8.1.6 Determination of Kc

Objective:

To determine the equilibrium constant,

$$K_c$$

for the esterification reaction between ethanol and ethanoic acid, forming ethyl ethanoate and water, using a titration method.

The equation for the reaction is:

$${C}_2\text{H}_5\text{OH (ethanol)} + \text{CH}_3\text{COOH (ethanoic acid)} \rightleftharpoons \text{CH}_3\text{COOCH}_2\text{CH}_3\text{ (ethyl ethanoate)} + \text{H}_2\text{O (water)}$$

Chemistry Background:

In this equilibrium reaction, the concentrations of reactants and products at equilibrium are used to calculate $K_c$ which provides an understanding of the extent of the reaction. The key steps involve determining the amount of ethanoic acid at equilibrium through titration with a strong base (sodium hydroxide), and then using these results to calculate $K_c$.

Apparatus & Chemicals:

• 6.0 g of ethanoic acid ($CH₃COOH$)
• 6.2 g of ethanol ($C₂H₅OH$)
• Concentrated sulfuric acid ($H₂SO₄$) as a catalyst (1 drop)
• Sodium hydroxide ($NaOH$), 1.0 mol dm⁻³
• Phenolphthalein indicator
• Distilled water
• 250 cm³ conical flasks
• Pipette and burette

Key Procedure Steps:

1. Preparation of Reaction Mixture:

• Add 6.0 g of ethanoic acid and 6.2 g of ethanol into a clean reaction flask (equivalent to 0.1 mol each).
• Add a drop of concentrated sulfuric acid to catalyse the reaction.
• Seal the flask with a stopper and gently shake to mix the contents.

2. Blank Setup:

• In a separate conical flask (the blank), add 20 cm³ of distilled water, one drop of sulfuric acid, and no ethanol or ethanoic acid.

3. Reaction Time:

• Leave both the reaction mixture and the blank to stand for at least one week to allow the equilibrium to be established.

4. Titration:

• After equilibrium is reached, titrate both the reaction mixture and the blank against 1.0 mol dm$⁻³$ $NaOH$, using phenolphthalein as an indicator.
• Phenolphthalein changes from colourless in acidic conditions to pink in basic conditions, indicating the end-point of the titration.

Practical Tips:

• Weighing: To achieve accurate results, weigh ethanoic acid and ethanol directly into the flask rather than measuring volumes.
• Safety: Ethanoic acid is corrosive, so wear safety goggles and gloves, and work in a well-ventilated area or fume cupboard.
• Control of Variables: Ensure both the reaction flask and blank undergo identical conditions (same volume of acid catalyst and temperature).

Specimen Results:

• Volume of $NaOH$ required to titrate the reaction mixture: 32.4 cm³
• Volume of $NaOH$ required to titrate the blank: 1.4 cm³

Analysis:

Titration Results:

• The volume of $NaOH$ required for the reaction mixture minus that for the blank gives the volume of $NaOH$ needed to neutralise the remaining ethanoic acid at equilibrium.
• This volume difference is used to calculate the moles of ethanoic acid remaining at equilibrium.

$$\text {Volume difference} = 32.4 \, \text{cm}^3 - 1.4 \, \text{cm}^3 = :highlight[31.0 \, \text{cm}^3]$$

Moles of Ethanoic Acid Remaining:

$$\text{Moles of CH}_3\text{COOH} = \frac{31.0}{1000} \times 1.0 = :highlight[0.0031 \, \text{mol}]$$

Moles of Ethanoic Acid Reacted: Initially, there was 0.1 mol of ethanoic acid. The amount reacted is:

$$\text{Moles reacted} = 0.1 - 0.0031 = :highlight[0.069 \, \text{mol}]$$

The same amount of ethanol has reacted.

Equilibrium Concentrations: At equilibrium, the concentration of ethyl ethanoate and water, both products, will be 0.069 mol since they are produced in a 1:1 ratio.

The equilibrium concentrations for each species can be summarised as follows:

Compound	Initial (mol)	Change (mol)	Equilibrium (mol)
Ethanol ($C₂H₅OH$)	0.100	–0.069	0.031
Ethanoic acid ($CH₃COOH$)	0.100	–0.069	0.031
Ethyl ethanoate ($CH₃COOCH₂CH₃$)	0	+0.069	0.069
Water ($H₂O$)	0	+0.069	0.069

Calculation of $K_c$: The expression for $K_c$ is:

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

Substituting the equilibrium concentrations:

$$K_c = \frac{(0.069)(0.069)}{(0.031)(0.031)} = :success[5.0]$$

Conclusion:

The equilibrium constant, $K_c$, for the esterification reaction is 5.0. This value indicates that at equilibrium, the concentration of the products (ethyl ethanoate and water) is higher than that of the reactants, showing the reaction favours the formation of the ester and water under the conditions used.

Further Considerations:

• Sources of Error:
  • Ensure accurate titration techniques to minimise errors.
  • If the reaction does not fully reach equilibrium, it can affect the $K_c$ value.
  • Calibration of glassware is essential for precise measurements.
• Improvement: Performing multiple trials and calculating an average $K_c$ value improves reliability.