1.

For a general nth order reaction A to P with initial concentration of the reactant 'a' and rate constant 'k', derive expression for time for 75% completion of the reaction in terms of a, n and k.

Answer»

Solution :For REACTIONS of 2nd order, `k=(1)/(t)[(1)/(C_(t))-(1)/(C_(0))]`
For reactions of 3RD order, `k=(1)/(2t)[(1)/(C_(t)^(2))-(1)/(C_(0)^(2))]`
For reaction of nth order, `t=(1)/((n-1)k)[(1)/(C_(t)^(n-1))-(1)/(C_(0)^(n-1))]`
When `75%` of the reaction is COMPLETE,
`C_(t)=25%" or "C_(0)=(1)/(4)C_(0)`
REPLACING `C_(0)` by a,
`t_(75%)=(1)/((n-1)k)[(1)/((a//4)^(n-1))-(1)/(a^(n-1))]=(1)/((n-1)k)[(4^(n-1))/(a^(n-1))-(1)/(a^(n-1))]=(1)/((n-1)k)[(2^(2n-2)-1)/(a^(n-1))]`


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