Assertion : For the reaction:- 

$2{\mathrm{I}}^{-}+{\mathrm{S}}_2{\mathrm{O}}_8^{2-}⟶{\mathrm{I}}_2+2{\mathrm{SO}}_4^{2-},\mathrm{Fe}\left(\mathrm{III}\right)$ catalyst is used 

Reason : $2{\mathrm{Fe}}^{3+}+2{\mathrm{I}}^{-}\to 2{\mathrm{Fe}}^{2+}+{\mathrm{I}}_2$

$2{\mathrm{Fe}}^{2+}+{\mathrm{S}}_2{\mathrm{O}}_8^{2-}⟶2{\mathrm{Fe}}^{3+}+2{\mathrm{SO}}_4^{2-}$

The reaction takes place as,

$\begin{array}{l}2{\mathrm{Fe}}^{+3}+2{\mathrm{I}}^{-}\to 2{\mathrm{Fe}}^{+2}+{\mathrm{I}}_2\\ 2{\mathrm{Fe}}^{+2}+{\mathrm{S}}_2{\mathrm{O}}_8^{2-}\to 2{\mathrm{Fe}}^{+3}+2{\mathrm{SO}}_4^{2-}\end{array}$

Here, F(iii) catalyst is used.

Also,

$2{\mathrm{Fe}}^{3+}+2{\mathrm{I}}^{-}\to 2{\mathrm{Fe}}^{2+}+{\mathrm{I}}_2$

$2{\mathrm{Fe}}^{2+}+{\mathrm{S}}_2{\mathrm{O}}_8^{2-}\to 2{\mathrm{Fe}}^{3+}+2{\mathrm{SO}}_4^{2-}$

Thus, both assertion and reason are correct.