Question

How would you calculate the standard entropy change for the combustion of methanol at \[{25^ \circ }{\text{C}}\]? \[{\text{2C}}{{\text{H}}_3}{\text{OH(}}\lambda {\text{) + 3}}{{\text{O}}_2}({\text{g}}) \to 2{\text{C}}{{\text{O}}_2}({\text{g}}) + 4{{\text{H}}_2}{\text{O(g)}}\]

Species	\[{S^ \circ }({\text{J/K - mol}})\]
\[{\text{C}}{{\text{H}}_3}{\text{OH(}}\lambda {\text{)}}\]	\[127.2\]
\[{{\text{O}}_2}({\text{g}})\]	\[205.1\]
\[{\text{C}}{{\text{O}}_2}(g)\]	\[213.7\]
\[{{\text{H}}_2}{\text{O(g)}}\]	\[188.8\]

Answer 1

Hint: The standard entropy of reaction helps us determine whether the reaction will take place or not because molar entropy is not the same for all gases. Under identical conditions, it is greater for a heavier gas. According to the second law of thermodynamics, a spontaneous reaction always results in an increase in total entropy of the system and its surroundings.

Complete step-by-step answer:
To calculate entropy first we need to know what it actually stands for, entropy is a scientific concept, as well as a measurable physical property that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynamics, where it was first recognized, to the microscopic description of nature in statistical physics, and to the principles of information theory. It has found far-ranging applications in chemistry and physics, biological systems and their relation to life, cosmology, economics, sociology, weather science and climate change, and information system and the transmission of information in telecommunication.
\[\Delta {{\text{S}}^ \circ } = \sum\limits_{}^{} {[{{\text{S}}^ \circ }{\text{products}}] - \sum\limits_{}^{} {[{{\text{S}}^ \circ }{\text{reactants}}]} } \]
The standard molar entropy is the entropy content of one mole of pure substance under a standard state [not standard temperature and pressure]. The standard molar entropy is generally given the symbol \[{{\text{S}}^ \circ }\], and has units of joules per mole kelvin (\[{\text{J}} \cdot {\text{mo}}{{\text{l}}^{ - 1}} \cdot {{\text{K}}^{ - 1}}\]), the value of \[{{\text{S}}^ \circ }\] is absolute. That is, an element in its standard state has a definite, nonzero value of S at room temperature. The entropy of a pure crystalline structure can be 0 \[{\text{J}} \cdot {\text{mo}}{{\text{l}}^{ - 1}} \cdot {{\text{K}}^{ - 1}}\] only at \[{\text{0 K}}\], according to the third law of thermodynamics.


However, this assumes that the material forms a 'perfect crystal' without any frozen entropy (crystallographic defects, dislocations), which is never completely true because crystals always grow at a finite temperature. However, this residual entropy is usually quite negligible.
\[\Rightarrow \Delta {{\text{S}}^ \circ } = \sum\limits_{}^{} {[{{\text{S}}^ \circ }{\text{products}}] - \sum\limits_{}^{} {[{{\text{S}}^ \circ }{\text{reactants}}]} } \]
\[\Rightarrow \Delta {{\text{S}}^ \circ }\] = \[(2 \times 213.7 + 4 \times 188.8) - (2 \times 127.2 + 3 \times 205.1)\]
\[\Rightarrow \Delta {{\text{S}}^ \circ }\]= \[1,182.6 - 869.7\]
\[\Rightarrow \Delta {{\text{S}}^ \circ }\]= \[ + 312.9{\text{J/K}}{\text{.mol}}\]

Note: The standard entropy change is equal to the sum of all the standard entropies of the products minus the sum of all the standard entropies of the reactants. As the temperature of the substance increases, its entropy increases because of an increase in molecular motion. The entropy of a pure crystalline substance at absolute zero is defined to be equal to zero.