1.

Derive the expression for integrated rate law(equation) for the first order reaction.

Answer»

Solution :CONSIDER the FOLLOWING first order reaction, A`to` B.
The rate of the chemical reaction is given by the rate lawexpression as,
Rate R = K [A] where [A] is the concentration of the reactant A and k is the velocity constant or specific rate of the reaction.
The instantaneous rate is given by,
`R = k[A] = (-d[A])/(dt)`
` (-d[A])/([A]) = k.dt`
If `[A_(0)]` is the INITIAL concentration of the reactant and `[A]_(t)` at TIME t. then by integrating the above equation,
`-underset([A_(0)])overset([A]_(t))int (d[A])/([A]) = k underset(0)overset(t)int dt`
` therefore- log_(e).([A_(0)])/([A]_(t)) = kt ""thereforelog_(e).([A_(0)])/([A]_(t)) = kt`
`therefore k = (1)/(t) log_(e).([A_(0)])/([A]_(t)) ""thereforek = (2.303)/(t) log_(10).([A_(0)])/([A]_(t))`
Thisis theintegranted rateequationfor the firstorderreaction .
Thisis also calledintegrated rate law.


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