   Chapter 17, Problem 86AE

Chapter
Section
Textbook Problem

# Consider the following reaction: H 2 O ( g ) + CI 2 O ( g )   ⇌   2 HOCI ( g )       K 298 = 0.090 For Cl2O(g), Δ G f o = 97.9   KJ/mol Δ H f o = 80.3   KJ/mol S ∘ = 266.1   J / K ⋅ mol a. Calculate ∆G° for the reaction using the equation ∆G°=−RT In(K).b. Use bond energy values (Table 3-3) to estimate ∆H° for the reaction.c. Use the results from parts a and b to estimate ∆S° for the reaction.d. Estimate Δ H f o and S° for HOCI(g).e. Estimate the value of K at 500. K.f. Calculate ∆G at 25°C when P H 2 O = 18   torr ,   P CI 2 O = 2.0   torr ,   a n d   P HOCI = 0.10   torr   .

(a)

Interpretation Introduction

Interpretation: The reaction corresponding to the formation of HOCl(g) , its equilibrium constant at 298K and values of ΔGf°,ΔHf°,S° are given. The questions are to be answered on the basis of the given data.

Concept introduction: Equilibrium constant, K , is defined as the ratio of the concentration of products to that of the reactants at equilibrium. If a given reaction is at equilibrium, the free energy change is,

ΔG=0Q=K

ΔG°=RTln(K)

The formula of ΔS° is,

ΔS°=npΔS°(product)nfΔS°(reactant)

To determine: The value of ΔG° for the given reaction, using the equation ΔG°=RTln(K) .

Explanation

Explanation

Given

Temperature is 298K .

The value of equilibrium constant is 0.090 .

The stated reaction is,

H2O(g)+Cl2O(g)2HOCl(g)

Formula

ΔG°=RTln(K)

Where,

• ΔG° is the standard Gibbs free energy change.
• R is the gas law constant (8.3145J/Kmol) .
• T is the absolute temperature.
• K is the equilibrium constant.

Substitute the values of R,T and K in the above expression.

ΔG°=RTln(K)=(8.3145J/Kmol)(298K)ln(0

(b)

Interpretation Introduction

Interpretation: The reaction corresponding to the formation of HOCl(g) , its equilibrium constant at 298K and values of ΔGf°,ΔHf°,S° are given. The questions are to be answered on the basis of the given data.

Concept introduction: Equilibrium constant, K , is defined as the ratio of the concentration of products to that of the reactants at equilibrium. If a given reaction is at equilibrium, the free energy change is,

ΔG=0Q=K

ΔG°=RTln(K)

The formula of ΔS° is,

ΔS°=npΔS°(product)nfΔS°(reactant)

To determine: The value of ΔG° for the given reaction, using the equation ΔG°=RTln(K) .

(c)

Interpretation Introduction

Interpretation: The reaction corresponding to the formation of HOCl(g) , its equilibrium constant at 298K and values of ΔGf°,ΔHf°,S° are given. The questions are to be answered on the basis of the given data.

Concept introduction: Equilibrium constant, K , is defined as the ratio of the concentration of products to that of the reactants at equilibrium. If a given reaction is at equilibrium, the free energy change is,

ΔG=0Q=K

ΔG°=RTln(K)

The formula of ΔS° is,

ΔS°=npΔS°(product)nfΔS°(reactant)

To determine: The value of ΔG° for the given reaction, using the equation ΔG°=RTln(K) .

(d)

Interpretation Introduction

Interpretation: The reaction corresponding to the formation of HOCl(g) , its equilibrium constant at 298K and values of ΔGf°,ΔHf°,S° are given. The questions are to be answered on the basis of the given data.

Concept introduction: Equilibrium constant, K , is defined as the ratio of the concentration of products to that of the reactants at equilibrium. If a given reaction is at equilibrium, the free energy change is,

ΔG=0Q=K

ΔG°=RTln(K)

The formula of ΔS° is,

ΔS°=npΔS°(product)nfΔS°(reactant)

To determine: The value of ΔG° for the given reaction, using the equation ΔG°=RTln(K) .

(e)

Interpretation Introduction

Interpretation: The reaction corresponding to the formation of HOCl(g) , its equilibrium constant at 298K and values of ΔGf°,ΔHf°,S° are given. The questions are to be answered on the basis of the given data.

Concept introduction: Equilibrium constant, K , is defined as the ratio of the concentration of products to that of the reactants at equilibrium. If a given reaction is at equilibrium, the free energy change is,

ΔG=0Q=K

ΔG°=RTln(K)

The formula of ΔS° is,

ΔS°=npΔS°(product)nfΔS°(reactant)

To determine: The value of ΔG° for the given reaction, using the equation ΔG°=RTln(K) .

(f)

Interpretation Introduction

Interpretation: The reaction corresponding to the formation of HOCl(g) , its equilibrium constant at 298K and values of ΔGf°,ΔHf°,S° are given. The questions are to be answered on the basis of the given data.

Concept introduction: Equilibrium constant, K , is defined as the ratio of the concentration of products to that of the reactants at equilibrium. If a given reaction is at equilibrium, the free energy change is,

ΔG=0Q=K

ΔG°=RTln(K)

The formula of ΔS° is,

ΔS°=npΔS°(product)nfΔS°(reactant)

To determine: The value of ΔG° for the given reaction, using the equation ΔG°=RTln(K) .

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