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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.
CH_{3} O CH_{3}(g) → CH_{4}(g) + H_{2}(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 preexponential 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 (k_{1}) at 300 K
(iii) Determination of energy of activation :Rate constant (k_{2}) at 320 K
(iv) Determination of the preexponential factor
16. One of the hazards of nuclear explosion is the generation of ^{90}Sr and its subsequent incorporation in bones. This nuclide has a halflife of 28.1 years. Suppose one microgram was absorbed by a newborn child, how much ^{90}Sr will remain in his bones after 20 years? (1995  2 Marks)
Solution:
17. At 380°C, the halflife period for the first order decomposition of H_{2}O_{2} 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, k_{723} K =6.81 ×10–2 min–1
Calculation of time for 75% decomposition at 723 K
Let the initial amount of H_{2}O_{2}, a = 1
∴ Amount at the required time, (a – x) = 0.25
Substituting the values in the given relation,
18. ^{227}Ac has a halflife of 21.8 years with respect to radioactive decay. The decay follows two parallel paths. one leading to ^{227}Th and the other to ^{223}Fr. 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 NH_{3} and H_{2}O at 25°C is 3.4×10^{10} L mol^{–1}s^{–1}. Calculate the rate constant for proton transfer from water to NH_{3}. (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 halflife 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,
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