Question

In $\Delta G$ = -177Kcal for,
(1) $2Fe(s)+\dfrac{3}{2}{{O}_{2}}(g)\to F{{e}_{2}}{{O}_{3}}(s)$ and, $\Delta G$= -19 Kcal for
(2) $4F{{e}_{2}}{{O}_{3}}(s)+Fe(s)\to 3F{{e}_{3}}{{O}_{4}}(s)$
What is the Gibbs free energy of the formation of $F{{e}_{3}}{{O}_{4}}$ ?
(A) +296kcal/mol
(B) -242.3kcal/mol
(C) -727 kcal/mol
(D) -229.6 kcal/mol

Answer 1

Hint: Gibbs free energy which combines enthalpy and entropy into a single value is denoted as G. the sum of enthalpy with a product of temperature and the entropy of the system indicates the change in free energy $\Delta G$ . The Gibbs free energy change can be predicting the direction of the chemical reactions at constant temperature and constant pressure.

Complete step by step solution:
The energy which is associated with a chemical reaction that can be used to do work is Gibbs free energy of a system, which is the sum of enthalpy, the product of temperature, and the entropy of the system.
$G = H – TS$
A spontaneous reaction is considered to be natural because this reaction occurs by itself without any external actions towards it and a non-spontaneous reaction needs constant energy during the process.
In a chemical reaction involving the change in thermodynamic quantities, the above equation changes into,
$\Delta G=\Delta H-T\Delta S$
Given chemical reactions,
$2Fe(s)+\dfrac{3}{2}{{O}_{2}}(g)\to F{{e}_{2}}{{O}_{3}}(s)$, $\Delta G$ = -177Kcal --- (1)
$4F{{e}_{2}}{{O}_{3}}(s)+Fe(s)\to 3F{{e}_{3}}{{O}_{4}}(s)$, $\Delta G$ = -19 Kcal --- (2)
Multiplying Equation (1) with $\dfrac{4}{3}$ ,
$\dfrac{8}{3}Fe(s)+2{{O}_{2}}(g)\to \dfrac{4}{3}F{{e}_{2}}{{O}_{3}}(s),\Delta G=-\dfrac{4}{3}(177)=-236Kcal$ ------ (3)
Multiplying equation (2) with $\dfrac{1}{3}$ ,
$\dfrac{4}{3}F{{e}_{2}}{{O}_{3}}(s)+\dfrac{1}{3}Fe(s)\to F{{e}_{3}}{{O}_{4}}(s),\Delta G=-\dfrac{19}{3}=-6.34Kcal$ ------ (4)
Equation (3) + equation (4)
$3Fe(s)+2{{O}_{2}}(g)\to F{{e}_{3}}{{O}_{4}},\Delta G=-242.3Kcal$
Hence, the Gibbs free energy of the formation of $F{{e}_{3}}{{O}_{4}}$= -242.3Kcal

The correct answer is option B.

Note: If the Gibbs free energy is positive for a reaction is nonspontaneous which means an input of external energy is required for the reaction and if Gibbs free energy is negative for a reaction is spontaneous which means the reaction occurred without external energy requirement.