Question

Equivalent weight of $C{{r}_{2}}O_{7}^{2-}$ (molecular weight = M) in the following reaction is: \[\text{C}{{\text{r}}_{\text{2}}}\text{O}_{\text{7}}^{\text{2-}}\,\text{+}\,\text{6}{{\text{I}}^{\text{-}\,}}\text{+}\,\text{14}{{\text{H}}^{+}}\to \,\text{2C}{{\text{r}}^{\text{3+}}}\,\text{+}\,\text{3}{{\text{I}}_{\text{2}}}\,\text{+}\,\text{7}{{\text{H}}_{\text{2}}}\text{O}\]

Answer 1

Hint: The equivalent weight of a substance is the number of parts by weight of the substance that combines displaces directly or indirectly 8 parts of weight of oxygen and 108 parts by silver.

Complete Solution :
Equivalent weight is the amount of substance displaced or liberated by passing 96500C of electricity. Two or more elements combined or displaced in the mass ratio equal to the ratio of its equivalent weight. Equivalent weight of an element may vary with the variation of its valence.
- In a redox reaction equivalent weight of any atom \[\text{=}\dfrac{\text{molar}\,\text{weight}}{\text{change}\,\text{in}\,\text{the}\,\text{oxidation}\,\text{number}}\]
- In the above reaction in$C{{r}_{2}}O_{7}^{2-}$, \[\,\text{Cr}\] atom have its maximum oxidation state, so \[\,\text{Cr}\]atom can only gain electron and it acts an oxidizing agent. It receives electrons from \[{{\text{I}}_{\text{2}}}\] which are present in its minimum oxidation state and get reduced. For one \[\,\text{Cr}\] atom there is a change of 3e-and for two atoms this change will be 6e-. So in this redox reaction\[\,\text{Cr}\] atom acts as an oxidizing agent while \[{{\text{I}}_{\text{2}}}\] acts as a reducing agent.
                                    \[\text{equivalent}\,\text{weight}\,\text{of}\,\text{an}\,\text{oxydent}\,\,\text{=}\,\,\dfrac{\text{molar}\,\text{weight}}{\text{number}\,\text{of}\,\text{electron}\,\text{gained}\,\text{by}\,per\,molecule}\]
In this reaction\[\,\text{Cr}\] atoms act as an oxidant and get reduced. \[\,\text{Cr}\]Atom oxidation state changes from +6 to +3.
- So equivalent of $C{{r}_{2}}O_{7}^{2-}$ = \[\dfrac{\text{molar}\,\text{weight of C}{{\text{r}}_{\text{2}}}\text{O}_{\text{7}}^{\text{2-}}}{\text{3 }\!\!\times\!\!\text{ 2}}\,\text{=}\,\dfrac{\text{M}}{\text{6}}\]

Note: An oxidizing agent oxidized the chemical reaction but it gets reduced, however a reducing agent reduces the chemical reaction and increases its oxidation state.
\[\text{equivalent}\,\text{weight}\,\text{of}\,\text{an}\,reducing\,\,agen\text{t}\,\,\text{=}\,\,\dfrac{\text{molar}\,\text{weight}}{\text{number}\,\text{of}\,\text{electron}\,\text{gained}\,\text{by}\,per\,molecule}\]