91Ó°ÊÓ

In the realm of chemical equilibrium, the equilibrium constant, denoted as \( K_{c} \), is a fundamental concept to understand. It provides a quantitative measure to describe the proportion of products to reactants at equilibrium in a reversible chemical reaction. The equilibrium constant expression for a reaction is derived from the balanced chemical equation. For the synthesis of ethyl acetate from acetic acid and ethanol, the expression is as follows:\[K_{c} = \frac{[\text{CH}_3\text{CO}_2\text{CH}_2\text{CH}_3][\text{H}_2\text{O}]}{[\text{CH}_3\text{CO}_2\text{H}][\text{CH}_3\text{CH}_2\text{OH}]} \]It is essential to remember that only concentrations of substances in the gaseous or aqueous state are included in these expressions. The value of \( K_{c} \) helps us determine the position of equilibrium; whether it favors products (\( K_{c} > 1 \)) or reactants (\( K_{c} < 1 \)).
Understanding the equilibrium constant gives insight into how a system behaves when achieving a state of balance. This allows chemists to manipulate conditions to drive reactions towards the desired products.

Concentration calculations are pivotal when determining the equilibrium constant \(K_{c}\). Initially, concentrations are calculated based on the initial amounts of reactants and their volume, even though the specific volume value ultimately does not affect calculations of \(K_{c}\).
In our given problem, we start with \(1.00\,\mathrm{mol}\) each of acetic acid and ethanol in solution. Their concentrations can be expressed as \(\frac{1.00}{V}\), where \(V\) is the volume. As the reaction progresses to equilibrium, \(0.65\,\mathrm{mol}\) of ethyl acetate is produced, meaning the concentrations of acetic acid and ethanol decrease equally to \(\frac{1.00-0.65}{V} = \frac{0.35}{V}\).
This method ensures that we accurately calculate the changes in concentration at equilibrium, which is necessary for plugging into the \(K_{c}\) expression. Such calculations emphasize the stoichiometric relationship between the reactants and products, making them essential for reaction analysis.

Reaction stoichiometry involves the quantitative relationships between reactants and products in a chemical reaction. This stoichiometric relationship is foundational when predicting product formation or determining reactant depletion.
In our exercise, the balanced reaction equation between acetic acid and ethanol brings forth a 1:1:1:1 stoichiometry, meaning that for every mol of acetic acid reacting, one mol of ethanol is also consumed while forming one mol each of ethyl acetate and water.
Understanding stoichiometry is crucial for calculating the concentration changes in our equation. As the reaction reaches equilibrium, 0.65 mol of ethyl acetate and water are formed, reflecting the stoichiometric balance. This relationship allows us to conclude the changes in concentration of acetic acid and ethanol have been equal at 0.35 mol, which is critical for determining \(K_{c}\).

• Helps in predicting quantities of products formed.
• Assists in determining limiting reactants.
• Ensures proper balance and conservation of mass.

Mastering stoichiometry simplifies pursuing equilibrium constant values and enhances understanding of chemical interactions.