   # The K sp of Al(OH) 3 is 2 × 10 −32 . At what pH will a 0.2- M Al 3+ solution begin to show precipitation of Al(OH) 3 ? ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243

#### Solutions

Chapter
Section ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243
Chapter 15, Problem 58E
Textbook Problem
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## The Ksp of Al(OH)3 is 2 × 10−32. At what pH will a 0.2-M Al3+ solution begin to show precipitation of Al(OH)3?

Interpretation Introduction

Interpretation: The solubility product of Al(OH)3 and concentration of Al3+ is given. By using these values, the pH value at which given concentration of Al3+ solution begins to show precipitation of Al(OH)3 is to be calculated.

Concept introduction: The formation of solid in a solution is known as precipitation.

The solubility product, Ksp is defined as the concentration of ions in a saturated solution where each ion is raised to the power of their coefficients. Ion product, Q is defined as the initial concentration of ions in any solution where each ion is raised to the power of their coefficients.

The relation between ion product, Q and the solubility product, Ksp is as follows.

• If Ksp>Q , then no precipitate will form.
• If Ksp<Q , then precipitate will form.
• If Ksp=Q , then the solution will be in just saturation.

### Explanation of Solution

Explanation

To determine: The pH value at which given concentration of Al3+ solution begins to show precipitation of Al(OH)3 .

The concentration of Al(OH)3 is 4.64×1011M_ .

Given

Concentration of Al3+ is 0.2M .

Solubility product of Al(OH)3 is 2×1032 .

The Al(OH)3 will only precipitate out during mixing of Al3+ and OH if,

Ksp<Q

The dissociation reaction of Al(OH)3 is,

Al(OH)3(s)Al3+(aq)+3OH(aq)

The initial concentration of OH will be same as the minimum concentration of Al(OH)3 . If the concentration of OH exceeds the Ksp=Q condition, then precipitate will form.

Formula

The ion product of Al(OH)3 at Ksp=Q is calculated as,

Q=[Al3+]0[OH]03

Where,

• Q is ion product.
• [Al3+]0 is initial concentration of Al3+ .
• [OH]0 is initial concentration of OH .

Substitute the value of [Al3+]0 and Ksp in the above expression

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