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Q.

For the 1^st order reaction $A \to B + C,$ carried out at 27⁰C, If $3.8 \times 10^{- 16} %$ of the reactant molecules exist in the activated state, the activation energy (Ea) of reaction is

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a

84.5kJ/mol

b

831.4kJ/mol

c

100kJ/mol

d

120kJ/mol

answer is C.

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Detailed Solution

$e^{- E a / R T} = \frac{3.8 \times 10^{- 16}}{100} = 3.8 \times 10^{- 18}$

$- E a / R T = I n (3.8 \times 10^{- 18}) = 2.303 \log (3.8 \times 10^{- 18})$

$- E a = 2.303 \times 8.314 \times 300 \times \log (3.8 \times 10^{- 18})$

$E a = 100 k J / m o l .$

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For the 1st order reaction A→B+C, carried out at 270C, If 3.8×10−16% of the reactant molecules exist in the activated state, the activation energy (Ea) of reaction is