Problem 62 - Chemistry: An Atoms-Focused Approach

Question

Reactions between carboxylic acids and alcohols to produce esters typically do not go to completion. Ethyl acetate, a compound used industrially to decaffeinate coffee and tea, is made in the following reaction for which \(K_{c}=3.87\) at \(75^{\circ} \mathrm{C}\) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}(\ell)+\mathrm{CH}_{3} \operatorname{cooH}(\ell) \rightleftharpoons\) $$ \mathrm{CH}_{3} \mathrm{COOCH}_{2} \mathrm{CH}_{3}(e)+\mathrm{H}_{2} \mathrm{O}(\ell) $$ Is a mixture of \(125 \mathrm{g}\) of ethanol \(\left(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\right), 125 \mathrm{g}\) of acctic acid \(\left(\mathrm{CH}_{3} \mathrm{COOH}\right), 125 \mathrm{g}\) of cthyl acctate \(\left(\mathrm{CH}_{3} \mathrm{COOCH}_{2} \mathrm{CH}_{3}\right),\) and \(125 \mathrm{g}\) of watcr in a \(5 \mathrm{L}\) reactor at equilibrium? b. If not, in which direction will the reaction shift to reach equilibrium?

Step-by-Step Solution

Answer

If not, in which direction will the reaction shift to reach equilibrium? Answer: No, the given mixture is not at equilibrium. The reaction will shift towards the products (right) to reach equilibrium.

Step 1: Find moles of each substance

We are given the mass of each substance, so first, we must find the number of moles in each substance. Number of moles = mass / molar mass Ethanol: n(CH3CH2OH) = 125g / (12.01 * 2 + 1.01 * 6 + 16.00)g/mol ≈ 2.72 mol Acetic Acid: n(CH3COOH) = 125g / (12.01 * 2 + 1.01 * 4 + 16.00*2)g/mol ≈ 2.08 mol Ethyl Acetate: n(CH3COOCH2CH3) = 125g / (12.01 * 4 + 1.01 *6 + 16.00*2)g/mol ≈ 1.56 mol Water: n(H2O) = 125g / (1.01 * 2 + 16.00)g/mol ≈ 6.94 mol

Step 2: Calculate the concentration

We are given the volume of the reactor, so we can now calculate the concentration (in mol/L) of each substance. Concentration = moles / volume [CH3CH2OH] = 2.72 mol / 5 L ≈ 0.54 M [CH3COOH] = 2.08 mol / 5 L ≈ 0.42 M [CH3COOCH2CH3] = 1.56 mol / 5 L ≈ 0.31 M [H2O] = 6.94 mol / 5 L ≈ 1.39 M Step 2: Calculate the reaction quotient (Q)

Step 3: Calculate Q

The reaction quotient (Q) for the reaction will be calculated as follows: Q = [CH3COOCH2CH3][H2O] / ([CH3CH2OH][CH3COOH]) By plugging in the concentrations from step 1, we have: Q ≈ (0.31)(1.39) / (0.54)(0.42) ≈ 1.96 Step 3: Determine if the mixture is at equilibrium and find the direction of the reaction

Step 4: Compare Q to Kc

We are given Kc = 3.87. Now we'll compare Q to Kc: If Q > Kc, the reaction will shift toward the reactants (left). If Q < Kc, the reaction will shift toward the products (right). If Q = Kc, the reaction is at equilibrium. In our case, Q (1.96) is less than Kc (3.87). Therefore, the reaction will shift towards the products (right) to reach equilibrium.

Key Concepts

Acid-Base Reactions

Acid-base reactions are a fundamental concept in chemistry where an acid donates a proton (H⁺) to a base. These reactions are crucial because they help us understand the behavior of acids and bases in various chemical processes.
In a typical acid-base reaction, the acid and base react to form a salt and water. For example, in the reaction between hydrochloric acid (HCl) and sodium hydroxide (NaOH), the base NaOH accepts the proton from HCl, resulting in the formation of water (H₂O) and sodium chloride (NaCl).
Understanding these reactions can also help explain phenomena such as neutralization and buffer action, which are essential in both laboratory and real-world applications. In the context of esterification, an acid can participate by providing the acidic environment necessary for the reaction to proceed, illustrating how interconnected these reactions can be.

Esterification

Esterification is a chemical reaction between an alcohol and an acid, resulting in the formation of an ester and water. This process is an example of a condensation reaction, where two smaller molecules combine to form a larger one, with the release of a small molecule such as water.
In the case of forming ethyl acetate, ethanol (the alcohol) reacts with acetic acid to produce ethyl acetate (the ester) and water. This reaction is influenced by factors such as temperature and the presence of a catalyst, which can improve the rate and yield of the ester product.
Esterification is a reversible reaction, which means it does not proceed to completion—some reactants always remain. The equilibrium established between the reactants and products is a crucial aspect of this process. The reaction can be intensified toward ester formation by removing water, thereby shifting the equilibrium in favor of the products.

Reaction Quotient

The reaction quotient, represented as Q, is a measure of the relative amounts of products and reactants present during a reaction at a given time. It is calculated in the same way as the equilibrium constant, but under any set of conditions, not necessarily at equilibrium.
For a given reaction, the formula to find the reaction quotient is: \[ Q = \frac{[\text{products}]}{[\text{reactants}]} \] where the concentrations are those at a specific time point. By comparing Q to the equilibrium constant, Kc, you can predict the direction in which the reaction will proceed to reach equilibrium.

• If Q < Kc, the reaction will proceed in the forward direction to form more products.
• If Q > Kc, the reaction will proceed in the reverse direction to form more reactants.
• If Q = Kc, the system is at equilibrium, and no net change occurs.

This theoretical tool is incredibly useful in predicting and controlling the output of a chemical process, aiding in the design of industrial chemical reactions.