# Calculate the standard entropy change for the following reactions at 25 °C. Comment on the sign of Δ r S °. (a) 2 Na(s) + 2 H 2 O( ℓ ) → 2 NaOH(aq) + H 2 (g) (b) Na 2 CO 3 (s) + 2 HCl(aq) → 2 NaCl(aq) + H 2 O( ℓ ) + CO 2 (g)

### Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640

Chapter
Section

### Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640
Chapter 18, Problem 8PS
Textbook Problem
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## Calculate the standard entropy change for the following reactions at 25 °C. Comment on the sign of ΔrS°.(a) 2 Na(s) + 2 H2O(ℓ) → 2 NaOH(aq) + H2(g)(b) Na2CO3(s) + 2 HCl(aq) → 2 NaCl(aq) + H2O(ℓ) + CO2(g)

(a)

Interpretation Introduction

Interpretation:

The standard entropy changes for reaction 2Na(s)+2H2O(l)2NaOH(aq)+H2(g) 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 of Solution

The standard entropy change for the reaction of sodium with water is calculated below.

Given: 2Na(s)+2H2O(l)2NaOH(aq)+H2(g)

The standard entropy of NaOH(aq) is 48.1 J/Kmol

The standard entropy of Na(s) is 51.21 J/Kmol

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

The standard entropy of H2O(l) is 69.95 J/Kmol

The balanced chemical equation for the reaction of sodium with water is 2Na(s)+2H2O(l)2NaOH(aq)+H2(g)

The expression for the standard entropy change is,

ΔrS°=nS°(products)nS°(reactants)=[[(2 mol NaOH(aq)/mol-rxn)S°[NaOH(aq)]+(1 mol H2(g)/mol-rxn)S°

(b)

Interpretation Introduction

Interpretation:

The standard entropy changes for reaction Na2CO3(s)+2HCl(aq)2NaCl(aq)+H2O(l)+CO2(g) 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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