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Calculate the rate constant and half-lif...

Calculate the rate constant and half-life period for first order reaction gaving activation energy `39.3 kcal mol^(-1)` at `300^(@)C` and the frequency constant `1.11xx10^(11) sec^(-1)`

Text Solution

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Given: `A=1.11xx10^(11) sec^(-1)`
`E_(a)=39.3xx10^(3) cal mol^(-1)`,
`R=1.987 cal`,
`T=573 K`
`:' K=Ae^(-E_(a)//RT)`
`:. ln K=ln A-E_(a)/(RT)`
or `log_(10) K=log_(10) A-E_(a)/(2.303RT)`
`log_(10) K=log_(10) 1.11xx10^(11)`
`-{(39.3xx10^(3))/(2.303xx1.987xx573)}`
`:. K=1.14xx10^(-4) sec^(-1)`
Also for first order, `t_(1//2)=0.693/K`
`=0.693/(1.14xx10^(-4))=6078 sec`
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