   Chapter 17, Problem 57PS

Chapter
Section
Textbook Problem

Calculate the molar solubility of silver thiocyanate, AgSCN, in pure water and in water containing 0.010 M NaSCN.

Interpretation Introduction

Interpretation:

The solubility of silver thiocyanate AgSCN salt has to be calculated in pure water and in water 0.010 M NaSCN

Concept introduction:

The solubility of a salt is defined as the maximum amount of salt that can be dissolved in definite amount of solvent. It is expressed in moles per liter or grams per liter. Solubility in terms of moles per liter is called molar solubility and is defined as the number of moles of solute (salt) dissolved in per liter of solution.

Solubility product constant Ksp is an equilibrium constant and is defined as the product of the equilibrium concentration of the ions of the salt raised to the power of their coefficients in the balanced chemical equation.

For example, general salt AxBy when dissolved in water dissociates as,

AxBy(s)xAy+(aq)+yBx(aq)

The expression for Ksp of a salt is,

Ksp=[Ay+]x[Bx]y (1)

The ICE table(1) for salt AxBy, which relates the equilibrium concentration of ions in the solution is given as follows,

EquationAxByxAy++yBxInitial(M)00Change(M)+xs+ysEquilibrium(M)xsys

From the table,

[Ay+]=xs[Bx]=ys

Substitute xs for [Ay+] and ys for [Bx] in equation (1).

Ksp=(xs)x(ys)y=xxyy(s)x+y

Rearrange for s.

s=(Kspxxyy)1/(x+y)

Here,

• x is the coefficient of cation A+y.
• y is the coefficient of anion Bx.
• s is the molar solubility.

The value of Ksp is calculated by using molar solubility of the salt.

Explanation
• The solubility of the salt AgSCN in pure water is calculated below;

Given:

Refer to the Appendix J in the textbook for the value of Ksp.

The value of solubility product constant,Ksp of AgSCN is 1.0×1012.

The balanced chemical reaction for the dissolution of AgSCN in water is,

AgSCN(s) Ag+(aq)+ SCN(aq)

The ICE table(2) is as follows,

EquationAgSCN(s)Ag+(aq)+SCN(aq)Initial (M)00Change (M)+s+sEquilibrium (M) ss

The Ksp expression for AgSCN is,

Ksp=[Ag+][SCN1] (2)

From the table,

[Ag+]=s[SCN1]=s

Substitute s for [Ag+] and [SCN1] in equation (2).

Ksp=(s)(s)

Here,

• Ksp is solubility product constant
• s is the molar solubility of the salt AgSCN.

Ksp=s2

Rearrange for s.

s=Ksp2

Substitute 1.0×1012 for Ksp.

s=1.0×10122= 1.0×106molL1

The solubility of AgSCN in pure water is 1.0×106molL1.

• The solubility of the salt AgSCN in the presence of 0.010 M NaSCN is calculated below;

Given:

Refer to the Appendix J in the textbook for the value of Ksp.

The value of solubility product constant,Ksp of AgSCN is 1.0×1012

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