For a second order reaction, `2Ararr` Products, a plot of log `t_(1//2)` vs log a (where a is initial concentration) will give an intercept equal to which one of the following?

Options

A. `1//k`
B. `log(1//2" k")`
C. `log (1//k)`
D. `log k`

Answer

D

Explanation

For a second order reaction, `2A to ` products,
`k= (1)/(t)[(1)/([A])-(1)/([A]_(0))]`
When `t = t_(1//2), [A] = ([A]_(0))/(2)`
Hence, `t_(1//2) = (1)/(k)[(2)/([A]_(0))-(1)/([A]_(0))] = (1)/(k[A]_(0))`
`therefore log t_(1//2) = - log k - log [A]_(0) =- log k - log a`
Plot of log `t_(1//2)` vs log a will be linear with intercept = log k.