Q20.44 P - Chemistry: Molecular Nature Of Matter And Change

Question

Oxyacetylene welding is used to repair metal structures, including bridges, buildings, and even the Statue of Liberty. Calculate ${\mathbf{\Delta S}}^{\mathbf{o}}$ for the combustion of $\mathbf{1}$ mole of acetylene ${\mathbf{C}}_{\mathbf{2}}{\mathbf{H}}_{\mathbf{2}}$.

Step-by-Step Solution

Answer

The ${\mathrm{\Delta S}}^{\mathrm{o}}$ for the combustion of $1$mole of acetylene is $\left({\mathrm{C}}_2{\mathrm{H}}_2\right)$ is ${\mathrm{\Delta S}}^{\circ }=-97.23\mathrm{J}/\mathrm{K}$.

Step 1: Concept Introduction.

Entropy is a measure of a system's unpredictability or disorder in general.

Entropy is a thermodynamic property that describes how a system behaves in terms of temperature, pressure, entropy, and heat capacity.

Step 2: Reaction and values for Entropy of Compounds.

First, write and balance the reaction of the combustion of 1 mole of ${\mathrm{C}}_2{\mathrm{H}}_2$.

${\mathrm{C}}_2{\mathrm{H}}_2\left(\mathrm{g}\right)+\frac{5}{2}{\mathrm{O}}_2\left(\mathrm{g}\right)\to 2{\mathrm{CO}}_2\left(\mathrm{g}\right)+{\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right)$

Next, list the values for ${\mathrm{S}}^{\circ }$of each compound.

$\begin{array}{c}{\mathrm{S}}^{\circ }\left({\mathrm{C}}_2{\mathrm{H}}_2\left(\mathrm{g}\right)\right) = 200.85\mathrm{J}/\mathrm{mol}·\mathrm{K}\\ {\mathrm{S}}^{\circ }\left({\mathrm{O}}_2\left(\mathrm{g}\right)\right) =205.0\mathrm{J}/\mathrm{mol}·\mathrm{K}\\ {\mathrm{S}}^{\circ }\left({\mathrm{C}}_2\right) = 213.7\mathrm{J}/\mathrm{mol}·\mathrm{K}\\ {\mathrm{S}}^{\circ }\left({\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right)\right) = 188.72\mathrm{J}/\mathrm{mol}·\mathrm{K}\end{array}$

Step 3: Calculation for Entropy.

Solve to find the value for entropy –

$\begin{array}{c}{\mathrm{\Delta S}}^{\circ }= \sum {\mathrm{n}}_{\mathrm{p}}{\mathrm{S}}^{\circ }\left(\mathrm{product}\right)-\sum {\mathrm{n}}_{\mathrm{r}}{\mathrm{S}}^{\circ }\left(\mathrm{reactant}\right)\\ = \left[{\mathrm{nS}}^{\circ }\left({\mathrm{CO}}_2\left(\mathrm{g}\right)\right)+{\mathrm{nS}}^{\circ }\left({\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right)\right)\right]-\left[{\mathrm{nS}}^{\circ }\left({\mathrm{C}}_2{\mathrm{H}}_2\left(\mathrm{g}\right)\right)+{\mathrm{nS}}^{\circ }\left({\mathrm{O}}_2\left(\mathrm{g}\right)\right)\right]\\ = \left(\left[2\right(213.7)+1(188.72\left)\right]-\left[1(200.85)+\frac{5}{2}(205.0)\right]\right)\mathrm{J}/\mathrm{K}\\ {\mathrm{\Delta S}}^{\circ }= -97.23\mathrm{J}/\mathrm{K}\end{array}$

 

Therefore, the value for entropy is obtained as ${\mathrm{\Delta S}}^{\circ }= -97.23\mathrm{J}/\mathrm{K}$.