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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 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 (k_{1}) at 300 K**(iii) **Determination of energy of activation :Rate constant (k_{2}) at 320 K**(iv) **Determination of the pre-exponential 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 half-life of 28.1 years. Suppose one microgram was absorbed by a new-born child, how much ^{90}Sr 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 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 half-life 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 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,

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