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The law of mass action is a fundamental principle in chemistry that helps us understand how concentrations of substances influence the behavior of chemical reactions at equilibrium. According to this law, the equilibrium constant expression for a chemical reaction can be determined by the formula:

• \[K_c = \frac{[C]^c [D]^d}{[A]^a [B]^b}\]

Here,

• \([A]\), \([B]\), \([C]\), and \([D]\) are the molar concentrations of the reactants and products at equilibrium.
• The letters \(a\), \(b\), \(c\), and \(d\) serve as stoichiometric coefficients, representing the number of moles of each substance involved in the reaction.

By using this expression, we can relate the concentrations of different substances in a reversible reaction and predict the composition of the mixture at equilibrium.
Understanding the law of mass action is crucial when analyzing any reaction, and particularly when solving equilibrium problems like the decomposition of hydrogen sulfide (\(\mathrm{H}_2\mathrm{S}\)).This helps in constructing the correct equilibrium expressions necessary for calculating equilibrium constants.

A decomposition reaction is a type of chemical reaction where one compound breaks down into two or more simpler substances.
In the given problem, the decomposition of hydrogen sulfide, \(\mathrm{H}_2\mathrm{S}\), occurs:

• \[2 \mathrm{H}_{2} \mathrm{S}(g) \rightarrow 2 \mathrm{H}_{2}(g)+\mathrm{S}_{2}(g)\]

This reaction shows that each molecule of hydrogen sulfide decomposes to produce hydrogen gas and sulfur gas.
This process of breaking down can often be initiated by heat, which provides the energy needed to overcome the energy barrier of the decomposition.

Important Features of Decomposition Reactions:

- **Energy Requirement**: Often require an external energy source like heat or light.
- **Simplicity**: A single reactant gives multiple products.
- **Unidirectional**: Generally proceed in one direction, leading to simpler components.Understanding decomposition reactions helps in predicting the products and determining the stoichiometric coefficients used in chemical equilibrium expressions.

Stoichiometric coefficients are the numbers used to balance chemical equations. These numbers indicate the ratio in which substances react or form in a given chemical reaction.
In the decomposition of \(\mathrm{H}_{2}\mathrm{S}\), the balanced equation is:

• \[2 \mathrm{H}_{2} \mathrm{S}(g) \rightarrow 2 \mathrm{H}_{2}(g)+\mathrm{S}_{2}(g)\]

Key Points About Stoichiometric Coefficients:

- **Quantitative Measure**: They tell us the exact amount of reactants needed and products formed.
- **Determining Factors**: Help in establishing the correct proportions of substances involved.
- **Connected with Mole Concept**: Directly associated with the number of molecules, often corresponding to moles.Understanding stoichiometric coefficients allows us to write the correct equilibrium expression. This assures that the relationships between reactants and products are balanced, consistent with the law of mass action, which uses these coefficients to formulate accurate predictions of equilibrium constants.

Chemical equilibrium expressions provide a snapshot of the chemical system at the point where the rates of the forward and reverse reactions are equal.
At equilibrium, the actual amounts of substances in the reaction mixture remain constant over time.
In the case of \(\mathrm{H}_{2}\mathrm{S}\)'s decomposition, the chemical equilibrium expression is derived from the law of mass action, using the balanced equation:

• \[ K_c = \frac{[\mathrm{H}_2]^2 [\mathrm{S}_2]}{[\mathrm{H}_2\mathrm{S}]^2}\]

The equilibrium constant \(K_c\) helps us predict the concentrations of products and reactants at equilibrium.

Significance of Chemical Equilibrium Expressions:

- **Predictive Measure**: Indicates how far the reaction proceeds toward the products.
- **Reaction Direction**: A larger \(K_c\) means more product is formed; a smaller \(K_c\) implies more reactants remain.
- **Equilibrium Position**: Helps in assessing if the equilibrium lies to the left (favoring reactants) or right (favoring products).Crafting accurate chemical equilibrium expressions ensures a comprehensive understanding of the dynamic balance in chemical reactions, such as the one presented in this exercise.