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A 50 mL sample of hard water containing ...

A 50 mL sample of hard water containing `Ca^(2+)` and `Mg^(2+)` ions is titrated with 50 mL 0.005 M EDTA solution at `pH=10`, using eriochrome black-T indicator to reach equivalence point.
In an equal another amount of hard water sample, `Mg^(2+)` ions are precipitated as `Mg(OH)_2` by adding suitable amount of NaOH. The solution after precipitation of `Mg(OH)_2`, is stirred and then titrated with EDTA solution using calcon as indicator, and it requires 10 " mL of " above EDTA solution to reach equivalence point.
(a). Calculate the strength of `Ca^(2+)` and `Mg^(2+)` ions present in hard water.
(b). Calculate the hardness due to `Ca(2+)` ions in ppm of `CaCO_3`.
(c). Calculate the hardness due to `Mg^(2+)` ions in ppm of `CaCO_3`.
(d) Calculate the total hardness of water in ppm of `CaCO_3`.

Text Solution

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(a) Case I: Using eriochrome black-`T` indicator
`M_(1)V_(1)(EDTA)=M_(2)V_(2)(Ca^(2+)` and `Mg^(2+)` in hard water)
`50xx0.005=M_(2)xx50`
`M_(2)` of `(Ca^(2+)` and `Mg^(2+))=0.005 M=5m` moles `L^(-1)`
Case II: Using calcon indicator
`M_(1)V_(1)(EDTA)=M_(2)V_(2)H_(2)O`
`Ca^(2+)=10^(-3) M=1.0 m mol L^(-1)`
`M mol L^(-1)` of `Mg^(2+)=5-1=4 m mol L^(-1)` ltbRgt Strength of `Mg^(2+)=4xx24xx10^(-3)=.096 g L^(-1)`
Strength of `Ca^(2+)=1xx40xx10^(-3)=0.04 gL^(-1)`
(b) Hardness of `Ca^(2+)`ions of the sample in gram of `CaCO_(3)` in `10^(6) mL of H_(2)O`
`=(M(Ca^(2+)xxMW(CaCO_(3))xx10^(6)))/(10^(3))=100 p p m`
Hardness due to `Mg^(2+)` ions of the sample in grams of `CaCO_(3)` in `10^(6)mL of H_(2)O=(M Mg^(2+)xxMW(CaCO_(3))xx10^(6))/(10^(3))`
`=(4xx10^(-3)xx100xx10^(6))/(10^(3))=400 p p m`
(d) Total hardness
`=(M(Ca^(2+)and Mg^(2+))xxMW(CaCO_(3))xx10^(6))/(10^(3))`
`=(5xx10^(-3)xx100xx10^(6))/(10^(3))=500 p p m`
(Alternatively, total hardness =Harndess due to `Ca^(2+)+` Hardness due to `Mg^(2+)=100+400=500 p p m`)
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