   Chapter 13, Problem 89AE

Chapter
Section
Textbook Problem

# The creation of shells by mollusk species is a fascinating process. By utilizing the Ca2+ in their food and aqueous environment, as well as some complex equilibrium processes, a hard calcium carbonate shell can be produced. One important equilibrium reaction in this complex process is     HCO 3 − ( a q )   ⇌   H + ( a q )   +   CO 3 2 − ( a q )   K = 5.6   ×   10 − 11   If 0.16 mole of HCO 3 − , is placed into 1.00 L of solution, what will be the equilibrium concentration of CO 3 2 − ?

Interpretation Introduction

Interpretation:

The mollusk species create a hard calcium carbonate shell by utilizing the Ca2+ in their food and the aqueous environment.  One of the complex equilibrium reactions that occur in this process is given.  If 0.16mole of HCO3 is placed into 1.00L of solution, the equilibrium concentration of CO32 is to be calculated.

Concept introduction:

The state when the reactants involved in a chemical reaction and the products formed in the reaction exist in concentrations having no further tendency to change is known as an equilibrium state of the reaction.

When the equilibrium constant is expressed in terms of concentration, it is represented as K .

Explanation

The equilibrium constant expression for the given reaction is,

K=[H+][CO32][HCO3]

Given data

The stated reaction is,

HCO3(aq)H+(aq)+CO32-(aq)

The initial number of moles of HCO3 = 0.16mole .

The volume of the solution = 1.00L .

The equilibrium constant value = 5.6×1011 .

At equilibrium, the equilibrium ratio is expressed by the formula,

K=ConcentrationofproductsConcentrationofreactants

Where,

K is the equilibrium constant.

The equilibrium constant expression for the given reaction is,

K=[H+][CO32][HCO3]

Calculation of amount of HCO3- reacted till the equilibrium stage

Amount of HCO3 that reacted till the equilibrium stage

The initial concentration of the HCO3 is 0.16mol/L that is 0.16M .

Let assume the amount of HCO3 that reacted till the equilibrium stage is to be x .

The equilibrium concentrations are represented as,

HCO3-(aq)H+(aq)+CO32-(aq)Initialconcentration0.1600Change-x+x+xEquilibriumconcentration0.16-xxx

According to the ICE table formed,

The equilibrium concentration of HCO3 = (0.16x)M .

The equilibrium concentration of H+ is xM .

The equilibrium concentration of CO32 is xM .

Substitute the equilibrium concentration values of HCO3 , H+ and CO32 into K

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