In a chrome plating plant, `CrO_4^(2-)` (chromate) ions are present in waste water. The chromate ions are reduced to insoluble chromium hydroxide, `Cr(OH)_3`, by dithionate ion, `S_2O_4^(2-)` in basic medium.
`CrO_4^(2-)+S_2O_4^(2-)+overset(ɵ)(O)H+H_2OtoCr_2(OH_3)+SO_3^(2-)` 10 L of water requires 522 g of `Na_2S+2O_4`. Calculate the normality and molarity of `CrO_4^(2-)` in waste water. Also express the concentration of `Na_2CrO_4` in ppm.

Explanation

`{:[undersetunderset(2x=6)(x-8=-2)(S_2O_4^(2-))toundersetunderset(2x=8)(2x-12=-4)(2SO_3^(2-))+2e^(-):}](n=2)`
`{:[undersetunderset(x=6)(x-8=-2)(CrO_4^(2-)+3e^(-))toundersetunderset(x=3)(x-3=0)(Cr(OH))]:}(n=3)`
`Mw(Na_2S_2O_4)=2xx23+2xx32+16xx4=174g` `(Ew=(174)/(2))`
`S_2O_4^(2-)-=CrO_4^(2-)`
`Eq-=Eq`
`("Weight")/("Equivalent weight")-=Eq`
`(522)/((174)/(2))-=Eq`
`therefore` 6 " Eq of "`S_2O_4^(2-)-=(6" Eq of "CrO_4^(2-))/(10L of "water")`
`-=(6)/(10)=0.6EqL^(-1)`
`therefore` Normality of `CrO_4^(2-)=0.6N`
Molarity of `CrO_4^(2-)=(N)/("n-factor")=(0.6)/(3)=0.2M`
Strength of `Na_2CrO_4=MxxMw`
`(Mw Na_2CrO_4=2xx23+52+16xx4=162g)`
`0.2xx162`
`=32.4gL^(-1)`
Concentration in ppm
`=("Weight of" Na_2CrO_4" in "1000 mL xx10^(6))/(1000mL)`
`=(32.4xx10^(6))/(10^(3))=32400p p m`