   Chapter 16, Problem 111IP

Chapter
Section
Textbook Problem

# Consider 1.0 L of an aqueous solution that contains 0.10 M sulfuric acid to which 0.30 mole of barium nitrate is added. Assuming no change in volume of the solution, determine the pH, the concentration of barium ions in the final solution, and the mass of solid formed.

Interpretation Introduction

Interpretation:

0.30mole of Barium nitrate is added to 1L of an aqueous solution that contains 0.10M sulfuric acid. Assuming no change in volume of the solution, the pH , the concentration of barium ions in the final solution and the mass of solid formed is to be calculated.

Concept introduction:

The solubility product is the mathematical product of a substance’s dissolved ion concentration raised to its power of its stoichiometric coefficients. When sparingly soluble ionic compound releases ions in the solution, it gives relevant solubility product. The solvent is generally water.

Explanation

To determine: The pH , the concentration of barium ions in the final solution and the mass of solid formed when 0.30mole of barium nitrate is added to 1L of an aqueous solution that contains 0.10M sulfuric acid.

value of Koverall

The reaction for dissociation of sulfuric acid and barium nitrate are,

HSO4(aq)H+(aq)+SO42(aq)K1=1.2×102 (1)

Ba+2(aq)+SO42(aq)BaSO4(s)K2=1/Ksp=6.7×108 (2)

The equation (1) and equation (2) are added to get the overall reaction which is,

Ba+2(aq)+HSO4(aq)H++ BaSO4

The equilibrium constant (Koverall) for the overall reaction is calculated as,

Koverall=K1×K2

Where,

• K1 is the equilibrium constant of equation(1).
• K2 is the equilibrium constant of equation(2).

Substitute the values of K1 and K2 in the above equation.

Koverall=1.2×102×6.7×108=8×106_

The value of Koverall is 8×106_ .

pH calculation:

The rate constant for overall reaction is very high; therefore it is assumed that reaction goes to completion. Sulfuric acid is a strong acid, it will dissociate completely. Therefore, the [H+]=[HSO4]=0.10M .

The change in concentration of the species is assumed to be x . The ICE table for the reaction is,

Ba+2(aq)+HSO4(aq)H+(aq)+BaSO4(s)Initial0.30M0.100.10M0.100.10M+0.10Change0.20+x0+x0.20MxEquilibrium0.20+xx0.20Mx

The equilibrium constant (Koverall) for the above reaction is calculated by the formula,

Koverall=[H+][Ba2+][HSO4]

Substitute the equilibrium concentration in the above formula

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