Question

The energy of activation for Ist order reaction is 104.5 kJ $mo{l}^{-1}$ and pre-exponential factor A in Arrhenius equation is $5\times {10}^{13}se{c}^{-1}$. The temperature at which reaction have half-life of 1 minute in K is __________.

Answer 1

$k=\frac{0.693}{t_{1/2}}=\frac{0.693}{60}$......(1)

$k=A{e}^{-E_a/RT}=5\times {10}^{13}\times e^{\frac{-104500}{8.314T}}$......(2)

From (1) and (2)

$\frac{0.693}{60}=5\times {10}^{13}\times e^{\frac{-104500}{8.314T}}$

$2.31\times {10}^{-16}=e^{\frac{-104500}{8.314T}}=e^{\frac{-12569.2}{T}}$

$ln(2.31\times {10}^{-16)}=\frac{-12569.2}{T}$

$-36=\frac{-12569.2}{T}$

$T=349K$