Question

Given
(i) ${\text{2F}}{{\text{e}}_{\text{2}}}{{\text{O}}_{\text{3}}}{\text{(s)}} \to {\text{4Fe(s) + 3}}{{\text{O}}_{\text{2}}}{\text{(g)}}$; ${\Delta _{\text{r}}}{{\text{G}}^o} = 1487.0{\text{kJmo}}{{\text{l}}^{ - 1}}$
(ii) ${\text{2CO(g) + }}{{\text{O}}_{\text{2}}}{\text{(g)}} \to {\text{2C}}{{\text{O}}_{\text{2}}}{\text{(g)}}$; ${\Delta _{\text{r}}}{{\text{G}}^o} = - 514.4{\text{kJmo}}{{\text{l}}^{ - 1}}$
Free energy change, ${\Delta _r}{G^o}$for the reaction, $2{\text{F}}{{\text{e}}_{\text{2}}}{{\text{O}}_{\text{3}}}{\text{(s)}} + 6{\text{CO(g)}} \to {\text{4Fe(s)}} + 6{\text{C}}{{\text{O}}_2}(g)$ will be?
A. $ - 112.4{\text{kJmo}}{{\text{l}}^{ - 1}}$
B. $ - 56.2{\text{kJmo}}{{\text{l}}^{ - 1}}$
C. $ - 208.0{\text{kJmo}}{{\text{l}}^{ - 1}}$
D. $ - 168.2{\text{kJmo}}{{\text{l}}^{ - 1}}$

Answer 1

Hint: Gibbs free energy is a thermodynamic potential that is used to calculate the maximum work that can be performed by a system at a constant pressure and temperature. Gibbs free energy is an intrinsic property, that is, its value depends on the amount of the substance. We shall add the two equations using appropriate amounts of substance to find the required value of free energy.

Complete step by step solution:
For the reaction (i)
${\text{2F}}{{\text{e}}_{\text{2}}}{{\text{O}}_{\text{3}}}{\text{(s)}} \to {\text{4Fe(s) + 3}}{{\text{O}}_{\text{2}}}{\text{(g)}}$, the free energy change is ${\Delta _{\text{r}}}{{\text{G}}^o} = 1487.0{\text{kJmo}}{{\text{l}}^{ - 1}}$
For the reaction (ii)
${\text{2CO(g) + }}{{\text{O}}_{\text{2}}}{\text{(g)}} \to {\text{2C}}{{\text{O}}_{\text{2}}}{\text{(g)}}$, the free energy change is ${\Delta _{\text{r}}}{{\text{G}}^o} = - 514.4{\text{kJmo}}{{\text{l}}^{ - 1}}$
We have to find the free energy change of the reaction, $2{\text{F}}{{\text{e}}_{\text{2}}}{{\text{O}}_{\text{3}}}{\text{(s)}} + 6{\text{CO(g)}} \to {\text{4Fe(s)}} + 6{\text{C}}{{\text{O}}_2}(g)$.
If we look carefully, we can see that the given reaction is a combination of the two given reactions as, $({\text{i}}) + 3({\text{ii}})$
So, the change in Gibbs free energy for the given reaction can be calculated on similar terms as it is an intrinsic property.
Thus, we can write that, ${\Delta _r}{G^o} = {\Delta _r}G_i^o + 3 \times {\Delta _r}G_{ii}^o$
${\Delta _r}{G^o} = 1487 + 3 \times \left( { - 514.4} \right)$
$\therefore {\Delta _r}{G^o} = - 56.2{\text{kJmo}}{{\text{l}}^{ - 1}}$

Thus, the correct option is B.

Note: The importance of the Gibbs function is that it is the single master variable that can determine whether a certain chemical change is thermodynamically possible. If the free energy of the reactants is greater than that of the products the reaction takes place spontaneously or in other words, if the free energy change is negative for a reaction, then it is spontaneous. $\Delta {G^o}$ is a key quantity in determining whether a reaction will take place in a given direction or not.