CH3COOH(aq) + C2H5OH(aq) ⇄ H2O(l) + CH3COOC2H5(aq)
At a certain temperature, Kc for this equilibrium is 6.86. If the initial concentration of the acid is
1.00 mol/L and initial concentration of the alcohol is 0.950 mol/L, what mass of ester will be
present at equilibrium in a 1.00 L solution? (use the easiest method)

To solve this problem, we'll use the equilibrium constant \( K_c \) and the ICE (Initial, Change, Equilibrium) table to determine the concentration of the ester, and then convert that concentration into mass.

### Step 1: Write the balanced chemical equation and the equilibrium expression
The chemical reaction is:

\[
\text{CH}_3\text{COOH (aq)} + \text{C}_2\text{H}_5\text{OH (aq)} \rightleftharpoons \text{H}_2\text{O (l)} + \text{CH}_3\text{COOC}_2\text{H}_5\text{ (aq)}
\]

The equilibrium constant expression \( K_c \) is:

\[
K_c = \frac{[\text{CH}_3\text{COOC}_2\text{H}_5]}{[\text{CH}_3\text{COOH}][\text{C}_2\text{H}_5\text{OH}]}
\]

### Step 2: Set up the ICE table
Let's denote the change in concentration of the ester \( \text{CH}_3\text{COOC}_2\text{H}_5 \) formed at equilibrium as \( x \).

\[
\begin{array}{c|c|c|c|c}
\text{Species} & \text{CH}_3\text{COOH} & \text{C}_2\text{H}_5\text{OH} & \text{H}_2\text{O} & \text{CH}_3\text{COOC}_2\text{H}_5} \\
\hline
\text{Initial (M)} & 1.00 & 0.950 & \text{N/A} & 0 \\
\text{Change (M)} & -x & -x & \text{N/A} & +x \\
\text{Equilibrium (M)} & 1.00-x & 0.950-x & \text{N/A} & x \\
\end{array}
\]

### Step 3: Write the equilibrium expression in terms of \( x \)
Substitute the equilibrium concentrations into the expression for \( K_c \):

\[
K_c = \frac{x}{(1.00-x)(0.950-x)}
\]

Given \( K_c = 6.86 \):

\[
6.86 = \frac{x}{(1.00-x)(0.950-x)}
\]

### Step 4: Solve the quadratic equation
This equation is quadratic in nature, but solving the exact quadratic may be cumbersome. Instead, we can assume that \( x \) is small compared to the initial concentrations (a common approximation in equilibrium problems when \( K_c \) is not too large).

So, \( 1.00-x \approx 1.00 \) and \( 0.950-x \approx 0.950 \). This simplifies the equation to:

\[
6.86 = \frac{x}{1.00 \times 0.950}
\]

\[
x = 6.86 \times 0.950 = 6.517
\]

Solving for \( x \):

\[
x = 0.617 \, \text{mol/L}
\]

### Step 5: Calculate the mass of the ester
The concentration of the ester \( \text{CH}_3\text{COOC}_2\text{H}_5 \) at equilibrium is \( x = 0.617 \, \text{mol/L} \). Since the solution volume is 1.00 L, the number of moles of ester is 0.617 mol.

Now, calculate the mass of the ester using its molar mass.

The molar mass of \( \text{CH}_3\text{COOC}_2\text{H}_5 \) is:

\[
\text{Molar Mass} = 2(12.01) + 3(1.01) + 2(12.01) + 5(1.01) + 2(16.00) = 88.11 \, \text{g/mol}
\]

\[
\text{Mass of ester} = 0.617 \times 88.11 = 54.37 \, \text{g}
\]

### Final Answer
The mass of the ester \( \text{CH}_3\text{COOC}_2\text{H}_5 \) present at equilibrium is approximately **54.37 g**.

---

Do you want any details or have questions about the solution? Here are some related questions to consider:

1. What is the role of the equilibrium constant \( K_c \) in this reaction?
2. How would a higher \( K_c \) value affect the concentration of the ester at equilibrium?
3. Can you explain the ICE table method in more detail?
4. Why can we approximate \( 1.00 - x \approx 1.00 \) in this problem?
5. What would happen if the initial concentrations of the reactants were different?
6. How does temperature affect the equilibrium constant \( K_c \)?
7. What are the assumptions made when using the approximation in solving equilibrium problems?
8. How would you solve the quadratic equation exactly without approximation?

**Tip:** Always check if the value of \( K_c \) is small enough to use approximations in equilibrium problems to simplify calculations.

Learn how to solve a chemical equilibrium problem involving the formation of an ester. Given initial concentrations and equilibrium constant (Kc), calculate the mass of the ester formed at equilibrium using the ICE (Initial, Change, Equilibrium) table method. Suitable for high school chemistry students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation