   # A solution contains 0.018 mole each of I − , Br − , and Cl − . When the solution is mixed with 200. mL of 0.24 M AgNO 3 , what mass of AgCl( s ) precipitates out, and what is [Ag + ]? Assume no volume change. AgI: K sp = 1.5 × 10 − 16 AgBr: K sp = 5.0 × 10 − 13 AgCl: K sp = 1.6 × 10 − 10 ### 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 77AE
Textbook Problem
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## A solution contains 0.018 mole each of I−, Br−, and Cl−. When the solution is mixed with 200. mL of 0.24 M AgNO3, what mass of AgCl(s) precipitates out, and what is [Ag+]? Assume no volume change. AgI:   K sp   =   1.5   ×   10 − 16 AgBr:   K sp   =   5.0   ×   10 − 13 AgCl:   K sp   =   1.6   ×   10 − 10

Interpretation Introduction

Interpretation: A solution containing 0.018mole each of I,Br and Cl is given. The mass of AgCl(s) that precipitates out, when the given solution is mixed with 200mL of 0.24M AgNO3 and the [Ag+] is to be calculated.

Concept introduction: Solubility is defined as the maximum amount of solute that can dissolve at a certain amount of solvent at certain temperature. The solubility product, Ksp is the equilibrium constant that is applied when salt partially dissolve in a solvent. The solubility product of dissociation of AxBy is calculated by the formula,

Ksp=[A]x[B]y

### Explanation of Solution

Explanation

To determine: The mass of AgCl(s) that precipitates out, when the given solution is mixed with 200mL of 0.24M AgNO3 and the [Ag+] .

The number of moles of [Ag+] present is 0.048mol_ .

Given

The molarity of AgNO3 is 0.24M .

The volume of AgNO3 is 200mL(0.200L) .

The number of moles of a substance is calculated by the formula,

Numberofmoles=Molarity×Volume(L)

Substitute the value of molarity and the volume of AgNO3 in the above expression to get the number of moles of [Ag+] present.

Numberofmoles=(0.24M)×(0.200L)=0.048mol_

The [Ag+] is 5.33×10-9M_ .

The addition of the silver ions leads to the formation of a precipitate.

The given Ksp values are very small. Hence, it is assumed that the precipitation goes to completion.

The compound that has he least Ksp value will be the least soluble.

The Ksp value of AgI is 1.5×1016 .

The Ksp value of AgBr is 5.0×1013 .

The Ksp value of AgCl is 1.6×1010 .

The AgI precipitate first as it has the least Ksp value, so it is least soluble.

The stoichiometry of the reaction of silver with the iodide ions,

Ag+(aq)+I(aq)AgI(s)Beforereaction0.048mol0.018mol0Afterreaction(0.0480.018)mol=0.030mol(0.0180.018)mol=00.018mol

The stoichiometry of the reaction of silver with the bromine ions,

Ag+(aq)+Br(aq)AgBr(s)Beforereaction0.030mol0.018mol0Afterreaction(0.0300.018)mol=0.012mol(0.0180.018)mol=00.018mol

The stoichiometry of the reaction of silver with the chlorine ions,

Ag+(aq)+Cl(aq)AgCl(s)Beforereaction0

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