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")`
For the reaction `I_(2)+2S_(2)O_(3)^(2-) rarr S_(4)O_(6)^(2-) + 2I^(ɵ)`
I. `(-d[I_(2)])/(dt) = -(1)/(2) (d[S_(2)O_(3)^(2-)])/(dt)`
II. `(-d[I_(2)])/(dt) = -2 (d[S_(2)O_(3)^(2-)])/(dt)`
III. `(-d[I_(2)])/(dt) = -2 (d[I^(ɵ)])/(dt) xx (d[S_(2)O_(3)^(2-)])/(dt)`
IV. `(d[S_(4)O_(6)^(2-)])/(dt) = (1)/(2)(d[I^(ɵ)])/(dt)`
The correct option is

Options

A. Only I
B. I and IV
C. II and IV
D. Only III

Answer

B

Explanation

`I_(2)+2S_(2)O_(3)^(2-) rarr S_(4)O_(6)^(2-) + 2I^(ɵ)`
Rate `= (-d[I_(2)])/(dt) = (-d[S_(2)O_(3)^(2-)])/(2dt)`
`= (+d[S_(4)O_(6)^(2-)])/(dt) = = (+d[I^(ɵ)])/(2dt)`
Hence, correct options are I and IV.