Question

d. \(\left[\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{C}_{2} \mathrm{H}_{5}\right]=4.4 \mathrm{M},\left[\mathrm{H}_{2} \mathrm{O}\right]=4.4 M\) \(\left[\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}\right]=0.88 M,\left[\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right]=10.0 \mathrm{M}\). e. What must the concentration of water be for a mixture with \(\left[\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{C}_{2} \mathrm{H}_{5}\right]=2.0 \mathrm{M},\left[\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}\right]=0.10 M,\) and \(\left[\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right]=5.0 \mathrm{M}\) to be at equilibrium? f. Why is water included in the equilibrium expression for this reaction?

Short answer

The concentration of water at equilibrium must be 0.1 M for the given mixture. Water is included in the equilibrium expression for this reaction because it is involved in the reaction, and its concentration changes during the esterification process, thus affecting the position of the equilibrium.

Step-by-step solution

Write the equilibrium constant expression

For the given reaction, the equilibrium constant expression Kc is represented as: \[K_{c} = \frac{[\mathrm{CH3CO2H}][\mathrm{C2H5OH}]}{[\mathrm{CH3CO2C2H5}][\mathrm{H2O}]}\]

Calculate the equilibrium constant Kc using the given concentrations

Now, we will use the concentrations given in part d to find the equilibrium constant Kc: \[\frac{0.88 \times 10}{4.4 \times 4.4} = 0.2\] So, Kc = 0.2

Setting up a new equilibrium equation

Now, we are given the concentrations of ethyl acetate, acetic acid, and ethanol and are asked to find the concentration of water at equilibrium. Let's set up a new equilibrium equation with the given values: \[0.2 = \frac{(0.10)(5)}{(2)([\mathrm{H2O}])}\]

Solve for the concentration of water at equilibrium

Now, let's solve the equation for the concentration of water at equilibrium: \[\frac{0.2}{2} = \frac{0.1 \times 5}{[\mathrm{H2O}]}\] \[0.1 = [\mathrm{H2O}]\] Therefore, the concentration of water at equilibrium must be 0.1 M. For part f:

Explain why water is included in the equilibrium expression for this reaction

Water is included in the equilibrium expression for this reaction because it is involved in the reaction and has a changing concentration during the esterification process. In some reactions, water is not included in the equilibrium expressions because its concentration remains constant (for example, when water is a solvent in large excess). However, in this problem, the concentration of water is given and it is affecting the position of the equilibrium. Therefore, it is included in the equilibrium expression to accurately describe the relationship between the concentrations of reactants and products.

Key concepts

Chemical Equilibrium

Chemical equilibrium occurs when a chemical reaction proceeds in both the forward and reverse directions at the same rate, resulting in no net change in the concentrations of products and reactants over time. This dynamic state doesn't mean the reaction has stopped; instead, the rate of production and consumption of substances is equal.

In the context of an esterification reaction, achieving equilibrium means that the rate at which the ester (in this case, ethyl acetate) and water form from the acid (acetic acid) and alcohol (ethanol) is equal to the rate at which the ester and water react to form the acid and alcohol again. The reaction can be represented by the following equation:
\[\text{Acetic acid (CH}_3\text{CO}_2\text{H) + Ethanol (C}_2\text{H}_5\text{OH) } \leftrightarrow \text{ Ethyl acetate (CH}_3\text{CO}_2\text{C}_2\text{H}_5\text{) + Water (H}_2\text{O)}\].

Understanding chemical equilibrium is crucial for determining the conditions required to maximize the yield of products in industrial processes, including the synthesis of esters.

Esterification Reaction

Esterification is a chemical reaction in which a carboxylic acid reacts with an alcohol to form an ester and water. This type of reaction is important for creating a wide variety of ester compounds, which are used in industrial applications such as solvents, flavors, and fragrances.

The reversible nature of esterification makes the understanding of equilibrium principles especially important. By manipulating conditions such as the concentration of reactants, temperature, and the presence of catalysts, chemists can shift the equilibrium to favor the formation of the desired ester over the reactants.

The esterification reaction involved in our exercise is a classic example where acetic acid reacts with ethanol to produce ethyl acetate and water. This reaction can be influenced by things like the concentrations of reactants and products, which brings us to our next key topic - concentration calculation.

Concentration Calculation

Concentration calculations are a fundamental aspect of chemistry, particularly when it comes to understanding and applying the concept of chemical equilibrium. The concentration of a substance in a solution is typically expressed in molarity (M), which is moles of solute per liter of solution.

In our exercise, we were provided with the concentrations of the reactants and products involved in the esterification reaction. To solve for equilibrium concentrations, we set up a ratio using these values, reflecting the balanced chemical equation. From there, we use algebra to resolve the unknown concentration. This kind of calculation is pivotal in various chemical disciplines, including reaction stoichiometry, quantitative analysis, and industrial process control.

Reaction Quotient

The reaction quotient, Q, is a measure that tells us how far a system is from reaching equilibrium at any given moment. It is calculated in the same way as the equilibrium constant, K, but with the actual concentrations of the reactants and products at that point in time.

For the equation \[Q = \frac{[\text{Products}]}{[\text{Reactants}]}\], Q can be compared with the equilibrium constant K to predict the direction in which the reaction will proceed to reach equilibrium. If \(Q < K\), the forward reaction is favored to produce more products. If \(Q > K\), the reaction will proceed in the reverse direction to produce more reactants. Finally, if \(Q = K\), the system is at equilibrium. Understanding the reaction quotient is essential for predicting how a reaction mixture will shift under different conditions, and it is a critical tool in the design and control of chemical processes.