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Derive a relation between t_(1//2) and temperature for an n^(th) order reaction where n gt 2? |
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Answer» Solution :`lnk=lnA-(E_(a))/(RT)` (ARRHENIUS equation) ………………….`(i)` `t_(1//2)=((2^(n-1)-1))/(K(n-1)a_(0)^(n-1))`……………….`(II)` `ln(t_(1//2))=ln.(2^(n-1)-1)/((n-1)a_(0)^(n-1))-lnk` ……………….`(iii)` From the Eqs. `(i)` and `(iii)` `ln(t_(1//2))=ln.(2^(n-1)-1)/((n-1)a_(0)^(n-1))-lnA+(E_(a))/(RT)` `impliesln(t_(1//2))=lnA.+(E_(a))/(RT)` where `A.=(2^(n-1)-1)/((n-1)a_(0)^(n-1)xxA)` That is `t_(1//2)` decreases with increases in temperture. A PLOT of `t_(1//2)` vs `(1)/(T)` GIVES a straight line with slope `E_(a)`. |
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