   # Calculate the standard entropy change for the following reactions at 25 °C. Comment on the sign of Δ r S °. (a) 2 Al(s) + 3 Cl 2 (g) → 2 AlCl 3 (s) (b) 2 CH 3 OH( ℓ ) + 3 O 2 (g) → 2 CO 2 (g) + 4 H 2 O(g) ### Chemistry & Chemical Reactivity

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

#### Solutions

Chapter
Section ### Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640
Chapter 18, Problem 7PS
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 Al(s) + 3 Cl2(g) → 2 AlCl3(s) (b) 2 CH3OH(ℓ) + 3 O2(g) → 2 CO2(g) + 4 H2O(g)

(a)

Interpretation Introduction

Interpretation:

The standard entropy changes for reaction 2Al(s)+3Cl2(g)2AlCl3(s) 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 formation of AlCl3 is calculated below.

Given: 2Al(s)+3Cl2(g)2AlCl3(s)

The standard entropy of AlCl3(s) is 109.29 J/Kmol

The standard entropy of Al(s) is 28.3 J/Kmol

The standard entropy of Cl2(g) is 223.08 J/Kmol

The balanced chemical equation for the formation of AlCl3 is 2Al(s)+3Cl2(g)2AlCl3(s).

The expression for the standard entropy change is,

ΔrS°=nS°(products)nS°(reactants)=[[(2 mol AlCl3(s)/mol-rxn)S°[ AlCl3(s)

(b)

Interpretation Introduction

Interpretation:

The standard entropy changes for reaction 2CH3OH(l)+3O2(g)2CO2(g)+4H2O(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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