Question

The gibbs free energy of formation of $MO$ and $CO$ at temperature $1000{}^{\circ }C$ and $1900{}^{\circ }$ are given.
$2M+O_2\to 2MO;\Delta G_{1900{}^{\circ }C}=-300\text{kJ/mol}$
$\Delta G_{1000{}^{\circ }C}=-921\text{kJ/mol}$
$2C+O_2\to 2CO;\Delta G_{1900{}^{\circ }C}=-624\text{kJ/mol}$
$\Delta G_{1000{}^{\circ }C}=-423\text{kJ/mol}$

$MO+C\stackrel{\Delta }{\to }M+CO\uparrow$
The reaction is feasible at temperature $x$ then what is the value of $\frac{x}{500}$:

Answer 1

The given reactions are,
$2M+O_2\to 2MO$ ....(i)
If we reverse the direction of this reaction,
$2MO\to 2M+O_2$ ...(ii)
$2C+O_2\to 2CO$ ...(ii)

So (ii)+(iii) $\Rightarrow$
$2MO+2C\to 2M+2CO$

So, for the reaction,
$MO+C\stackrel{\Delta }{⟶}M+CO\uparrow \Delta G_{1000{}^{o}C}=\frac{921+(-423)}{2}\text{kJ/mol}=249\text{kJ/mol}$
Since $\Delta G_{1000{}^{o}C}$ has a positive value thus at this temperature the reaction is not spontaneous.
Again,
$\Delta G_{1900{}^{o}C}=\frac{300+(-624)}{2}\text{kJ/mol}=-162\text{kJ/mol}$

Since the $\Delta G_{1900{}^{o}C}$ has a negative value, hence at this temperature the reaction is spontaneous.

$\therefore x=1900{}^{\circ }C\Rightarrow \frac{x}{500}=\frac{1900}{500}=3.8$