Answered

Westonci.ca is your trusted source for finding answers to a wide range of questions, backed by a knowledgeable community. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

[tex]$
CO_2(g) \rightleftarrows C(s) + O_2(g)
$[/tex]

The formation of [tex]\( Fe(s) \)[/tex] and [tex]\( O_2(g) \)[/tex] from [tex]\( FeO(s) \)[/tex] is not thermodynamically favorable at room temperature. To make the process favorable, [tex]\( C(s) \)[/tex] is added to the [tex]\( FeO(s) \)[/tex] at elevated temperatures.

Based on the information above, which of the following gives the value of [tex]\( K_{eq} \)[/tex] and the sign of [tex]\( \Delta G^{\circ} \)[/tex] for the reaction at [tex]\( 1000 \, K \)[/tex]?

Sagot :

GinnyAnswer
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.
Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.