR CHEMISTRY 10. The concentration of R in the reaction R  P was measured as a function of time and the following data is obtained [R](molar ) 1.0 0.75 0.40 0.10 t(min .) 11. (A) 12. 13. 0.0 0.05 0.12 0.18 The order of the reaction is : Plots showing the variation of the rate constant (k) with temperature (T) are given below. The plot that follows Arrhenius equation is : (B) (C) For the first order reaction 2N2O5 (g)  4NO2(g) + O2 (g) (A) The concentration of the reaction decreases exponentially with time (B) The half-life of the reaction decreases with increasing temperature (C) The half-life of the reaction depends on the initial concentration of the reactant (D) The reaction proceeds to 99.6% completion in eight half-life duration An organic compound undergoes first-order decomposition. The time taken for its decomposition to 1/8 and 1/10 of its initial concentration are t1/8 and t1/10 respectively. What is the value of 14. (D) [1t / 8 ]  10 ?(log102 = 0.3) [ t1/ 10 ] In the reaction, P + Q  R + S the time taken for 75% reaction of P is twice the time taken for 50% reaction of P. The concentration of Q varies with reaction time as shown in the figure. The overall order of the reaction is : (A) 2 (C) 0 (B) 3 (D) 1 15. According to the Arrhenius equation, (A) a high activation energy usually implies a fast reaction (B) rate constant increases with increase in temperature. This is due to a greater number of collisions whose energy exceeds the activation energy (C) higher the magnitude of activation energy, stronger is the temperature dependence of the rate constant (D) the pre – exponential factor is a measure of the rate at which collisions occur, irrespective of their energy. 16. In a bimolecular reaction, the steric factor P was experimentally determined to be 4.5. The correct option(s) among the following is(are) (A) Experimentally determined value of frequency factor is higher than that predicted by Arrhenius equation (B) The value of frequency factor predicted by Arrhenius equation is higher than that determined experimentally (C) The activation energy of the reaction is unaffected by the value of the steric factor (D) Since P = 4.5, the reaction will not proceed unless an effective catalyst is used 17. For a first order reaction A(g)  2B(g) + C(g) at constant volume and 300 K, the total pressure at the beginning (t = 0) and at time t are Po and Pt, respectively. Initially, only A is present with concentration [A]0, and t1/3 is the time required for the partial pressure of A to reach 1/3rd of its initial value. The correct option(s) is (are) (Assume that all these gases behave as ideal gases) t1/3 ln(3p0 - Pt ) (A) (B) [A]0 ln(p0 - Pt) (C) (D) Rate constant Time Time 18. [A]0 Consider the following reversible reaction A(g)  B(g) ‡ˆ ˆˆ †ˆ AB(g) The activation energy of the backward reaction exceeds that of the forward reaction by 2 RT (in J mol–1). If the preexponential factor of the forward reaction is 4 times that of the reverse reaction, the absolute value of G° (in J mol –1) for the reaction at 300 K is _______. (Given : ln(2) = 0.7, RT = 2500 J mol–1 at 300 K and G is the Gibbs energy) EXERCISE - 5 : PART # I 1. A 14. C 2. D 15. C 3. C 16. B 4. A 17. A 5. A 18. A 6. C 19. D 7. D 8. B 9. B 10. A 11. B 12. C 13. D 20. D PART # II 1. A 11. A 2. A R0 = k[A0], B 0.5 sec–1. 12. A,B,D 13. 9 14. D 3. 950 mm of Hg 4. C 15. B, C, D 16. B, C 5. B 6. 17. A, D A 7. D 8. A 18. –8500 J/mole 9. D 10. 0