   Chapter 18, Problem 93SCQ

Chapter
Section
Textbook Problem

Calculate the standard molar entropy change, ΔrS°, for each of the following reactions at 25 °C: (a) C(s) + 2 H2(g) → CH4(g) (b) CH4(g) + ½ O2(g) → CH3OH(ℓ) (c) C(s) + 2 H2(g) + ½ O2(g) → CH3OH(ℓ) Verify that these values are related by the equation ΔrS°(1) + ΔrS°(2) = ΔrS°(3). What general principle is illustrated here?

(a)

Interpretation Introduction

Interpretation:

The standard molar entropy change for the given reaction should be calculated.

Concept introduction:

Entropy is a measure of the randomness of the system. It is a thermodynamic quantity and an extensive property. It is represented by the symbol S. It can also be defined as the degree of energy dispersal. More the dispersal in energy, more is the value if entropy.

The standard entropy change for any reaction is the sum of standard molar entropies of product, subtracted from the sum of standard molar entropies of reactants. The standard molar entropies are multiplied by the stoichiometric coefficient which is as per the balanced equation.

ΔrS°nS°(products)-nS°(reactants)

Explanation

The standard molar entropy change for the formation of CH4(g) is calculated below.

Given:

Refer to Appendix L for the values of standard entropies and enthalpies.

The standard entropy of CH4(g) is 186.26 J/Kmol.

The standard entropy of H2(g) is 130.7 J/Kmol.

The standard entropy of C(s) is 5.6 J/Kmol.

The balanced chemical equation is:

C(s) + 2H2(g)CH4(g)

The expression for the standard entropy change is,

ΔrS°nS°(products)-nS°(reactants)[[(1 mol CH4(g)/mol-rxn)S°[CH4(g)]

(b)

Interpretation Introduction

Interpretation:

The standard molar entropy change for the given reaction should be calculated.

Concept introduction:

Entropy is a measure of the randomness of the system. It is a thermodynamic quantity and an extensive property. It is represented by the symbol S. It can also be defined as the degree of energy dispersal. More the dispersal in energy, more is the value if entropy.

The standard entropy change for any reaction is the sum of standard molar entropies of product, subtracted from the sum of standard molar entropies of reactants. The standard molar entropies are multiplied by the stoichiometric coefficient which is as per the balanced equation.

ΔrS°nS°(products)-nS°(reactants)

(c)

Interpretation Introduction

Interpretation:

The standard molar entropy change for the given reaction should be calculated.

Concept introduction:

Entropy is a measure of the randomness of the system. It is a thermodynamic quantity and an extensive property. It is represented by the symbol S. It can also be defined as the degree of energy dispersal. More the dispersal in energy, more is the value if entropy.

The standard entropy change for any reaction is the sum of standard molar entropies of product, subtracted from the sum of standard molar entropies of reactants. The standard molar entropies are multiplied by the stoichiometric coefficient which is as per the balanced equation.

ΔrS°nS°(products)-nS°(reactants)

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