Principles of General Chemistry
Principles of General Chemistry
3rd Edition
ISBN: 9780073402697
Author: SILBERBERG, Martin S.
Publisher: McGraw-Hill College
Question
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Chapter 4, Problem 4.94P

(a)

Interpretation Introduction

Interpretation:Ratio of CO2 to CO molecules in 5 % of gasoline exhaust is to be calculated.

Concept introduction: Reactant when reacted in presence of oxygen molecule to form desired product such type of reaction is called combustion reaction. In this reaction, energy is produced in large amount with release of heat. Molecular oxygen is generally required for such kind of reaction that acts as an oxidizing agent.

The expression used for the calculation of number of moles of any species is as follows:

  Number of moles=massmolar mass

(a)

Expert Solution
Check Mark

Answer to Problem 4.94P

Ratio of CO2 to CO molecules in 5 % of gasoline exhaust is 19 .

Explanation of Solution

Incomplete combustion of gasoline, C8H18 is given by the equation as follows:

  2C8H18(l)+17O2(g)16CO(g)+18H2O(g)

Complete combustion of gasoline, C8H18 is given by the equation as follows:

  2C8H18(l)+25O2(g)16CO2(g)+18H2O(g)

  5 % of gasoline undergoes incomplete combustion to form CO molecule. It means that out of total mass of gasoline that is 100g , 95g of gasoline undergoes complete combustion and 5g of gasoline undergoes incomplete combustion.

The expression used for the calculation of number of moles of gasoline is as follows:

   Moles of complete combustion C8H18=mass of  complete combustion of C8H18molar mass of C8H18 

Mass of complete combustion of C8H18 is 95g .

Molar mass of C8H18 is 114.22 g/mol .

Substitute the values in above equation.

   Moles of complete combustion C8H18= mass of  complete combustion of C8H 18 molar mass of C8H 18 =95g114.22 g/mol=0.8317282 mol

The expression used for the calculation of number of moles of gasoline is as follows:

   Moles of incomplete  combustion  C8H18=mass of  incomplete combustion of C8H18molar mass of C8H18 

Mass of incomplete combustion of C8H18 is 5g .

Molar mass of C8H18 is 114.22 g/mol .

Substitute the values in above equation.

   Moles of incomplete  combustion  C8H18= mass of  incomplete combustion of C8H 18 molar mass of C8H 18 =5g114.22 g/mol=0.0437751 mol

According to the balanced equation of complete combustion of gasoline, two moles of C8H18 reacts with oxygen to form sixteen moles of CO2 . Therefore, the number of molecules of CO2 is calculated as follows:

  Molecules of CO2=[(  Moles of complete combustion of C 8 H 18)( 16 mol CO 2 2 mol C 8 H 18 )( 6.022× 10 23 molecules 1mol)]

Moles of complete combustion of C8H18 is 0.8317282 mol .

Substitute the values in above equation.

  Molecules of CO2=[(  Moles of complete  combustion  C 8 H 18 )( 16 mol CO 2 2 mol C 8 H 18 )( 6.022× 10 23 molecules 1mol )]=[( 0.8317282 mol)( 16 mol CO 2 2 mol C 8 H 18 )( 6.022× 10 23 molecules 1mol )]=4.00693×1024 molecules

According to the balanced equation of incomplete combustion of gasoline, two moles of C8H18 reacts with oxygen to form sixteen moles of CO . Therefore, number of molecules of CO is calculated as follows:

  Molecules of CO=[(  Moles of incomplete combustion of C 8 H 18)( 16 mol CO 2 mol C 8 H 18 )( 6.022× 10 23 molecules 1mol)]

Moles of incomplete combustion of C8H18 is 0.0437751 mol .

Substitute the values in above equation.

  Molecules of CO=[(  Moles of incomplete  combustion  C 8 H 18 )( 16 mol CO 2 2 mol C 8 H 18 )( 6.022× 10 23 molecules 1mol )]=[( 0.0437751 mol)( 16 molCO 2 mol C 8 H 18 )( 6.022× 10 23 molecules 1mol )]=2.10891×1023 molecules

The ratio of molecules of CO2 to CO is as follows:

  Ratio=(Molecules of CO2Molecules ofCO)

Molecules of CO2 is 4.00693×1024 molecules .

