Subjective Type Questions: Chemical Kinetics & Nuclear Chemistry- 2 | JEE Advanced | 35 Years Chapter wise Previous Year Solved Papers for JEE PDF Download

11. The nucleidic ratio,    in a sample of water is 8.0 × 10^–18 : 1. Tritium undergoes decay with a half life period of 12.3 years. How many tritium atoms would 10.0 g of such a sample contain 40 years after the original sample is collected?             (1992 - 4 Marks)

Solution: 

No. of atoms left after 40 years are derived as follows using the relation

12. A first order reaction A→ B , requires activation energy of 70kJ mol^–1. When a 20% solution of A was kept at 25°C for 20 minutes, 25% decomposition took place. What will be the percent decomposition in the same time in a 30% solution maintained at 40°C? Assume that activation energy remains constant in this range of temperature. (1993 - 4 Marks)

Solution: 

13. The gas phase decomposition of dimethyl ether follows first order kinetics.
   CH₃ -O- CH₃(g) → 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 0.40 atmosphere.
What is the total pressure of the system after 12 minutes? Assume ideal gas behaviour.             (1993 - 4 Marks)

Solution: 

Since volume and temp. are constant, final pressure :

Hence total pressure = 0.4 – 0.175 + 3 × 0.175 = 0.749 atm

14. The progress of the reaction, A      nB  with time, is presented in figure given below. Determine 

(i) the value of n
(ii) the equilibrium constant, K and
(iii) the initial rate of conversion of A.             (1994 - 3 Marks)

Solution: 

(i) According to Fig. in the given time of 4 hours (1 to 5) concentration of A falls from 0.5 to 0.3 M, while in the same time concentration of B increases from 0.2 M to

0.6 M.

Decrease in concentration of A in 4 hours

= 0.5 – 0.3 = 0.2 M

Increase in concentration of B in 4 hours

= 0.6 – 0.2 = 0.4 M

Thus increase in concentration of B in a given time is twice the decrease in concentration of A. Thus n = 2.

15. From the following data for the reaction between A and B.                (1994 - 5 Marks)

Calculate
   (i) the order of the reaction with respect to A and with
   respect to B,
   (ii) the rate constant at 300K
   (iii) the energy of activation, and
   (iv) the pre-exponential factor

Solution:

Let the order with respect to A is x and the order with respect to B is y

 
∴ The rate equation for the reaction is

Rate = k [A]²[B]

(i) Thus order of reaction with respect to A = 2 and order of reaction with respect to B = 1.

(ii) Rate constant (k₁) at 300 K

(iii) Determination of energy of activation :Rate constant (k₂) at 320 K


(iv) Determination of the pre-exponential factor

16. One of the hazards of nuclear explosion is the generation of ⁹⁰Sr and its subsequent incorporation in bones. This nuclide has a half-life of 28.1 years. Suppose one microgram was absorbed by a new-born child, how much ⁹⁰Sr will remain in his bones after 20 years?                (1995 - 2 Marks)

Solution: 

17. At 380°C, the half-life period for the first order decomposition of H₂O₂ is 360 min. The energy of activation of the reaction is 200 kJ mol^-1 . Calculate the time required for 75% decomposition at 450°C.                    (1995 - 4 Marks)

Solution:
 

On usual calculations, k₇₂₃ K =6.81 ×10–2 min–1

Calculation of time for 75% decomposition at 723 K

Let the initial amount of H₂O₂, a = 1

∴ Amount at the required time, (a – x) = 0.25

Substituting the values in the given relation,

18. ²²⁷Ac has a half-life of 21.8 years with respect to radioactive decay. The decay follows two parallel paths. one leading to ²²⁷Th and the other to ²²³Fr. The percentage yields of these two daughter nuclides are 1.2 and 98.8 respectively. What are the decay constants (l) for each of the separate paths?            (1996 - 2 Marks)

Solution: 

19. The ionisation constant of   in water is 5.6×10^–10 at 25°C. The rate constant for the reaction of  and OH^- to form NH₃ and H₂O at 25°C is 3.4×10¹⁰ L mol^–1s^–1. Calculate the rate constant for proton transfer from water to NH₃.            (1996 - 3 Marks)

Solution: 

20. The rate constant for the first order decomposition of a certain reaction is described by the equation

              (1997 - 5 Marks)

(i) What is the energy of activation for this reaction?
(ii) At what temperature will its half-life period be 256 minutes?

Solution: 
(i) The Arrhenius equation is

k = A exp (–E_a/RT)

Taking natural logarithm, we get

ln k = ln A – E_a/RT

(ii) The reaction is first order as the unit of rate constant is s^–1. For a first order reaction,