91Ó°ÊÓ

Thermodynamics is the study of the connections between heat, work, temperature, and energy. Thermodynamic principles specify how energy develops within a system and whether it is capable of having a positive impact on its surroundings.

First, construct and balance the ${\mathrm{SO}}_2$and$\mathrm{Ca}(\mathrm{OH}{)}_2$ reaction equation.

role="math" localid="1663363989729" ${\mathrm{SO}}_2\left(\mathrm{g}\right)+\mathrm{Ca}(\mathrm{OH}{)}_2\left(\mathrm{s}\right)→{\mathrm{CaSO}}_3\left(\mathrm{s}\right)+{\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right)$

After that, make a list of the ${\mathrm{Δ³\S }}^{\mathrm{o}}$values for each compound.

$\begin{array}{c}\mathrm{S}°\left({\mathrm{SO}}_2\left(\mathrm{g}\right)\right)=248.1\mathrm{J}/\mathrm{mol}\mathrm{K}\\ \mathrm{S}°\left(\mathrm{Ca}(\mathrm{OH}{)}_2\left(\mathrm{s}\right)\right)=83.39\mathrm{J}/\mathrm{mol}\mathrm{K}\\ \mathrm{S}°\left({\mathrm{CaSO}}_3\left(\mathrm{s}\right)\right)=101.4\mathrm{J}/\mathrm{mol}\mathrm{K}\\ \mathrm{S}°\left({\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right)\right)=69.94\mathrm{J}/\mathrm{mol}\mathrm{K}\end{array}$

Solve for the ${\mathrm{Δ³\S }}^{\mathrm{o}}$now as:

role="math" localid="1663363974961" $\begin{array}{c}{\mathrm{Δ³\S }}^{\mathrm{o}}=∑{\mathrm{n}}_{\mathrm{p}}{\mathrm{S}}^{\mathrm{o}}\left(\mathrm{product}\right)-∑{\mathrm{n}}_{\mathrm{r}}{\mathrm{S}}^{\mathrm{o}}\left(\mathrm{reactant}\right)......................\left(1\right)\\ =\left[{\mathrm{nS}}^{\mathrm{o}}\left({\mathrm{CaSO}}_3\left(\mathrm{s}\right)\right)+{\mathrm{nS}}^{\mathrm{o}}({\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right))\right]-\left[{\mathrm{nS}}^{\mathrm{o}}(\mathrm{S}{\mathrm{O}}_2\left(\mathrm{g}\right))+\mathrm{n}{\mathrm{S}}^{\mathrm{o}}\left(\mathrm{Ca}(\mathrm{OH}{)}_2\left(\mathrm{s}\right)\right)\right]..............\left(2\right)\\ =\left(\left[1\right(101.4)+1(69.94\left)\right]-\left[1(248.1)+1(83.39)\right]\right)\mathrm{J}/\mathrm{K}........................\left(3\right)\\ {\mathrm{Δ³\S }}^{\mathrm{o}}=-160.15\mathrm{J}/\mathrm{K}...............................................................\left(4\right)\end{array}$

Therefore, the value is ${\mathrm{Δ³\S }}^{\mathrm{o}}=-160.15\mathrm{J}/\mathrm{K}$.

The balanced equation is ${\mathrm{SO}}_2\left(\mathrm{g}\right)+\mathrm{Ca}(\mathrm{OH}{)}_2\left(\mathrm{s}\right)→{\mathrm{CaSO}}_3\left(\mathrm{s}\right)+{\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right)$ .