Title Chemical Kinetics - 02.pdf ✅

1 JEE ADVANCED 2024 Chemical Kinetics Single Correct (1 – 12) 1. The following reactions are occurring simultaneously in a vessel such that the temperature of the system is not changing. A + 3 B → P: ΔH = −2x kJ M → 2Q + R: ΔH = + x kJ If the rate of disappearance of ' B ' is yMs −1 , the rate of appearance of ' Q ' (in Ms −1 ) is (1) yMs −1 (2) 1.33yMs −1 (3) 0.75yMs −1 (4) 2yMs −1 2. The reaction X(g) → Y(g) follows first-order kinetics. The correct graph representing the rate of formation (R) of Y(g) with time (t) is (1) (2) (3) (4) 3. A substance ‘A’ decomposes in solution following first-order kinetics. Flask 1 contains 1 L of 1 M solution of ‘A’ and flask 2 contains 100 ml of 0.6 M solution of ‘A’. After 8.0 h, the concentration of ‘A’ in flask 1 becomes 0.25 M. In what time, the concentration of ‘A’ in fl ask 2 becomes 0.3 M? (1) 8.0 h (2) 3.2 h (3) 4.0 h (4) 9.6 h 4. The order of the reaction A → products is 0.5. The time for complete reaction T and time for 50% reaction, t1/2 will be related as (1) T = 2 × t1/2 (2) T = 4 × t1/2 (3) t1/2 = 0.3T (4) t1/2 = 0.7T 5. In the biological processes, the time taken by certain virus or bacteria to double its population is called generation time. In milk, at 37°C, Lactobacillus acidophilus has a generation time of about 75 minutes. The population relative to the initial value at 60 minutes is (ln 2 = 0.7) (1) 0.8 (2) e 0.56 (3) e 0.8 (4) e 0.875 6. The reaction A(g) → 2B(g) + C(g) follows first order kinetics. The reaction is started with pure ‘A’ in a rigid closed vessel maintained at constant temperature. After 10 s, a pin hole is developed in the vessel. If the molar ratio of gases ‘A’ and ‘B’ coming out initially is 1: 2, the rate constant of reaction is (Molar masses of A, B and C are 16, 4 and 8 g/mol, respectively, ln 2 = 0.7, ln 3 = 1.1) (1) 0.04 s−1 (2) 0.4 s−1 (3) 0.11 s−1 (4) 0.07 s−1 7. The rate expression for a reaction is −dC dt = α.C 1 + βC, where α, β are constants and C is the concentration of reactant at time t. The half-life for this reaction is (1) 1 α ln 2 + β⋅C0 2α (2) 1 β ln 2 + β⋅C0 2α (3) β⋅ln 2 α (4) α β DPP - 02
2 8. In Lindemann theory of unimolecular reactions, it is shown that the apparent rate constant for such a reaction is kapp = k1C 1 + αC , where C is the concentration of the reactant, k1 and α are constants. The value of C for which kapp has 90% of its limiting value at C tending to infinitely large is (α = 9 × 105 ) (1) 10−6 mole litre (2) 10−4 mole/ litre (3) 10−5 mole litre (4) 5 × 10−5 mole/litre 9. In the given first-order sequential reactions A ⟶ K1 B ⟶ K2 C ⟶ K3 D, what is the ratio of number of atoms of A to the number of atoms of B after long time interval starting with pure A? (K1 = ln 2 1200 and K2 = ln 2 30 ) (1) 0.67 (2) 10 (3) 20 (4) 40 10. An organic compound A decomposes the following two parallel first-order reactions A ⟶ K1 B and A ⟶ K2 C. If K1 is 1.25 × 10−5 s −1 and K1 K2 = 1 9 , then the value of [C] [A] after one hour of start of reaction by taking only A, is (ln 1.568 = 0.45) (1) 1 9 (2) 0.5112 (3) 1.4112 (4) 9 20 11. For certain reaction it is observed that ln K = α + βln T − γ T , where K is the rate constant, T is the temperature (Kelvin) and α, β and γ are constants. What is the Arrhenius activation energy? (1) βRT + γR (2) γR (3) β + γR (4) βRT − γR 12. A first-order reaction A → B, activation energy is 9.6 kcal/mol. When a 20% solution of ‘A’ was kept at 27°C for 21.6 minutes, 75% decomposition took place. What will be the percent decomposition in 8.0 minutes in a 30% solution maintained at 47°C? Assume that activation energy remains constant in this range of temperature (e = 2.7). (1) 25% (2) 50% (3) 75% (4) 87.5% One or More than one Correct 13. Initial concentration of reactant for nth order reaction is C0. Which of the following relation is/ are not correct about t1/2 of the reaction? (1) ln t1/2 = Constant − (n − 1) ln C0 (2) ln t1/2 = ln n + Constant − ln C0 (3) t1/2·ln n = Constant + ln C0 (4) ln t1/2 = n ln C0 14. Consider the following statements. The law for the acid-catalysed hydrolysis of an ester being given as rate = K [H+] [ester] = K ′ [ester]. If the acid (strong) concentration is doubled at constant ester concentration, 1. the second-order rate constant, K, is doubled. 2. the pseudo first-order rate constant, K ′ is doubled. 3. the rate of reaction is doubled. Which of the above statement is correct? (1) 1 and 2 (2) 2 and 3 (3) 1 and 3 (4) 1, 2 and 3 15. The decomposition reaction 3A(g) → 2B(g) + 2C(s) follows first-order kinetics. Starting with pure ‘A’ (at 6 atm), the pressures of system after 20 minutes and after a very long time are 5.05 atm and 4.05 atm, respectively. Identify the correct statement(s) related with the reaction. (1) Time for 75% completion of reaction is slightly more than 40 minutes. (2) Time for 87.5% completion of reaction is slightly less than 60 minutes. (3) Time for 93.75% completion of reaction is exactly 80 minutes. (4) The pressure of system after 40 minutes will be 4.55 atm.
