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Question: Equivalent weight of \(C{{r}_{2}}O_{7}^{2-}\) (molecular weight = M) in the following reaction is: \...

Equivalent weight of Cr2O72−C{{r}_{2}}O_{7}^{2-} (molecular weight = M) in the following reaction is: Cr2O72- + 6I- + 14H+→ 2Cr3+ + 3I2 + 7H2O\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}

Explanation

Solution

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 =molar weightchange in the oxidation number\text{=}\dfrac{\text{molar}\,\text{weight}}{\text{change}\,\text{in}\,\text{the}\,\text{oxidation}\,\text{number}}
- In the above reaction inCr2O72−C{{r}_{2}}O_{7}^{2-},  Cr\,\text{Cr} atom have its maximum oxidation state, so  Cr\,\text{Cr}atom can only gain electron and it acts an oxidizing agent. It receives electrons from I2{{\text{I}}_{\text{2}}} which are present in its minimum oxidation state and get reduced. For one  Cr\,\text{Cr} atom there is a change of 3e-and for two atoms this change will be 6e-. So in this redox reaction Cr\,\text{Cr} atom acts as an oxidizing agent while I2{{\text{I}}_{\text{2}}} acts as a reducing agent.
equivalent weight of an oxydent  =  molar weightnumber of electron gained by per molecule\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 Cr\,\text{Cr} atoms act as an oxidant and get reduced.  Cr\,\text{Cr}Atom oxidation state changes from +6 to +3.
- So equivalent of Cr2O72−C{{r}_{2}}O_{7}^{2-} = molar weight of Cr2O72-3 !!×!! 2 = M6\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.
equivalent weight of an reducing  agent  =  molar weightnumber of electron gained by per molecule\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}