Chemical Kinetics - Result Question 75
74. In Arrhenius equation for a certain reaction, the value of $A$ and $E _a$ (activation energy) are $4 \times 10^{13}$ $ s^{-1}$ and $98.6$ $ kJ $ $mol^{-1}$ respectively. If the reaction is of first order, at what temperature will its half-life period be $10$ $ min$ ?
(1990, 3M)
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Answer:
Correct Answer: 74. $(311.34$ $ K)$
Solution:
- Arrhenius equation is :
$\log k=\log A-\dfrac{E _a}{2.303 R T} $
$\text { when } t _{1 / 2}=10 min, k =\dfrac{\ln 2}{t _{1 / 2}}=\dfrac{0.693}{10 \times 60}=1.115 \times 10^{-3} s^{-1} $
$\Rightarrow \quad \dfrac{E _a}{2.303 R T} =\log A-\log k $
$ = \quad \log \dfrac{A}{k}=\log \dfrac{4 \times 10^{13}}{1.115 \times 10^{-3}}=16.54 $
$\Rightarrow \quad T=\dfrac{E _a}{2.303 R \times 16.54} =\dfrac{98.6 \times 1000}{2.303 \times 16.54 \times 8.314} $
$ = \quad 311.34 K$
BETA
