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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

ConceptIonization of Acids and Bases Common Ion Effect in the Ionization of Acids and Bases

#### 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

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

Is there an error in this question or solution?

#### APPEARS IN

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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