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Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074

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BuyFindarrow_forward

Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074
Textbook Problem

When vapors from hydrochloric acid and aqueous ammonia come in contact, they react, producing a white “cloud” of solid NH4C1 (Figure 18.9).

HCI(g) + NH3(g) ⇄ NH4Cl(s)

Defining the reactants and products as the system under study:

  1. (a) Predict whether ΔS°(system), ΔS°(surroundings), ΔS°(universe), ΔrH°, and ΔrG° (at 298 K) are greater than zero, equal to zero, or less than zero; and explain your prediction. Verify your predictions by calculating values for each of these quantities.
  2. (b) Calculate the value of Kp for this reaction at 298 K.

(a)

Interpretation Introduction

Interpretation:

It should be predicted that whether the entropy change for the system, surroundings and universe also the change in enthalply, free energy change, are greater, lesser or equal to zero. The prediction should be explained by calculation of these quantites.

Concept introduction:

The universe consists of two parts, systems and surroundings. The entropy change for the universe is the sum of entropy change for the system and for surroundings.

  ΔSo(universe)= ΔSo(system)+ΔSo(surroundings)

The ΔSo(universe) should be greater than zero for a spontaneous process.

The  ΔSo(system) can be calculated by the following expression,

  ΔrS°nS°(products)-nS°(reactants)

The ΔSo(surroundings) can be calculated by the following expression,

  ΔSo(surroundings)rHoT

Here, ΔrHo is the enthalpy change for the reaction.

The Gibbs free energy or the free energy change is a thermodynamic quantity represented by ΔGo. It is related to entropy and entropy by the following expression,

  ΔGo= ΔHo- TΔSo

ΔrGo is also related to the equilibrium constant K by the equation,

  ΔrGo=-RTlnKp

The rearranged expression is,

  Kp= e-ΔrGoRT

Explanation

The entropy change for the system, surroundings and universe and also the enthalply, free energy change for the given reaction of formation of NH4Cl(s) is calculated below.

Given:

The Appendix L referred for the values of standard entropies and enthalpies.

The standard entropy of NH4Cl(s) is 94.85 J/Kmol.

The standard entropy of HCl(g) is 186.2 J/Kmol.

The standard entropy of NH3(g) is 192.77 J/Kmol.

The standard enthalpy of NH4Cl(s) is 314.55 kJ/mol.

The standard enthalpy of HCl(g) is 92.31 kJ/mol.

The standard enthalpy of NH3(g) is 45.90 kJ/mol.

The balanced chemical equation is:

  HCl(g) + NH3(g)NH4Cl(s)

The  ΔS(system) can be calculated by the following expression,

  ΔSo(system)=ΔrS°nS°(products)-nS°(reactants)=[(1 mol NH4Cl(s)/mol-rxn)S°[NH4Cl(s)][(1 mol HCl(g)/mol-rxn)S°[HCl(g)]+(1 mol NH3(g)/mol-rxn)S°[NH3(g)]]]

Substituting the respective values

  ΔSo(system)=[(1 mol NH4Cl(s)/mol-rxn)(94.85 J/K×mol)-[(1 mol HCl(g)/mol-rxn)(186.2 J/K×mol)+(1 mol NH3(g)/mol-rxn)(192.77 J/K×mol)]]= -284

(b)

Interpretation Introduction

Interpretation:

The value of Kp for the given reaction should be calculated at 298K.

Concept introduction:

The universe consists of two parts, systems and surroundings. The entropy change for the universe is the sum of entropy change for the system and for surroundings.

  ΔSo(universe)= ΔSo(system)+ΔSo(surroundings)

The ΔSo(universe) should be greater than zero for a spontaneous process.

The  ΔSo(system) can be calculated by the following expression,

  ΔSo(system)rS°nS°(products)-nS°(reactants)

The ΔSo(surroundings) can be calculated by the following expression,

  ΔSo(surroundings)rHoT

Here, ΔrHo is the enthalpy change for the reaction.

The Gibbs free energy or the free energy change is a thermodynamic quantity represented by ΔGo. It is related to entropy and entropy by the following expression,

  ΔGo= ΔHo- TΔSo

ΔGo is also related to the equilibrium constant K by the equation,

  ΔrGo=-RTlnKp

The rearranged expression is,

Kp= e - ΔrGoRT

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