Question

Using Appendix 4 and the following data, determine $S^o$for
$Fe{\left(CO\right)}_5\left(g\right)$
$\text{Fe}\left(s\right)+5CO\left(g\right)\to Fe{\left(CO\right)}_5\left(g\right)\Delta S^o=?$
${\text{Fe(CO)}}_5(l)\to Fe{\left(CO\right)}_5(g)∆S^o=107J/K$

${\text{Fe(s)+5CO(g)→Fe(CO)}}_5(l)∆S^o=-677J/K$

Short answer

The$S^o$ for $\text{Fe}{\left(CO\right)}_5\left(g\right)$is $447J/mol-K$.

Step-by-step solution

Introduction to the Concept

Entropy is a characteristic of a system that quantifies the unpredictability or degree of chaos. It’s a state function. 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:

$\Delta S_R^{o}298=\sum n_p{S}_f^{o}298\left(Products\right)-\sum n_r{S}_f^{o}298\left(Reactants\right)-----\left(1\right)$

In the balanced chemical equation, $n_p$ and $n_r$ indicate the coefficients of reactants and products.

Explanation

The given reaction is:

$Fe{\left(CO\right)}_5(l)\to Fe{\left(CO\right)}_5(g)∆{S^o}_1=107J/K-----(1)$

$Fe\left(s\right)+5CO(g)\to Fe{\left(CO\right)}_5(l)∆S^o=-677J/K-----(2)$

Let’s add equations (1) and (2).

$Fe\left(s\right)+5CO\left(g\right)\to Fe{\left(CO\right)}_5\left(l\right)\Delta S^o=\Delta S_1^o+\Delta S_2^o$

$\Delta S^o=107-677$

$∆S^o=-570J/K$

From equation (1),

$\Delta S_R^o=\left[1S_f^{o}Fe{\left(CO\right)}_5\left(g\right)\right]-\left[1S_f^o\left(Fe\left(s\right)\right)+5S_f^o\left(CO\left(g\right)\right)\right]$

$-570J/K=[{S_f}^{o}Fe{\left(CO\right)}_5(g\left)\right]-[1mole\times 27J/mol-K+5mole\times 198J/mol-K]$

$-570J/K=[{S_f}^{o}Fe{\left(CO\right)}_5(g\left)\right]-27-990$

${S_f}^{o}Fe{\left(CO\right)}_5(g)=447J/mol-K$

Therefore the value of localid="1648624439262" $Fe{\left(CO\right)}_5\left(g\right)$is 447 J/mol-k .