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151. 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 present of 0.40 atmosphere. What is the total pressure of the system after 12 minutes?
(Assume ideal gas behaviour).

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152. The half-life for radioactive decay of

14_{C}

is 5730 years. An archaeological artifact containing wood had only 80% of the

{}^{14}C

activity found in living tree. Estimate the age of the sample or calculate the age of the artefact.

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153. During nuclear explosion, one of the products is ⁹⁰Sr with half-life of 28.1 Years. If 1 μg of ⁹⁰Sr was absorbed in the bones of a newly born baby instead of calcium, how much of it will remain after 10 years and 60 years if it is not lost metabolically.

All radioactive decay are first order process.

∴

decay constant.

λ = \frac{0.693}{t_{1 / 2}} = \frac{0.693}{28.1} = 0.0247 {year}^{- 1}

(i) where t = 10 years,

λ = \frac{2.303}{t} \log \frac{N_{0}}{N} t = 10 years N_{0} = 1 microgram = 1 \times 10^{- 6} g, N = ? 10 = \frac{2.303}{0.0247} \log \frac{1 \times 10^{- 6}}{N}

\log \frac{1 \times 10^{- 6}}{N} = \frac{10 \times 0.0247}{2.303} = 0.1072 \frac{1 \times 10^{- 6}}{N} = Antilog 0.1072 = 1.1280 N = \frac{1 \times 10^{- 6}}{1.1280} = 0.7842 \log

(ii)

t = 60 years 60 = \frac{2.303}{0.0247} \log \frac{1 \times 10^{- 6}}{N} \log \frac{1 \times 10^{- 6}}{N} = \frac{60 \times 0.0247}{2.303} = 0.6435 \frac{1 \times 10^{- 6}}{N} = \frac{60 \times 0.0247}{2.303} = 0.6435 \frac{1 \times 10^{- 6}}{N} = Antilog 0.6453 = 4.400 N = \frac{1 \times 10^{- 6}}{4.400} = 0.227 μg

Thus, after 10 years and 60 years, 0.7842 log and 0.227 log of ⁹⁰Sr will be left as undecayed.

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Short Answer Type

154. A first order decomposition reaction takes 40 minutes for 30% of decomposition. Calculate t_1/2 value for it.

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Long Answer Type

155. For first order reaction show that time required for 99% completion is twice the time required for the completion of 90% of reaction.

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Short Answer Type

156. A first order reaction has a specific reaction rate of 2.31 x 10^–3 sec^–1. Calculate the half-life period of the reaction.

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157. The difference in energy of activation for uncatalysed reaction and catalysed reaction is 20 kJ/mol. How many times the rate constant of catalysed reaction will increase over the uncatalysed reaction?

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158. Show that the time required for the completion of 3/4th reaction of first order is twice the time required for completion of 1/2 of the reaction.

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159. If half-life of a first order reaction involving reactant A is 5 min. How long will it take [A] to react 25% of its initial concentration?

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160. A first order reaction is 15% complete in 20 minutes. How long will it take to be 60% completed ?

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Previous Year Papers

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Long Answer Type

153. During nuclear explosion, one of the products is 90Sr with half-life of 28.1 Years. If 1 μg of 90Sr was absorbed in the bones of a newly born baby instead of calcium, how much of it will remain after 10 years and 60 years if it is not lost metabolically.

Short Answer Type

Long Answer Type

Short Answer Type

153. During nuclear explosion, one of the products is ⁹⁰Sr with half-life of 28.1 Years. If 1 μg of ⁹⁰Sr was absorbed in the bones of a newly born baby instead of calcium, how much of it will remain after 10 years and 60 years if it is not lost metabolically.