# Calculate the solubility, in moles per liter, of iron(II) hydroxide, Fe(OH) 2 , in a solution buffered to a pH of 7.00.

### Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640

Chapter
Section

### Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640
Chapter 17, Problem 61PS
Textbook Problem
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## Calculate the solubility, in moles per liter, of iron(II) hydroxide, Fe(OH)2, in a solution buffered to a pH of 7.00.

Interpretation Introduction

Interpretation:

Molar solubility of iron(II) hydroxide in a solution buffered to a pH7.0 has to be calculated.

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.

The pOH of the solution is calculated by using the relation,

pH+pOH=pKw (2)

The value of pKw is 14.0.

The concentration of [OH] is calculated using the following expression.

[OH]=10pOH (3)

### Explanation of Solution

The concentration of the Fe2+ ions in the solution gives the true value of molar solubility of Fe(OH)2 not the concentration of the hydroxide ions because the concentration of hydroxide will be affected by the pH of the solution or hydroxide ion already present in the buffer solution as a result of common ion effect. The molar solubility for Fe(OH)2 is calculated as below.

Given:

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

The value of solubility product constant, Ksp, for Fe(OH)2 is 4.9×1017.

pH of the buffered solution is 7.0.

Calculate pOH using equation (2).

pH+pOH=pKw

Rearrange the expression for pOH.

pOH=pKwpH= 14.07.0=7.0

Substitute 7.0 for pOH in equation (3) to calculate concentration of hydroxide ion.

[OH]=107.0=107 M

The initial concentration of hydroxide ion is equal to 107 M coming from buffer solution.

Now, Fe(OH)2 when dissolved in water dissociates as follows,

Fe(OH)2(s)Fe2+(aq)+2OH1(aq)

The ICE table (2) is as follows,

EquationFe(OH)2(s)Fe2+(aq)+2OH1(aq)Initial (M)0107Change (M)+s+2sEquilibrium (M) s107+2s

From the table,

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