   # What mass of ZnS ( K sp = 2.5 × 10 −22 ) will dissolve in 300.0 mL of 0.050 M Zn(NO 3 ) 2 ? Ignore the basic properties of S 2− . ### 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 47E
Textbook Problem
561 views

## What mass of ZnS (Ksp = 2.5 × 10−22) will dissolve in 300.0 mL of 0.050 M Zn(NO3)2? Ignore the basic properties of S2−.

Interpretation Introduction

Interpretation: The solubility product of ZnS , concentration and volume of Zn(NO3)2 solution is given. The mass of ZnS that can be dissolved in the given Zn(NO3)2 solution is to be calculated.

Concept introduction: Solubility is defined as the maximum amount of solute that can dissolve in a certain amount of solvent at a given temperature. The solubility product, Ksp , is defined as the product of the concentrations of the dissolved ions of a substance raised to the power equivalent to the stoichiometric coefficients of the respective ions. The solubility product corresponding to the dissociation of AxBy is calculated by the expression,

Ksp=[A]x[B]y

### Explanation of Solution

Explanation

To determine: The mass of ZnS that can be dissolved in 300.0mL of 0.050M Zn(NO3)2 solution.

The solubility of ZnS is 50×1022mol/L_ .

Given

The solubility product of ZnS is 2.5×1022 .

The major species in the solution are Zn2+,S2 and H2O . The dissociation reaction of ZnS is,

ZnS(s)Zn2+(aq)+S2(aq)

The ratio of moles between ions is 1:1 .

It is assumed that smol/L of solid is dissolved to reach equilibrium. The meaning of 1:1 stoichiometry of salt is,

smol/LZnSsmol/LZn2++smol/LS2

The concentrations are as follows,

Initialconcentration(mol/L)Equilibriumconcentration(mol/L)[Zn2+]=0.050M[Zn2+]=0.050+s[S2]=0Mdissociatestoreachequilibriumsmol/LofZnS[S2]=s

Formula

The solubility product of ZnS is calculated by the formula,

Ksp=[Zn2+][S2]=(0.050+s)(s)

Where,

• Ksp is the solubility product.
• [Zn2+] is the concentration of Zn2+ .
• [S2] is the concentration of S2 .
• s is the solubility.

The value of s is assumed to be very small, therefore,

(0.050+s)0.050

Substitute this value in the solubility product expression.

Ksp=(0.050+s)(s)=(0.050)(s)

Substitute the value of s in the above expression

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