Q19.80P - Chemistry: Molecular Nature Of Matter And Change

Question

Which compound in each pair is more soluble in water? 

(a) Barium sulphate or calcium sulphate 

(b) Calcium phosphate or magnesium phosphate 

(c) Silver chloride or lead (II) sulfate

Step-by-Step Solution

Answer

(a) Calcium sulfate is more soluble in water than Barium sulfate.

(b) Magnesium phosphate is more soluble in water than Calcium phosphate.

(c) Lead (II) sulfate is more soluble in water than Silver chloride.

Introduction

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

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

 Solid and liquid state is not included in the K_sp equations.

 ${\mathbf{\text{K}}}_{\mathbf{\text{sp}}}{\mathbf{\text{ = [M}}}^{\mathbf{\text{2 + }}}{\mathbf{\text{][X}}}^{\mathbf{\text{ - }}}{\mathbf{\text{]}}}^{\mathbf{\text{2}}}$

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

The salt with more K_sp value will be dissolved more.

Subpart (a)

To compare the solubility of each compound, just compare their   K_sp values.

The K_sp value of Barium Sulphate ${\text{BaSO}}_4$ is –

 ${\mathrm{K}}_{\mathrm{sp}}=1.1\times {10}^{-10}$

The K_sp value of Calcium Sulphate ${\text{CaSO}}_4$ is –

 ${\mathrm{K}}_{\mathrm{sp}}=2.4\times {10}^{-5}$

It can be observed that the K_sp of ${\text{CaSO}}_4\text{ > }$K_sp of ${\text{BaSO}}_4$. 

Therefore,  ${\text{CaSO}}_4$ is more soluble in water.

Subpart (b)

To compare the solubility of each compound, just compare their   K_sp values.

The K_sp value of Calcium Phosphate ${\text{Ca}}_{\text{3}}{\text{(PO}}_{\text{4}}{\text{)}}_{\text{2}}$ is –

 ${\mathrm{K}}_{\mathrm{sp}}=1.2\times {10}^{-29}$

The K_sp value of Magnesium Phosphate ${\text{Mg}}_{\text{3}}{\text{(PO}}_{\text{4}}{\text{)}}_{\text{2}}$ is –

 $K_{sp}=5.2\times {10}^{-24}$

It can be observed that the K_sp of ${\text{Mg}}_{\text{3}}{\text{(PO}}_{\text{4}}{\text{)}}_{\text{2}}$ >  K_sp of ${\text{Ca}}_{\text{3}}{\text{(PO}}_{\text{4}}{\text{)}}_{\text{2}}$. 

 

Therefore, ${\text{Mg}}_{\text{3}}{\text{(PO}}_{\text{4}}{\text{)}}_{\text{2}}$  is more soluble in water.

 

Subpart (c)

To compare the solubility of each compound, just compare their   K_sp values.

The K_sp    value of Silver Chloride $\mathrm{AgCl}$ is –

 ${\mathrm{K}}_{\mathrm{sp}}=1.8\times {10}^{-10}$

The K_sp    value of Lead sulphate ${\text{PbSO}}_{\text{4}}$ is –

 ${\mathrm{K}}_{\mathrm{sp}}=1.6\times {10}^{-8}$

It can be observed that the K_sp of  ${\text{PbSO}}_{\text{4}}$ >  K_sp of $\mathrm{AgCl}$.

 

Therefore, ${\text{PbSO}}_{\text{4}}$ is more soluble in water.