Question

Which compound in each pair is more soluble in water?

(a) Magnesium hydroxide or nickel (II)hydroxide

(b) Lead (II)sulphide or copper (II)sulphide

(c) Silver sulphate or magnesium fluoride

Short answer

(a) Magnesium hydroxide is more soluble in water than Nickel(II) hydroxide.

(b)Lead (II) sulphide is more soluble in water than Copper (II) sulphide.

(c)Silver sulphate is more soluble in water than magnesium fluoride.

Step-by-step solution

Concept Introduction

Q_sp - ion-product expression; Q_spvalue is obtained when the concentrations of ions formed by dissolution of some compound are multiplied. When the solution is saturated Q_spvalue is called K_spvalue (solubility-product constant).

${\mathbf{\text{MX}}}_{\mathbf{\text{2}}}\mathbf{\to }{\mathbf{\text{M}}}^{\mathbf{\text{2 +}}}{\mathbf{\text{+ 2X}}}^{\mathbf{\text{-}}}$

The solid and liquid state is not included in the K_spequations.

role="math" localid="1663353498667" ${\mathbf{\text{K}}}_{\mathbf{\text{sp}}}{\mathbf{\text{= [M}}}^{\mathbf{\text{2 +}}}{\mathbf{\text{][X}}}^{\mathbf{\text{-}}}{\mathbf{\text{]}}}^{\mathbf{\text{2}}}$

S (Molar solubility) is equal to the concentration of one mol of the ion formed by the dissolution of some compound.

Compound More Soluble between Mg(OH)2 and role="math" localid="1663353650637" Ni(OH)2

(a)

To compare the solubility of each compound, just compare their K_spvalues.

The K_sp value of Magnesium Hydroxide $\mathrm{MgOH}{)}_2$is –

role="math" localid="1663353945373" ${\mathrm{K}}_{\mathrm{sp}}=6.3\times {10}^{-10}$

TheK_sp value of Nickel (II) Hydroxide${\text{Ni(OH)}}_{\text{2}}$ is –

role="math" localid="1663353962004" ${\mathrm{K}}_{\mathrm{sp}}=6\times {10}^{-16}$

It can be observed that the K_spof ${\text{Mg(OH)}}_{\text{2}}\text{>}$K_spof ${\text{Ni(OH)}}_{\text{2}}$.

Therefore, ${\text{Mg(OH)}}_{\text{2}}$is more soluble in water.

Compound More Soluble between PbSand CuS

(b)

To compare the solubility of each compound, just compare their K_spvalues.

The K_sp value of Lead (II) Sulphide $\mathrm{PbS}$is –

${\mathrm{K}}_{\mathrm{sp}}=3\times {10}^{-25}$

The K_sp value of Copper (II) Sulphide $\mathrm{CuS}$is –

localid="1663354607726" ${\mathrm{K}}_{\mathrm{sp}}=8\times {10}^{-34}$

It can be observed that the K_sp of $\mathrm{PbS}$> K_sp of $\mathrm{CuS}$.

Therefore, is $\mathrm{PbS}$more soluble in water.

Compound More Soluble between Ag2SO4 and MgF2

(c)

To compare the solubility of each compound, just compare their K_spvalues.

The K_sp value of Silver Sulphate ${\text{Ag}}_{\text{2}}{\text{SO}}_{\text{4}}$is –

${\mathrm{K}}_{\mathrm{sp}}=1.5\times {10}^{-5}$

The K_sp value of Magnesium Fluoride ${\text{MgF}}_{\text{2}}$is –

role="math" localid="1663355211619" ${\mathrm{K}}_{\mathrm{sp}}=7.4\times {10}^{-9}$

It can be observed that the K_sp of ${\text{Ag}}_{\text{2}}{\text{SO}}_{\text{4}}$> K_sp of ${\text{MgF}}_{\text{2}}$.

Therefore,${\text{Ag}}_{\text{2}}{\text{SO}}_{\text{4}}$ is more soluble in water.