   Chapter 16, Problem 29E

Chapter
Section
Textbook Problem

# Cream of tartar, a common ingredient in cooking, is the common name for potassium bitartrate (abbreviated KBT, molar mass = 188.2 g/mol). Historically, KBT was a crystalline solid that formed on the casks of wine barrels during the fermentation process. Calculate the maximum mass of KBT that can dissolve in 250.0 mL of solution to make a saturated solution. The Ksp value for KBT is 3.8 × 10−4.

Interpretation Introduction

Interpretation: The solubility product and molar mass of KBT is given. The maximum mass of KBT that can be dissolved in 250.0mL solution to make a saturated 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

Explanation

To determine: The maximum mass of KBT that can be dissolved in 250.0mL solution to make a saturated solution.

The solubility of KBT is 1.9×102mol/L_ .

Given

The solubility product of KBT is 3.8×104 .

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

KBTK+(aq)+BT(aq)

Since, KBT does not dissolved initially, hence,

[K+]initial=[BT]initial=0

The solubility of KBT 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/LKBTsmol/LK++smol/LBT

Formula

The solubility product of KBT is calculated as,

Ksp=[K+][BT]=(s)(s)

Where,

• Ksp is solubility product.
• [K+] is concentration of K+ .
• [BT] is concentration of BT .
• s is the solubility.

Substitute the value of Ksp in the above expression.

Ksp=(s)(s)3.8×104=s2=1.9×102mol/L_

Maximum mass of KBT is 0.89g_ .

Given

Solubility product of KBT is 1.9×102mol/L

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