Molecules of CO is 2.10891×1023 molecules .

Substitute the values in above equation.

  Ratio=( Molecules of CO 2 Molecules ofCO)=( 4.00693× 10 24  molecules 2.10891× 10 23  molecules)=18.9999819

(b)

Interpretation Introduction

Interpretation:The ratio of masses of CO2 to CO is to be calculated.

Concept introduction:The quantity of species that gives the relation between reactants and products is determined by the stoichiometry of a reaction. Consider the general reaction,

  2A+B3C

In the above reaction, two moles of A reacts with one mole of B to form three moles of C . Therefore, stoichiometric ratio of A and B is 2:2 , of A and C is 2:3 and of B and C is 1:3 .

(b)

Expert Solution
Check Mark

Answer to Problem 4.94P

Ratio of mass of CO2 to CO is 30.

Explanation of Solution

The formula used for the calculation of mass of CO2 is as follows:

  Mass ofCO2=[moles ofC8H18( 16mol CO 2 2mol C 8 H 18 )( molar mass of CO 2)]

Moles of C8H18 is 0.8317282 mol and molar mass of CO2 is 44.01 g/mol .

Substitute the values in above equation.

  Mass ofCO2=[moles of C 8 H 18( 16mol CO 2 2mol C 8 H 18 )( molar mass of CO 2 )]=[(0.8317282 mol)( 16mol CO 2 2mol C 8 H 18 )(44.01 g/mol)]=292.83g

The formula used for the calculation of mass of CO is as follows:

  Mass ofCO=[moles ofC8H18( 16molCO 2mol C 8 H 18 )(molar mass of CO)]

Moles of C8H18 is 0.0437751 mol and molar mass of CO is 28.01 g/mol .

Substitute the values in above equation.

  Mass ofCO=[moles of C 8 H 18( 16molCO 2mol C 8 H 18 )( molar mass of CO)]=[(0.0437751 mol)( 16molCO 2mol C 8 H 18 )(28.01 g/mol)]=9.8091g

The expression used for the calculation of ratioof mass of CO2 to CO is as follows:

  Ratio=(Mass of CO2Mass ofCO)

Mass of CO2 is 292.83g and mass of CO is 9.8091g .

Substitute the values in above equation.

  Ratio=( Mass of CO 2 Mass ofCO)=( 292.83g 9.8091g)=29.8528930

(c)

Interpretation Introduction

Interpretation:Percentage of gasoline that forms CO for mass ratio of CO2 to CO to be exactly 1/1 is to be calculated.

Concept introduction: Mass ratio of a component is defined as the ratio of mass of one component to that of other component. The ratio of two components A and B is expressed as follows:

  Mass ratio=(Mass of component AMass of component B)

(c)

Expert Solution
Check Mark

Answer to Problem 4.94P

Percentage of gasoline that forms CO for mass ratio of CO2 to CO to be exactly 1/1 is 61% .

Explanation of Solution

Suppose x be the fraction of CO2 and fraction of CO is 1x .

The expression used for the calculation of mass ratio of CO2 to CO is as follows:

  Ratio=((x)molar mass of CO2( 1x)molarmass ofCO)

Molar mass of CO2 is 44.01 g/mol , molar mass of CO is 28.01 g/mol and ratio is 1.

Substitute the values in above equation.

  Ratio=( ( x )molar mass of CO 2 ( 1x )molarmass ofCO)1=( ( x )( 44.01 g/mol ) ( 1x )( 28.01 g/mol ))44.01x=28.0128.01xx=0.39

The value of x is 0.39 and value of 1x is 0.61 . Therefore, percentage of gasoline that forms CO for mass ratio of CO2 to CO to be exactly 1/1 is 61% .

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Chapter 4 Solutions

Principles of General Chemistry

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