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Question
Derive an expression to calculate time required for completion of zero order reaction.
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Solution
Consider a reaction,
R → Pt = 0
Here R is the reactant and P is the product.
Rate = k[R]0 t = t
`(–dR)/dt` = k , dR = – kdt .....(Instantaneous rate)
On integrating both sides,
`intDr = -k intdt`
[R] = – kt + I
At t = 0,
[R] = [R0] which makes I = R0[R] = [R0] – kt. .......(i)
Here [R] = concentration of reactant at time ‘t’.
[R0] = initial concentration of the reactant.
This reaction is known as the integrated rate equation of zero order.
After completion of zero order reaction [R] = 0
Using [R] = 0 in (i)
[R0] = kt
∴ t = `([R_0])/k`
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