Question

Consider the reaction

$\mathit{F}{\mathit{e}}_{\mathbf{2}}{\mathit{O}}_{\mathbf{3}}\left(s\right)\mathbf{+}\mathbf{3}{\mathit{H}}_{\mathbf{2}}\left(g\right)\mathbf{\to }\mathbf{2}\mathit{F}\mathit{e}\left(s\right)\mathbf{+}\mathbf{3}{\mathit{H}}_{\mathbf{2}}\mathit{O}\left(g\right)$

Assuming $\mathit{\Delta }{\mathit{H}}^{\mathbf{o}}$and $\mathit{\Delta }{\mathit{S}}^{\mathbf{o}}$do not depend on temperature, calculate the temperature where K =1.00 for thisreaction.

Short answer

Thetemperature where K =1.00 for this reaction is 725 K

Step-by-step solution

Step 1: Introduction to the Concept

Entropy is a characteristic of a system that quantifies the unpredictability or degree of chaos. It's a state function, after all. With an increase in the universe's entropy, spontaneous change occurs.

The mathematical equation for the standard entropy value at room temperature is given as follows,

$\Delta G^o=\Delta {G^o}_{298}=\sum n{G^o}_{298}\left(Products\right)-\sum p{G^o}_{298}\left(Reactants\right)-----\left(1\right)$

In the balanced chemical equation, n and p indicate the coefficients of reactants and products.

$\Delta {G^o}_R=-RTlnK-----\left(2\right)$

Where

R=Universal gas constant ($R=8.314J/mol-K$)

T=Temperature

Step 2: Determination of ΔGoRat K=1

From equation (2),

$\Delta {G^o}_R=-RTlnK$

Let’s put K=1,

$\Delta {G^o}_R=-RTln\left(1\right)$

$=0$

Step 3: Determination of ΔHRo

$\Delta H_R^o=\left[2\Delta H_f°\left(Fe\left(s\right)\right)+3\Delta H_f°\left(H_{2}O\left(g\right)\right)\right]-\left[1\Delta H_f°\left(F{e}_2{O}_3\left(s\right)\right)+3\Delta H_f°\left(H_2\left(g\right)\right)\right]$