   Chapter 16, Problem 22E

Chapter
Section
Textbook Problem

# Use the following data to calculate the Ksp value for each solid.a. The solubility of Pb3(PO4) is 6.2 × 10−12 mol/L.b. The solubility of Li2CO3 is 7.4 × 10−2 mol/L.

(a)

Interpretation Introduction

Interpretation: The solubility of Pb3(PO4)2 and Li2CO3 is given. The solubility product of Pb3(PO4)2 and Li2CO3 is to be calculated.

Concept introduction: The solubility product, Ksp is the equilibrium constant that is applied when salt partially dissolve in a solvent. The solubility product of dissociation of AxBy is calculated as,

Ksp=[A]x[B]y

Explanation

Explanation

To determine: The solubility product of Pb3(PO4)2 .

The concentration of Pb2+ is 18.6×1012mol/L_ .

Given

Solubility of Pb3(PO4)2 is 6.2×1012mol/L .

Since, solid Pb3(PO4)2 is placed in contact with water. Therefore, compound present before the reaction is Pb3(PO4)2 and H2O . The dissociation reaction of Pb3(PO4)2 is,

Pb3(PO4)2(s)3Pb2+(aq)+2PO43(aq)

Since, Pb3(PO4)2 does not dissolved initially, hence,

[Pb2+]initial=[PO43]initial=0

The concentration at equilibrium can be calculated from the measured solubility of Pb3(PO4)2 . If 6.2×1012mol of Pb3(PO4)2 is dissolved in 1.0L of solution, the change in solubility will be equal to 6.2×1012mol/L . The reaction is,

Pb3(PO4)2(s)3Pb2+(aq)+2PO43(aq)

Therefore,

6.2×1012mol/LPb3(PO4)23(6.2×1012mol/L)Pb2++2(6.2×1012mol/L)PO43

The equilibrium concentration of Pb2+ is written as,

[Pb2+]=[Pb2+]initial+changetoreachequilibrium

Substitute the value of [Pb2+]initial and change to reach equilibrium in the above equation.

[Pb2+]=[Pb2+]initial+changetoreachequilibrium=0+3(6.2×1012mol/L)=18

(b)

Interpretation Introduction

Interpretation: The solubility of Pb3(PO4)2 and Li2CO3 is given. The solubility product of Pb3(PO4)2 and Li2CO3 is to be calculated.

Concept introduction: The solubility product, Ksp is the equilibrium constant that is applied when salt partially dissolve in a solvent. The solubility product of dissociation of AxBy is calculated as,

Ksp=[A]x[B]y

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