Answer :
Let's break down the problem step-by-step:
### Understanding the Reaction
The given reaction is:
[tex]\[ CO_2 (g) \rightleftarrows C (s) + O_2 (g) \][/tex]
The problem further states that the formation of iron ([tex]$Fe$[/tex]) and oxygen ([tex]$O_2$[/tex]) from iron(II) oxide ([tex]$FeO$[/tex]) is not thermodynamically favorable at room temperature. To overcome this issue, carbon ([tex]$C$[/tex]) is added to the [tex]$FeO (s)$[/tex] at elevated temperatures.
### Temperature and Thermodynamic Favorability
Since the formation reactions aren't favorable at room temperature, we analyze the conditions at an elevated temperature, specifically at 1000 K.
### Thermodynamic Parameters at Elevated Temperature
Given the conditions at 1000 K:
- The equilibrium constant ([tex]$K_{eq}$[/tex]) at this temperature is found to be 200.
- The change in Gibbs free energy ([tex]\(\Delta G^{\circ}\)[/tex]) is -20000 J (or -20 kJ considering conversion).
### Analyzing the Parameters
1. Equilibrium Constant [tex]\(K_{eq}\)[/tex]
- [tex]$K_{eq}$[/tex] value of 200 at 1000 K indicates a strongly favorable position for the products (C and [tex]\(O_2\)[/tex]) compared to the reactants ([tex]\(CO_2\)[/tex]).
2. Gibbs Free Energy, [tex]\(\Delta G^{\circ}\)[/tex]
- A negative [tex]\(\Delta G^{\circ}\)[/tex] value of -20000 J at 1000 K means the reaction is spontaneous at this temperature.
### Conclusion
For the reaction [tex]\( CO_2(g) \rightleftarrows C (s) + O_2(g)\)[/tex] at 1000 K:
- The equilibrium constant [tex]\(K_{eq}\)[/tex] is 200.
- The sign of [tex]\(\Delta G^{\circ}\)[/tex] is negative, specifically -20000 J.
These numerical results indicate that at 1000 K, the reaction is both thermodynamically favorable and spontaneous.
### Understanding the Reaction
The given reaction is:
[tex]\[ CO_2 (g) \rightleftarrows C (s) + O_2 (g) \][/tex]
The problem further states that the formation of iron ([tex]$Fe$[/tex]) and oxygen ([tex]$O_2$[/tex]) from iron(II) oxide ([tex]$FeO$[/tex]) is not thermodynamically favorable at room temperature. To overcome this issue, carbon ([tex]$C$[/tex]) is added to the [tex]$FeO (s)$[/tex] at elevated temperatures.
### Temperature and Thermodynamic Favorability
Since the formation reactions aren't favorable at room temperature, we analyze the conditions at an elevated temperature, specifically at 1000 K.
### Thermodynamic Parameters at Elevated Temperature
Given the conditions at 1000 K:
- The equilibrium constant ([tex]$K_{eq}$[/tex]) at this temperature is found to be 200.
- The change in Gibbs free energy ([tex]\(\Delta G^{\circ}\)[/tex]) is -20000 J (or -20 kJ considering conversion).
### Analyzing the Parameters
1. Equilibrium Constant [tex]\(K_{eq}\)[/tex]
- [tex]$K_{eq}$[/tex] value of 200 at 1000 K indicates a strongly favorable position for the products (C and [tex]\(O_2\)[/tex]) compared to the reactants ([tex]\(CO_2\)[/tex]).
2. Gibbs Free Energy, [tex]\(\Delta G^{\circ}\)[/tex]
- A negative [tex]\(\Delta G^{\circ}\)[/tex] value of -20000 J at 1000 K means the reaction is spontaneous at this temperature.
### Conclusion
For the reaction [tex]\( CO_2(g) \rightleftarrows C (s) + O_2(g)\)[/tex] at 1000 K:
- The equilibrium constant [tex]\(K_{eq}\)[/tex] is 200.
- The sign of [tex]\(\Delta G^{\circ}\)[/tex] is negative, specifically -20000 J.
These numerical results indicate that at 1000 K, the reaction is both thermodynamically favorable and spontaneous.
