Chemistry: The Molecular Nature of Matter and Change
Chemistry: The Molecular Nature of Matter and Change
8th Edition
ISBN: 9781259631757
Author: Martin Silberberg Dr., Patricia Amateis Professor
Publisher: McGraw-Hill Education
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Chapter 20, Problem 20.54P
Interpretation Introduction

Interpretation:

For the given set of reactions in problem 20.52 the standard free energy ΔGo value have to be calculated using the ΔHfoandSo values.

Concept introduction:

Enthalpy is the amount energy absorbed or released in a process.

The enthalpy change in a system Ηsys) can be calculated by the following equation.

  ΔHrxn = ΔH°produdcts-ΔH°reactants 

Where,

  ΔHro(reactants) is the standard enthalpy of the reactants

  ΔHro(produdcts) is the standard enthalpy of the products

Entropy is the measure of randomness in the system.  Standard entropy change in a reaction is the difference in entropy of the products and reactants.  (ΔS°rxn) can be calculated by the following equation.

  ΔS°rxn = S°Products- nS°reactants

Where,

  S°reactants is the standard entropy of the reactants

  S°Products is the standard entropy of the products

Standard entropy change in a reaction and entropy change in the system are same.

Free energy is the term that is used to explain the total energy content in a thermodynamic system that can be converted into work.  The free energy is represented by the letter G.  All spontaneous process is associated with the decrease of free energy in the system.  The equation given below helps us to calculate the change in free energy in a system.

  ΔG = ΔΗ- TΔS

Where,

  ΔG  is the change in free energy of the system

  ΔΗ is the change in enthalpy of the system

  T is the absolute value of the temperature

  ΔS is the change in entropy in the system

Free energy (Gibbs free energy) is the term that is used to explain the total energy content in a thermodynamic system that can be converted into work.  The free energy is represented by the letter G.  All spontaneous process is associated with the decrease of free energy in the system.  The standard free energy change (ΔG°rxn) is the difference in free energy of the reactants and products in their standard state.

ΔG°rxn=mΔGf°(Products)-nΔGf°(Reactants)

Where,

  nΔGf°(Reactants) is the standard entropy of the reactants

  mΔGf°(products) is the standard free energy of the products

Expert Solution & Answer
Check Mark

Answer to Problem 20.54P

Reaction-A the standard free energy value is ΔGrxno=2.4kJ_

Reaction-B the standard free energy value is ΔGrxno=-48.4kJ_

Reaction-C the standard free energy value is ΔGrxno=91.2kJ_

Explanation of Solution

Reaction-A

Given chemical reaction is,

         H2(g)+I2(g)2HI(g)

The number of particle also decreases, indicating a decrease in entropy.

So, given reaction ΔGfo value is zero.

Standard enthalpy change is,

The enthalpy change for the reaction is calculated as follows,

  ΔH°rxn = ΔH°f(Products)- nΔH°f(reactants)

  ΔH°rxn =[(2molHI)(ΔH°fofHI)][(1molH2)(ΔH°fofH2)+(1molI2)(ΔH°fofI2)]ΔH°rxn =[(2molHI)(25.9kJ/mol)][(1molH2)(0kJ/mol)+(1molI2)(0kJ/mol)]ΔH°rxn =-51.8kJ

The enthalpy change is negative.

Hence, the enthalpy (ΔH°rxn) value is -51.8kJ_

Entropy change  ΔS°system

Standard entropy change equation is,

  ΔS°rxn = S°Products- nS°reactants

Where, (m)and(n) are the stoichiometric co-efficient.

  ΔS°rxn =[(2molHI)(206.33J/mol×K)][(2molH2)(130.6J/mol×K)+(1molI2)(116.14J/mol×K)]ΔS°rxn =165.92J/K

Therefore, the (ΔS°rxn) of the reaction is 165.92J/K_ 

Next calculate the Free enrgy change  ΔGrxno

Standared Free energy change equation iss,

  ΔGrxno = ΔΗrxno- TΔSrxno

Free energy change  ΔGfo

Calcualted enthalpy and entropy  values are

  ΔΗrxno=-51.8kJ

  ΔSrxno=165.92J/K

These values are plugging above standard free energy equation,

   ΔGrxno=51.8kJ-[(298K)(165.92J/K)(1kJ/103J)]ΔGrxno=2.3558kJ

Therefore, the standard free energy value is ΔGrxno=2.4kJ_

Reaction-B

Given reaction is,

         MnO2(s)+2CO(g)Mn(s)+4CO2(g)

The number of particle also increases, indicating a increase in entropy.

Standard enthalpy change is,

The enthalpy change for the reaction is calculated as follows,

  ΔH°rxn = ΔH°f(Products)- nΔH°f(reactants)

  ΔΗrxno =[(1molMn)(0kJ/mol)+(2molCO2)(393.5kJ/mol)][(1molMnO2)(520.9kJ/mol)+(2molCO)(110.5kJ/mol)]ΔΗrxno =-45.1kJ

The enthalpy change is negative.

