Chemistry & Chemical Reactivity

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



Chemistry & Chemical Reactivity

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

Elemental boron, in the form of thin fibers, can be made by reducing a boron halide with H2.

BCl3(g) + 3 2 H2(g) → B(s) + 3 HCl(g)

Calculate ΔrH°, ΔrS°, and ΔrG° at 25 °C for this reaction. Is the reaction predicted to be product-favored at equilibrium at 25 °C? If so, is it enthalpy- or entropy-driven? [S° for B(s) is 5.86 J/K · mol.]

Interpretation Introduction


The value of ΔrH° ,ΔrS° and ΔrG for formation of elemental boron should be calculated under given conditions.

Concept introduction:

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


Here, ΔrH is the change in enthalpy and ΔrS is the change in entropy.


The value of ΔrH°, ΔrS° and ΔrG for formation of elemental boron calculated below.

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

The standard entropy of B(s) is 5.86 J/Kmol.

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

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

The standard entropy of BCl3(g) is  290.17 J/Kmol.

The standard enthalpy of B(s) is 0 kJ/mol.

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

The standard enthalpy of H2(g) is 0 kJ/mol.

The standard enthalpy of BCl3(g) is 402.96 kJ/mol.

The balanced chemical equation is:

  BCl3(g) + 32H2(g)B(s) + 3HCl(g)

ΔrH°=nΔfH°(products)nΔfH°(reactants)=[[(1 mol B(s)/mol-rxn)ΔfH°[B(s)]+(3 mol HCl(g)/mol-rxn)ΔfH°[HCl(g)]] [(1 mol BCl3(g)/mol-rxn)ΔfH°[BCl3(g)]+(1.5 mol H2(g)/mol-rxn)ΔfH°[H2(g)]]] 

Substituting the enthalpy values,

ΔrH°=[[(1 mol B(s)/mol-rxn)(0 kJ/mol)+(3 mol HCl(g)/mol-rxn)(92.31 kJ/mol)] [(1 mol BCl3(g)/mol-rxn)(402.96 kJ/mol)+(1

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