   # Barium sulfate is a contrast agent for X-ray scans that are most often associated with the gastrointestinal tract. Calculate the mass of BaSO 4 that can dissolve in 100.0 mL of solution. The K sp value for BaSO 4 is 1.5 × 10 −9 . ### 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 30E
Textbook Problem
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## Barium sulfate is a contrast agent for X-ray scans that are most often associated with the gastrointestinal tract. Calculate the mass of BaSO4 that can dissolve in 100.0 mL of solution. The Ksp value for BaSO4 is 1.5 × 10−9.

Interpretation Introduction

Interpretation: The solubility product of BaSO4 and volume of solution is given. The mass of BaSO4 that can be dissolved in 100.0mL solution 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 as,

Ksp=[A]x[B]y

Where,

• x is coefficient of concentration of A .
• y is coefficient of concentration of B .

### Explanation of Solution

Explanation

To determine: The mass of BaSO4 that can be dissolved in 100.0mL solution.

The solubility of BaSO4 is 3.9×105mol/L_ .

Given

The solubility product of BaSO4 is 1.5×109 .

Since, solid BaSO4 is placed in contact with water. Therefore, compound present before the reaction is BaSO4 and H2O . The dissociation reaction of BaSO4 is,

BaSO4Ba2+(aq)+SO42(aq)

Since, BaSO4 does not dissolved initially, hence,

[Ba2+]initial=[SO42]initial=0

The solubility of BaSO4 can be calculated from the concentration of ions at equilibrium.

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

smol/LBaSO4smol/LBa2++smol/LSO42

Formula

The solubility product of BaSO4 is calculated as,

Ksp=[Ba2+][SO42]=(s)(s)

Where,

• Ksp is solubility product.
• [Ba2+] is concentration of Ba2+ .
• [SO42] is concentration of SO42 .
• s is the solubility.

Substitute the value of Ksp in the above expression.

Ksp=(s)(s)1.5×109=s2=3.9×105mol/L_

Mass of BaSO4 that can dissolved in 100mL of solution is 9.1×104g_

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