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Chemistry

9th Edition
Steven S. Zumdahl
ISBN: 9781133611097

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Chemistry

9th Edition
Steven S. Zumdahl
ISBN: 9781133611097
Textbook Problem

A 50.0-mL sample of 0.00200 M AgNO3 is added to 50.0 mL of 0.0100 M NaIO3. What is the equilibrium concentration of Ag+ in solution? (Ksp for AgIO3 is 3.0 × 10−8.)

Interpretation Introduction

Interpretation: The concentration and volume of AgNO3,NaIO3 and solubility product of AgIO3 is given. The equilibrium concentration of Ag+ is to be calculated.

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

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 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

Explanation

To determine: The equilibrium concentration of Ag+ in a solution prepared by adding 50mL of 0.00200M AgNO3 to 50mL of 1.0M NaIO3 .

The initial concentration of Ag+ is 0.001M_ and initial concentration of IO3(aq) is 0.005M_ .

Given

Concentration of AgNO3 is 0.00200M .

Concentration of NaIO3 is 0.0100M .

Solubility product of AgIO3 is 3×108 .

Volume of AgNO3 is 50mL .

Volume of NaIO3 is 50mL .

The AgIO3 will only precipitate out during mixing of AgNO3 and NaIO3 if,

Ksp<Q

It is assumed that the concentration of Ag+ and IO3(aq) is same as the concentration of AgNO3 and NaIO3 . Hence, concentration of Ag+ and IO3(aq) is,

[Ag+]=0.00200M[IO3(aq)]=0.0100M

Formula

The initial concentration of compound is calculated using the formula,

Initialconcentration=Volumeofcompound(mL)×Givenconcentration[Volumeoforiginalsolution(mL)+(Volumeofcompoundadded(mL))] (1)

Substitute the values of volume, given concentration of Ag+ and volume of original solution in the above equation.

InitialconcentrationofAg+=Volumeofcompound(mL)×Givenconcentration[Volumeoforiginalsolution(mL)+(Volumeofcompoundadded(mL))]=(50mL)(0.00200M)50mL+50mL=0.001M_

Substitute the values of volume, given concentration of IO3 and volume of original solution in equation (1).

InitialconcentrationofIO3=Volumeofcompound(mL)×Givenconcentration[Volumeoforiginalsolution(L)+(Volumeofcompoundadded(L))]=50mL(0.0100)M50mL+50mL=0.005M_

The ion product of AgIO3 is 5×106_ .

Formula

The ion product of AgIO3 is calculated as,

Q=[Ag+]0[IO3]0

Where,

  • Q is ion product.
  • [Ag+]0 is initial concentration of Ag+ .
  • [IO3]0 is initial concentration of IO3 .

Substitute the value of [Ag+]0 and [IO3]0 in the above expression.

Q=[Ag+]0[IO3]0=(0

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