Hence, the enthalpy (ΔH°rxn) value is -45.1kJ_

Entropy change  ΔS°system

Standard entropy change equation is,

  ΔS°rxn = S°Products- nS°reactants

Where, (m)and(n) are the stoichiometric co-efficient.

ΔSrxno =[(1molMn)(31.8J/molK)+(2molCO2)(213.7J/molK)][(1molMnO2)(53.1J/molK)+(2molCO)(197.5J/molK)]ΔSrxno =11.1J/K

Therefore, the (ΔS°rxn) of the reaction is -91.28J/K_ 

Next calculate the Free energy change  ΔGrxno

Standared Free energy change equation iss,

  ΔGrxno = ΔΗrxno- TΔSrxno

Free enrgy change  ΔGfo

Calcualted enthalpy and entropy  values are

  ΔΗrxno=-45.1kJ

  ΔSrxno=-91.28J/K

These values are plugging above standard free energy equation,

   ΔGrxno=45.1kJ-[(298K)(11.1J/K)(1kJ/103J)]ΔGrxno=48.4078kJ

Therefore, the standard free energy value is ΔGrxno=-48.4kJ_

Reaction-C

Given reaction is,

         NH4Cl(s)NH3(g)+HCl(g)

Standard enthalpy change is,

The enthalpy change for the reaction is calculated as follows,

  ΔH°rxn = ΔH°f(Products)- nΔH°f(reactants)

  ΔΗrxno =[(1molNH3)(45.9kJ/mol)+(1molHCl)(92.3kJ/mol)][(1molNH4Cl)(314.4kJ/mol)]ΔΗrxno =176.2kJ

The enthalpy change is positive.

Hence, the enthalpy (ΔH°rxn) value is 176.2kJ_

Entropy change ΔS°system

Standard entropy change equation is,

  ΔS°rxn = S°Products- nS°reactants

Where, (m)and(n) are the stoichiometric co-efficient.

ΔSrxno =[(1molNH3)(193J/molK)+(1molHCl)(186.79J/molK)][(1molNH4Cl)(94.6J/molK)]ΔSrxno =285.19J/K