3 16. To very good approximations, the cooling of a hot body to room temperature follows first-order kinetics (in this case, however, the unit that is changing is temperature (in kelvin), not molarity). If the rate constant for a body is 0.04 s−1 , then [ln 2 = 0.7, ln(323/25) = 2.6] (1) the time taken for that body to go from 323°C to 25°C is 17.5 s. (2) the time taken for that body to go from 1192 K to 298 K is 35 s. (3) the time taken for that body to go from 323°C to 25°C is 65 s. (4) the time taken for that body to go from 1192 K to 298 K is 130 s 17. Consider the following reactions 2 1 1 6.93 10 min A B − − ⎯⎯⎯⎯⎯⎯→ K =  and 2 1 2 13.86 10 min A C − − ⎯⎯⎯⎯⎯⎯⎯→ K =  Here, A, B and C all are optically active compounds. If the optical rotations of A, B and C per unit concentration are 60°, −72° and 42°, respectively, and the initial concentration of A is 2 M, then (1) the solution will be optically active and dextrorotatory after very long time. (2) the solution will be optically active and laevorotatory after very long time. (3) half-life for overall reaction of A is 15 minutes. (4) after 75% conversion of A into B and C, the optical rotation of solution will be 36°. 18. For the reversible reaction A! B; ΔH = −2 kcal, the pre-exponential factors are same for the forward and backward reactions. If the activation energy of backward reaction is 8 kcal/mol, then which of the following statement is correct about the reaction? (1) The activation energy of forward reaction is 6 kcal/mol. (2) At 500 K, the fraction of ‘A’ molecules crossing the energy barrier for forward reaction is e−6 . (3) At 500 K, the fraction of ‘B’ molecules crossing the energy barrier for forward reaction is e−8 . (4) Equilibrium constant for the reaction is e−2 at 500 K. Integer Type Questions – Single Digit (0–9) 19. Hydrogen peroxide in aqueous solution decomposes by a first-order reaction to water and oxygen. The rate constant for this decomposition is 7.50 × 10−4 s −1 . What quantity of heat (in J) is initially liberated per second from 2.0 L of solution that is 0.02 M of H2O2? Given Δf H of H2O2(l) = −187.0 kJ/mol and Δf H H2O(l) = − 287.0 kJ/mol. 20. An optically active drug has one chiral centre and only dextrorotatory isomer is effective. Moreover, it becomes ineffective when its optical activity is reduced to 40% of the original. It was found that mutarotation of this drug was first-order reaction with rate constant 4.5 3.1536 × 10−8 s −1 . The expiration time of the drug (in years) is (ln 2 = 0.7, ln 3 = 1.1, ln 5 = 1.6) Integer Type Questions – Four Digit 21. The decomposition of benzene diazonium chloride in aqueous solution is a reaction of first order which proceeds as C6H5N2Cl → C6H5Cl + N2(g). A certain solution of benzene diazonium chloride contains initially an amount of this compound which gives 80 cm3 of nitrogen on complete decomposition. It is found that at 30°C, 40 cm3 of nitrogen are evolved in 40 minutes. How long (in min) after the start of the decomposition, will 70 cm3 of nitrogen have been evolved?
4 22. The decomposition of a compound ‘P’ at temperature T, according to the following equation 2P(g) → 4Q(g) + R(g) + S(l) is a first-order reaction. After 30 minutes, from the start of the decomposition in a closed vessel, the total pressure developed is found to be 445 mm and after a long time, the total pressure is 625 mm. The vapour pressure of S(l) at this temperature is 25 mm. The total pressure after 60 minutes is 23. The gas phase decomposition of dimethyl ether follows first-order kinetics. CH3−O−CH3 → CH4 (g) + H2 (g) + CO (g) The reaction is carried out in a constant volume container at 500°C and has a half-life of 14.5 minutes. Initially, only dimethyl ether is present at a pressure of 4.0 atmosphere. What is the total pressure of the system (in atm) after 43.5 minutes? Assume ideal gas behaviour.