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Determine the Solubilities of Silver Chromate, Barium Chromate, Ferric Hydroxide, Lead Chloride and Mercurous Iodide at 298k from Their Solubility Product Constants Given in Table 7.9 (Page 221). Determine Also the Molarities of Individual Ions - CBSE (Science) Class 11 - Chemistry

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Question

Determine the solubilities of silver chromate, barium chromate, ferric hydroxide, lead chloride and mercurous iodide at 298K from their solubility product constants given in Table 7.9 (page 221). Determine also the molarities of individual ions

Solution

(1) Silver chromate:

`Ag_2CrO_4 -> 2Ag^+ CrO_4^(2-)`

then

`K_(sp) = [Ag^+]^2[CrO_4^(2-)]`

Let the solubility of `Ag_2CrO_4` be s.

=> [Ag^+] 2s " and "  `[CrO_4^(2-)] = s`

Then

`K_(sp) = (2s)^2 s = 4s^3`

`=> 1.1 xx 10^(-12) = 4s^3`

`:.275 xx 10^(-12) = s^3`

`s = 0.65 xx 10^(-4) M`

Molarity of `Ag^+`= 2s = 2 × 0.65 × 10–4 = 1.30 × 10–4 M

Molarity of `CrO_4^(2-)`= s = 0.65 × 10–4 M

(2) Barium chromate:

`BaCr_4 -> Ba^(2+) + CrO_4^(2-)`

Then `K_(sp) = [Ba^(2+)][CrO_4^(2-)]`

Let s be the solubility of `BaCrO_(4+)`

Thus [Ba^(2+)] = s  and `[CrO_4^(2-)] = s`

`=> K_(SP) = s^2`

`=> 1.2 xx 10^(-10) = s^2`

`=>s = 1.09 xx 10^(-5) M`

Molarity of `Ba^(2+)`= Molarity of `CrO_4^(2-) = s = 1.09 xx 10^(-5) M` 

(3) Ferric hydroxide:

`Fe(OH)_3 -> Fe^(2+) + 3OH^(-)`

`K_(sp) = [Fe^(2+)] [OH^(-)]^3`

Let s be the solubility of  `Fe(OH)_3`

Thus `[Fe^(3+)]` = s and `[OH^-] = 3s`

`=> K_(sp) = s.(3s)^3`

`= s.27 s^3`

`K_(sp) =  27s^4`    

`1.0 xx 10^(-38 ) = 27 s^4`

`.037 xx 10^(-38) = s^4`

`.00037 xx 10^(-36) = s^4` ` => 1.39 xx  10^(-10) M = S`

Molarity of  `Fe^(3+) = s = 1.39 xx 10^(-10) M`

Molarity of` OH^(-) = 3s = 4.17 xx 10^(-10) M`

(4) Lead chloride:

`PbCl_2 -> Pb^(2+) + 2Cl^(-)`

`K_(SP) = [Pb^(2+)][Cl^-]^2`

Let KSP be the solubility of `PbCl_2`

`[PB^(2+)] = s and [Cl^(-)] = 2s`

Thus `K_(sp) = s.(2s)^2`

`= 4s^3`

`=> 1.6 xx 10^(-5) = 4s^3`

`=> 0.4 xx 10^(-5) = s^3`

`4xx10^(-6) = s^3 => 1.58 xx 10^(-2) M = S.1`

Molarity of `PB^(2+) = s = 1.58 xx 10^(-2) M`

Molarity of chloride =2s = `3.16 xx 10^(-2) M`

(5) Mercurous iodide:

`Hg_2I_2 -> Hg^(2+) + 2I^(-)`

`K_(sp) = [Hg_2^(2+)]^(2)[I^(-)]^2`

Let s be the solubility of `Hg_2I_2`

`=> [Hg_2^(2+)]` = s and `[I^(-)] =  2s`

Thus `K_(sp) = s(2s)^2 => K_(sp) = 4s^3`

`4.5 xx 10^(-29) = 4s^3`

`1.125 xx 10^(-29) = s^3`

`=>  s = 2.24 xx 10^(-10) M`

Molarity of  `Hg_2^(2+) = s = 2.24 xx  10^(-10)    M`

Molarity of `I^(-) = 2s = 4.48 xx 10^(-10) M`

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Solution Determine the Solubilities of Silver Chromate, Barium Chromate, Ferric Hydroxide, Lead Chloride and Mercurous Iodide at 298k from Their Solubility Product Constants Given in Table 7.9 (Page 221). Determine Also the Molarities of Individual Ions Concept: Ionization of Acids and Bases - Common Ion Effect in the Ionization of Acids and Bases.
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