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Question

# In Arrhenius's equation for a certain reaction, the value of A and E (activation energy) are 4×1013 s−1 and 92.12 kJ mol−1 respectively. If the reaction is of first order, at what temperature will its half-life period be 11.55 minutes?Take R=8 J mol−1K−1 andlog2=0.3)

A
301.2
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B
301.20
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C
301.21
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Solution

## Arrhenius’s equation represented as: k=Ae−E/RT lnk=lnA−ERT 2.303logk=2.303logA−ERT ⇒logk=logA−E2.303RT..........(1) Given that A=4×1013 s−1;E=92.12 kJ mol−1; t1/2=11.55×60 s;R=8×10−3 kJ mol−1K−1 For first-order reaction k=0.693t1/2=0.693693s−1 ⇒k=10−3 s−1 From equation (1) T=E2.303×R(logA−logk) T=92.122.303×8×10−3[log(4×1013)−log(10−3)] T=92.122.303×8×10−3[2log(2)+13log10)+3log(10)] ∴T=301.2 K.

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