   Chapter 13, Problem 59E

Chapter
Section
Textbook Problem

# At a particular temperature, K = 2.0 × 10–6 for the reaction 2 CO 2 ( g ) ⇌ 2 CO ( g ) + O 2 ( g )   If 2.0 moles of CO2 is initially placed into a 5.0-L vessel, calculate the equilibrium concentrations of all species.

Interpretation Introduction

Interpretation:

The equilibrium constant, number of moles of reactant and volume of vessel for the decomposition reaction of carbon dioxide is given. The value of equilibrium concentrations of all species 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

To determine: The concentrations of [CO2] , [CO] and [O2] for the given reaction.

Given

The equilibrium constant is 2.0×106 .

The given volume of the vessel is 5.00L .

The number of moles of CO2 is 2.0mol .

The stated reaction is,

2CO2(g)2CO(g)+O2(g)

The initial concentration is calculated by the formula,

Concentration=MolesVolume(L)

Substitute the values of number of moles and volume of reactant in the above equation.

Concentration=MolesVolume(L)[CO2]0=2.0mol5.0L=0.4M

The initial concentration of product is,

[CO]0=0[O2]0=0

It is assumed that the change in number of moles of oxygen gas (O2) is x .

On the reaction with two molecules of CO2 , the equilibrium reaction is,

2CO2(g)2CO(g)O2(g)Initialmolecules:0.4000Change(molecules):2x2xxEquilibrium(molecules):0

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