Question

For the reaction ${\mathbf{H}}_{\mathbf{2}}\mathbf{O}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{+}\mathbf{C}{\mathbf{l}}_{\mathbf{2}}\mathbf{O}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{\to }\mathbf{2}\mathbf{HClO}\mathbf{\left(}\mathbf{g}\mathbf{\right)}$, you know ${\mathbf{\Delta S}}_{\mathbf{rxn}}^{\mathbf{o}}$and role="math" localid="1663351267020" ${\mathbf{S}}^{\mathbf{o}}$of HClO(g) and of ${\mathbf{H}}_{\mathbf{2}}\mathbf{O}$(g). Write an expression that can be used to determine${\mathbf{S}}^{\mathbf{o}}$of${\mathbf{\text{Cl}}}_{\mathbf{2}}\mathbf{O}$(g).

Short answer

The expression which will be determined is: ${{\mathrm{S}}^o}_{{\mathrm{Cl}}_2\mathrm{O}\left(\mathrm{g}\right)}=2\times {{\mathrm{S}}^o}_{\mathrm{HClO}\left(\mathrm{g}\right)}-{\mathrm{S}}_{{\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right)}-{\mathrm{\Delta S}}_{\mathrm{rxn}}$.

Step-by-step solution

Entropy of a reaction.

The standard entropy of a reaction is the difference in the total standard entropy of the products and the total standard entropy of the reactants.

Explanation.

It is well understood that entropy is a state function (so it does not depend on the path, only on the beginning and end). As a result, the change in entropy may be estimated as follows:

${\mathrm{\Delta S}}_{\mathrm{rxn}}=\sum {\mathrm{S}}_{\mathrm{products}}+\sum {\mathrm{S}}_{\mathrm{reactants}}$

For the hypochlorous acid (HClO) production process as:

$\begin{array}{c}{\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right)+\mathrm{C}{\mathrm{l}}_2\mathrm{O}\left(\mathrm{g}\right)\to 2\mathrm{HClO}\left(\mathrm{g}\right)\\ \mathrm{\Delta }{{\mathrm{S}}^o}_{\mathrm{rxn}}=2{{\mathrm{S}}^o}_{\mathrm{HClO}\left(\mathrm{g}\right)}-({{\mathrm{S}}^o}_{{\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right)}+{{\mathrm{S}}^o}_{{\mathrm{Cl}}_2\mathrm{O}\left(\mathrm{g}\right)})\end{array}$

As a result, the ${\mathrm{S}}_{{\mathrm{Cl}}_2\mathrm{O}\left(\mathrm{g}\right)}$ may be written as:

${{\mathrm{S}}^o}_{{\mathrm{Cl}}_2\mathrm{O}\left(\mathrm{g}\right)}=2{{\mathrm{S}}^o}_{\mathrm{HClO}\left(\mathrm{g}\right)}-{{\mathrm{S}}^o}_{{\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right)}-\mathrm{\Delta }{{\mathrm{S}}^o}_{\mathrm{rxn}}$

Therefore, the expression is: ${{\mathrm{S}}^o}_{{\mathrm{Cl}}_2\mathrm{O}\left(\mathrm{g}\right)}=2{{\mathrm{S}}^o}_{\mathrm{HClO}\left(\mathrm{g}\right)}-{{\mathrm{S}}^o}_{{\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right)}-\mathrm{\Delta }{{\mathrm{S}}^o}_{\mathrm{rxn}}$.