Chapter 17, Problem 46PS

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074

Chapter
Section

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074
Textbook Problem

# Calcium hydroxide, Ca(OH)2, dissolves in water to the extent of 1.78 g per liter. What is the value of Ksp for Ca(OH)2? C a ( O H ) 2 ( s ) ⇄ C a 2 + ( a q ) + 2   O H − ( a q )

Interpretation Introduction

Interpretation:

Solubility product constant Ksp for Ca(OH)2 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.

The expression for Ksp of a salt is given as,

AxBy(s)xAy+(aq)+yBx(aq)Ksp=[Ay+]x[Bx]y

The relation between Ksp and s is derived as follows:

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

Ksp=[Ay+]x[Bx]yKsp=(xs)x(ys)y=xxyy(s)x+y

Rearrange the expression for s.

(s)x+y=Kspxxyy=(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

Ksp is calculated by using molar solubility of the salt.

Explanation

The solubility product constant Ksp for Ca(OH)2 is calculated below.

Given:

The solubility of Ca(OH)2 is 1.78Â gâ‹…l.

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

â€‚Â Ca(OH)2(s)â‡”Â Ca2+(aq)â€‰+Â 2OHâˆ’1(aq)

From above reaction, it can be concluded that for each mole of Ca(OH)2 dissolved, one mole of Ca2+ and two moles of OHâˆ’1 is produced.

Convert solubility in grams per liter to molar solubility by dividing the solubility by the molar mass of the given salt.

Molar mass of Ca(OH)2 is 74.09â€‰gâ‹…mol. So molar solubility of Ca(OH)2 is

sÂ =Â 1.78â€‰gâ‹…l74.09Â gâ‹…mol=Â 0.024â€‰molâ‹…l

This means when 0.024 moles of Ca(OH)2 is dissolved per liter of water, it produces 0.024 moles of Ca2+ and (2(0

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