The reaction `S_(2)O_(8)^(2-) + 3I^(ɵ) rarr 2SO_(4)^(2-) + I_(3)^(ɵ)` is of first order both with respect to persulphate and iofide ions. Taking the initial concentration as `a` and `b`, respectively, and taking `x` as the concentration of the triofide at time `t`, a differential rate equation can be written.
Two suggested mechanism for the reaction are:
I. `S_(2)O_(8)^(2-)+I^(ɵ) hArr SO_(4)I^(ɵ)+SO_(4)^(2-) ("fast")`
`I^(ɵ)+SO_(4)I^(ɵ) overset(k_(1))rarrI_(2) + SO_(4)^(2-)` (show)
`I^(ɵ) + I_(2) overset(k_(2))rarr I_(3)^(ɵ) ("fast")`
II. `S_(2)O_(8)^(2-) + I^(ɵ) overset(k_(1))rarr S_(2)O_(8) I^(2-) (slow)`
`S_(2)O_(8)I^(3-) overset(k_(2))rarr2SO_(4)^(2-)+I^(o+) ("fast")`
`I^(o+) + I^(ɵ) overset(k_(3)) rarr I_(2) ("fast")`
`I_(2) + I^(o+) overset(k_(4))rarr I_(3)^(ɵ) ("fast")`
The general difference equation for the above reaction is

Options

A. `(dx)/(dt) = k[a-x][b-3x] (kgt0)`
B. `(dx)/(dt) = -k[a-x][b-3x] (kgt0)`
C. `(dx)/(dt) = k[a-x][b-x] (kgt0)`
D. `(dx)/(dt) = -k[a-x][b-x] (kgt0)`

Answer

A

Explanation

`S_(2)O_(8)^(2-) + 3I^(ɵ) underset(k)rarr 2SO_(4)^(2-) + I_(3)^(ɵ)` [Net reaction]
`{:(a,b,0,0,),(a-x,b-3x,2x,x,):}`
Rate `= k[S_(2)O_(8)^(2-)][I^(ɵ)]` [from slowest step]
`= k(a-x)(b-3x) = (-d(a-x))/(dt) = (dx)/(dt)`