Therefore, the (ΔS°rxn) of the reaction is 285.19J/K_ 

Finally calculate the Free enrgy change  ΔGrxno

Standared Free energy change equation iss,

  ΔGrxno = ΔΗrxno- TΔSrxno

Free energy change  ΔGfo

Calcualted enthalpy and entropy  values are

  ΔΗrxno=176.2kJ

  ΔSrxno=285.19J/K

These values are plugging above standard free energy equation,

       ΔGrxno=176.2kJ-[(298K)(285.19J/K)(1kJ/103J)]ΔGrxno=91.213kJ

Therefore, the standard free energy value is ΔGrxno=91.2kJ_

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Chapter 20 Solutions

Chemistry: The Molecular Nature of Matter and Change

Ch. 20.3 - Prob. 20.6AFPCh. 20.3 - Prob. 20.6BFPCh. 20.3 - Prob. 20.7AFPCh. 20.3 - Prob. 20.7BFPCh. 20.3 - Prob. 20.8AFPCh. 20.3 - Prob. 20.8BFPCh. 20.3 - Prob. B20.1PCh. 20.3 - Nonspontaneous processes like muscle contraction,...Ch. 20.4 - Use Appendix B to find K at 298 K for the...Ch. 20.4 - Use the given value of K to calculate ΔG° at 298 K...Ch. 20.4 - Prob. 20.10AFPCh. 20.4 - Prob. 20.10BFPCh. 20.4 - At 298 K, ΔG° = −33.5 kJ/mol for the formation of...Ch. 20.4 - Prob. 20.11BFPCh. 20 - Prob. 20.1PCh. 20 - Distinguish between the terms spontaneous and...Ch. 20 - State the first law of thermodynamics in terms of...Ch. 20 - State qualitatively the relationship between...Ch. 20 - Why is ΔSvap of a substance always larger than...Ch. 20 - Prob. 20.6PCh. 20 - Prob. 20.7PCh. 20 - Which of these processes are spontaneous? (a)...Ch. 20 - Prob. 20.9PCh. 20 - Which of these processes are spontaneous? (a)...Ch. 20 - Prob. 20.11PCh. 20 - Prob. 20.12PCh. 20 - Prob. 20.13PCh. 20 - Prob. 20.14PCh. 20 - Prob. 20.15PCh. 20 - Prob. 20.16PCh. 20 - Prob. 20.17PCh. 20 - Prob. 20.18PCh. 20 - Prob. 20.19PCh. 20 - Prob. 20.20PCh. 20 - Prob. 20.21PCh. 20 - Prob. 20.22PCh. 20 - Prob. 20.23PCh. 20 - Prob. 20.24PCh. 20 - Predict which substance has greater molar entropy....Ch. 20 - Without consulting Appendix B, arrange each group...Ch. 20 - Without consulting Appendix B, arrange each group...Ch. 20 - Without consulting Appendix B, arrange each group...Ch. 20 - Without consulting Appendix B, arrange each group...Ch. 20 - In the reaction depicted in the molecular scenes,...Ch. 20 - Describe the equilibrium condition in terms of the...Ch. 20 - Prob. 20.32PCh. 20 - For each reaction, predict the sign and find the...Ch. 20 - For each reaction, predict the sign and find the...Ch. 20 - Find for the combustion of ethane (C2H6) to...Ch. 20 - Find for the combustion of methane to carbon...Ch. 20 - Find for the reaction of nitrogen monoxide with...Ch. 20 - Find for the combustion of ammonia to nitrogen...Ch. 20 - Find for the formation of Cu2O(s) from its...Ch. 20 - Find for the formation of HI(g) from its...Ch. 20 - Find for the formation of CH3OH(l) from its...Ch. 20 - Find for the formation of N2O(g) from its...Ch. 20 - Sulfur dioxide is released in the combustion of...Ch. 20 - Oxyacetylene welding is used to repair metal...Ch. 20 - What is the advantage of calculating free energy...Ch. 20 - Given that ΔGsys = −TΔSuniv, explain how the sign...Ch. 20 - Is an endothermic reaction more likely to be...Ch. 20 - Explain your answers to each of the following for...Ch. 20 - With its components in their standard states, a...Ch. 20 - How can ΔS° for a reaction be relatively...Ch. 20 - Calculate ΔG° for each reaction using ...Ch. 20 - Calculate ΔG° for each reaction using ...Ch. 20 - Prob. 20.53PCh. 20 - Prob. 20.54PCh. 20 - Consider the oxidation of carbon...Ch. 20 - Consider the combustion of butane gas: Predict...Ch. 20 - For the gaseous reaction of xenon and fluorine to...Ch. 20 - For the gaseous reaction of carbon monoxide and...Ch. 20 - One reaction used to produce small quantities of...Ch. 20 - A reaction that occurs in the internal combustion...Ch. 20 - As a fuel, H2(g) produces only nonpolluting H2O(g)...Ch. 20 - The U.S. government requires automobile fuels to...Ch. 20 - If K << 1 for a reaction, what do you know about...Ch. 20 - How is the free energy change of a process related...Ch. 20 - The scenes and the graph relate to the reaction of...Ch. 20 - What is the difference between ΔG° and ΔG? Under...Ch. 20 - Calculate K at 298 K for each reaction: MgCO3(s) ⇌...Ch. 20 - Calculate ΔG° at 298 K for each reaction: 2H2S(g)...Ch. 20 - Calculate K at 298 K for each reaction: HCN(aq) +...Ch. 20 - Calculate ΔG° at 298 K for each reaction: 2NO(g) +...Ch. 20 - Use ΔH° and ΔS° values for the following process...Ch. 20 - Use ΔH° and ΔS° values to find the temperature at...Ch. 20 - Prob. 20.73PCh. 20 - Use Appendix B to determine the Ksp of CaF2. Ch. 20 - For the reaction I2(g) + Cl2(g) ⇌ 2ICl(g),...Ch. 20 - For the reaction CaCO3(s) ⇌ CaO(s) + CO2(g),...Ch. 20 - The Ksp of PbCl2 is 1.7×10−5 at 25°C. What is ΔG°?...Ch. 20 - Prob. 20.78PCh. 20 - The equilibrium constant for the...Ch. 20 - The formation constant for the reaction Ni2+(aq) +...Ch. 20 - Prob. 20.81PCh. 20 - Prob. 20.82PCh. 20 - High levels of ozone (O3) cause rubber to...Ch. 20 - A BaSO4 slurry is ingested before the...Ch. 20 - According to advertisements, “a diamond is...Ch. 20 - Prob. 20.86PCh. 20 - Prob. 20.87PCh. 20 - Prob. 20.88PCh. 20 - Is each statement true or false? If false, correct...Ch. 20 - Prob. 20.90PCh. 20 - Prob. 20.91PCh. 20 - Prob. 20.92PCh. 20 - Prob. 20.93PCh. 20 - Write a balanced equation for the gaseous...Ch. 20 - Prob. 20.95PCh. 20 - Hydrogenation is the addition of H2 to double (or...Ch. 20 - Prob. 20.97PCh. 20 - Prob. 20.98PCh. 20 - Prob. 20.99PCh. 20 - Prob. 20.100PCh. 20 - From the following reaction and data, find (a) S°...Ch. 20 - Prob. 20.102PCh. 20 - Prob. 20.103PCh. 20 - Prob. 20.104PCh. 20 - Prob. 20.105PCh. 20 - Prob. 20.106PCh. 20 - Prob. 20.107PCh. 20 - Consider the formation of ammonia: N2(g) + 3H2(g)...Ch. 20 - Kyanite, sillimanite, and andalusite all have the...Ch. 20 - Prob. 20.110PCh. 20 - Prob. 20.111P
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