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The study of the relationships between heat, work, temperature, and energy is known as thermodynamics. The rules of thermodynamics define how energy evolves in a system and whether it can do beneficial work on its surroundings.

We can compute the amount of reactant molecules by first knowing that X is red and Y is green (on the left side). Initially, $3{\mathrm{X}}_2$molecules and $9{\mathrm{Y}}_2$molecules are interacting. On the right, we can see the reaction's results, which are molecules of ${\mathrm{XY}}_3$. As a result, we may write a response like this:

$3{\mathrm{X}}_2+9{\mathrm{Y}}_2→6{\mathrm{XY}}_3$

In general, to balance a chemical equation, the coefficients are reduced to the greatest extent feasible; in this example, we divide all of the coefficients by three, yielding a balanced reaction equation:

${\mathrm{X}}_2+3{\mathrm{Y}}_2→2{\mathrm{XY}}_3$

Therefore, the balanced equation is: ${\mathrm{X}}_2+3{\mathrm{Y}}_2→2{\mathrm{XY}}_3$.

The number of reacting/produced species may be used to assess the reaction entropy.

The total number of mol of substances interacting $1+3=4$is mol for reactants ( ${\mathrm{X}}_2$and ${\mathrm{Y}}_2$are employed).

A total of $2$mol of ${\mathrm{XY}}_3$molecules are created as products.

As a result of the reaction, the number of species drops from four to two, resulting in a reduction in system disorder. So, as the reaction progresses, the system's entropy lowers and we get: $\mathrm{Δ³\S }<0$.

Therefore, the sign is: $\mathrm{Δ³\S }<0$.

The molar entropy value may be compared based on the molecular complexity of the species, assuming that all of the species are present in the gaseous physical state (shown by the figure).

Both the reactants, ${\text{X}}_2$and ${\text{Y}}_2$, are diatomic simple molecules. Its product, ${\text{XY}}_3$, has four atoms bonded to one another. As a result, ${\text{XY}}_3$has a greater number of vibration modes and microstates, as well as a larger molar entropy.

Therefore, ${\text{XY}}_3$has the highest molar entropy