   Chapter 17.5, Problem 17.14CYU

Chapter
Section
Textbook Problem

You have 100.0 mL of 0.0010 M silver nitrate. Will AgCl precipitate if you add 5.0 mL of 0.025 M HCl?

Interpretation Introduction

Interpretation:

Predict whether AgCl will precipitate out or not upon addition of 0.001 M silver nitrate (AgNO3) solution to a 0.025M solution of hydrochloric acid (HCl).

Concept introduction:

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

Here,

• [Ay+] and [Bx] are equilibrium concentration.

Reaction quotient, Q, for a reaction is defined as the product of the concentration of the ions at any time of the reaction (other than equilibrium time ) of the salt raised to the power of their coefficients in the balanced chemical equation.

The expression for Q of a salt is given as,

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

Here,

• [Ay+] and [Bx] are the concentration at any time except equilibrium.
1. 1. If Q=Ksp, this implies that the solution is saturated solution and the concentration of the ions have reached their maximum limit.
2. 2. If Q<Ksp, this implies that the solution is not saturated and more salt can be added to the solution or the salt present in the solution already will dissolve more until the precipitation starts.
3. 3. If Q>Ksp, this implies that the solution is oversaturated and precipitation of salt will occur.

Mixing of two solutions of different concentration will result in the change in the initial concentration of the ions as the resultant volume will change. The final concentration or the concentration after mixing for ions is to be calculated using the following relation,

CiVi=CfVf (1)

Here,

• Ci is the initial concentration of the ions.
• Vi is the initial volume of the solution.
• Cf is the final concentration of the ions.
• Vf is the final volume of the solution.
Explanation

When silver nitrate solution is mixed with hydrochloric acid of given concentration reaction will take place and if the ionic product of the concentration of the Ag+ and Cl exceeds the solubility product constant, Ksp of AgCl then precipitation of AgCl will take place.

Given:

The initial concentration of AgNO3 solution and HCl solution  is 0.001M and 0.025M respectively.

The value of solubility product constant,Ksp, for AgCl is 1.8×1010 (refer Table 17.2).

AgNO3 and HCl both are strong electrolyte and therefore undergoes complete dissociation in water such that the concentration of their ions will be same as the initial concentration of the solution.

In water AgNO3 dissociates as follows,

AgNO3(s)Ag+(aq)+NO3(aq)

In water HCl dissociates as follows,

HCl(aq)H+(aq)+Cl(aq)

After mixing final volume of solution will be,

Vf=100.0 ml + 5.0 ml(105 ml)(1 L1000 ml)=0.105 L

For Ag+,

Vi=(100 ml)(1 L1000 ml)=0.1 L

Calculate the final concentration, Cf of Ag+ using equation (1).

CiVi=CfVf

Rearrange for Cf.

Cf=CiViVf

Substitute 0.001M for Ci, 0.1 L for Vi and 0.105 L for Vf.

Cf=(0.001 M)(0.1 L)0.105L=9.52×104 M

For Cl,

Vi=(5.0 ml)(1 L1000 ml)=0

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