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161. 75% of a reaction of the first order was completed in 32 minutes. When was its half-life completed?

The first order reaction can be
$t = \frac{2.303}{k} \log \frac{a}{a - x} w e h a v e g i v e n t = 32 l e t a = 100 x = 75 t h u s p u t t i n g t h e v a l u e i n a b o v e e q u a t i o n 32 = \frac{2.303}{k} l o g \frac{100}{100 - 75} 32 = \frac{2.303}{k} l o g \frac{100}{25} 32 = \frac{2.303}{k} l o g 4 k = \frac{2.303}{32} l o g 4 k = 0.07196 \log 4 k = 0.07196 x 0.6020 k = 0.0433 h a l f - t i m e r e a c t i o n o f f i r s t o r d e r c a n b e g i v e n b y t_{1 / 2} = \frac{0.693}{k} t_{1 / 2} = \frac{0.693}{0.0433} = 16$

Ans. 16 minutes

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162. For the reaction A + B → 2C at a given temperature, the rate of disappearance of A is found to be 10^-² moles L^–1 sec^–1. Calculate (i) rate of disappearance of B and (ii) rate of formation of C.

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163. Calculate the half-life of the following first order reaction
C₂H₄ O₂(g) → CH₄(g) + CO₂(g)
Given the initial partial pressure of C₂H₄O₂(g) is 84 mm and the total pressure at the end of 16 min is 110 mm.

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Long Answer Type

164. For the first order reaction R → P, deduce the integrated form of the rate law. What will be the nature of the curve when concentration is plotted against time for such a reaction?

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165. State the role of activated complex in a reaction and state the relation with energy of activation.

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166. The rate law for the gas phase reaction of chlorform with chlorine.
CHCl₃(g) + Cl₂(g) → CCl ₄(g) + HCl(g)
is given by rate = k[CHCl₃] [Cl₂]^1/2. How would the rate of reaction vary when (a) the concentration of CHCl₃ is doubled (b) the concentration of Cl₂ is doubled. What is the effect of each of these two changes on the rate constant.

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