Q20.39 P - Chemistry: Molecular Nature Of Matter And Change

Question

Find ${\mathbf{\Delta S}}^{\mathbf{o}}$ for the formation of  ${\mathbf{\text{CU}}}_{\mathbf{2}}\mathbf{\text{O}}$(s) from its elements.

Step-by-Step Solution

Answer

The ${\mathrm{\Delta S}}^{\circ }$is obtained as: $-75.6\mathrm{J}/\mathrm{K}$.

Step 1: Define Thermodynamics .

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.

Step 2: Evaluating the ΔS o .

Copper and oxygen combine to generate ${\mathrm{Cu}}_2\mathrm{O}$. Write the reaction equation for the creation of $1$ mole of ${\mathrm{Cu}}_2\mathrm{O}$ and balance it.

$2\mathrm{CuS}\left(\mathrm{s}\right)+\frac{1}{2}{\mathrm{O}}_2\left(\mathrm{g}\right)\to {\mathrm{Cu}}_2\mathrm{O}\left(\mathrm{s}\right)$

After that, make a list of each compound ${\mathrm{\Delta S}}^{\mathrm{o}}$ values:

$\begin{array}{l}{\mathrm{S}}^{\circ }\left(\mathrm{Cu}\left(\mathrm{S}\right)\right)=33.1\mathrm{J}/\mathrm{mol} \mathrm{K}\\ {\mathrm{S}}^{\circ }\left({\mathrm{O}}_2\left(\mathrm{g}\right)\right)=205.0\mathrm{J}/\mathrm{mol} \mathrm{K}\\ {\mathrm{S}}^{\circ }\left({\mathrm{Cu}}_2\mathrm{O}\left(\mathrm{S}\right)\right)=93.1\mathrm{J}/\mathrm{mol} \mathrm{K}\end{array}$

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

$\begin{array}{c}{\mathrm{\Delta S}}^{\circ }=\sum {\mathrm{n}}_{\mathrm{p}}{\mathrm{S}}^{\circ }\left(\mathrm{product}\right)-\sum {\mathrm{n}}_{\mathrm{r}}{\mathrm{S}}^{\circ }\left(\mathrm{reactant}\right)......................\left(1\right)\\ =\left[{\mathrm{nS}}^{\circ }\left({\mathrm{Cu}}_2\mathrm{O}\left(\mathrm{s}\right)\right)\right]-\left[{\mathrm{nS}}^{\circ }\left(\mathrm{Cu}\right(\mathrm{s}\left)\right)+{\mathrm{nS}}^{\circ }\left({\mathrm{O}}_2\left(\mathrm{g}\right)\right)\right]..............\left(2\right)\\ =\left(\left[\right(93.1\left)\right]-\left[2(33.1)+\frac{1}{2}(205.0)\right]\right)\mathrm{J}/\mathrm{K}........................\left(3\right)\\ {\mathrm{\Delta S}}^{\circ }=-75.6\mathrm{J}/\mathrm{K}...............................................................\left(4\right)\end{array}$

Therefore, the value is: ${\mathrm{\Delta S}}^{\circ }=-75.6\mathrm{J}/\mathrm{K}$.