Question

The standard free energies of formation and the standard enthalpies of formation at 298 K for difluoroacetylene (C) and hexafluorobenzene (${\mathit{C}}_{\mathbf{6}}{\mathit{F}}_{\mathbf{6}}$
) areFor the following reaction:

${\mathit{C}}_{\mathbf{6}}{\mathit{F}}_{\mathbf{6}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{\iff }\mathbf{3}{\mathit{C}}_{\mathbf{2}}{\mathit{F}}_{\mathbf{2}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}$

a. calculate$\mathit{\Delta }{\mathit{S}}^{\mathbf{o}}$at 298 K.
b. calculate K at 298 K.
c. estimate K at 3000. K, assuming $\Delta H^{\mathrm{o}}$and $\Delta S^{\mathrm{o}}$do not depend on temperature.

Short answer

a) $\mathit{\Delta }{\mathit{S}}^{\mathbf{o}}$at 298 K is $\mathbf{0}\mathbf{.}\mathbf{321}\mathit{k}\mathit{J}\mathbf{/}\mathit{m}\mathit{o}\mathit{l}\mathbf{-}\mathit{K}$.

b) K at 298 is $\mathbf{1}\mathbf{.}\mathbf{45}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{87}}$.

c) K at 3000 is$\mathbf{2}\mathbf{.}\mathbf{98}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{6}}$

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,

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

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

$\mathit{\Delta }{{\mathbf{G}}^{\mathbf{o}}}_{\mathbf{298}}\mathbf{=}\mathit{\Delta }{\mathit{H}}^{\mathbf{o}}\mathbf{-}\mathit{T}\mathit{\Delta }{\mathit{S}}^{\mathbf{o}}\mathbf{-}\mathbf{-}\mathbf{-}\mathbf{-}\mathbf{-}\left(2\right)$

$\mathit{\Delta }{{\mathbf{G}}^{\mathbf{o}}}_{\mathbf{R}}\mathbf{=}\mathbf{-}\mathit{R}\mathit{T}\mathit{l}\mathit{n}\mathit{K}\mathbf{-}\mathbf{-}\mathbf{-}\mathbf{-}\mathbf{-}\left(3\right)$

Step 2: Determination of ΔHo

The given reaction,

$C_6{F}_6\left(g\right)\iff 3C_2{F}_2\left(g\right)$