Question

Over time, as their free fatty acid (FFA) content increases, edible fats and oils become rancid. To measure rancidity, the fat or oil is dissolved in ethanol, and any FFA present is titrated with KOH dissolved in ethanol. In a series of tests on olive oil, a stock solution of \(0.050 \mathrm{M}\) ethanolic \(\mathrm{KOH}\) was prepared at \(25^{\circ} \mathrm{C},\) stored at \(0^{\circ} \mathrm{C},\) and then placed in a \(100-\mathrm{mL}\) buret to titrate oleic acid [an FFA with formula \(\left.\mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)_{7} \mathrm{CH}=\mathrm{CH}\left(\mathrm{CH}_{2}\right)_{7} \mathrm{COOH}\right]\) in the oil. Each of four \(10.00-\mathrm{g}\) samples of oil took several minutes to titrate: the first required \(19.60 \mathrm{~mL}\), the second \(19.80 \mathrm{~mL},\) and the third and fourth \(20.00 \mathrm{~mL}\) of the ethanolic \(\mathrm{KOH}\). (a) What is the apparent acidity of each sample, in terms of mass \(\%\) of oleic acid? (Note: As the ethanolic KOH warms in the buret, its volume increases by a factor of \(0.00104 /{ }^{\circ} \mathrm{C}\).) (b) Is the variation in acidity a random or systematic error? Explain. (c) What is the actual acidity? How would you demonstrate this?

Short answer

(a) Calculate the mass % of oleic acid for each sample using the titration data and correct for temperature. (b) Determine if errors are random/systematic. (c) Find actual acidity using corrected volumes and explain demonstration of results.

Step-by-step solution

- Calculate the moles of KOH used in titrations

For each sample, the volume of KOH solution used is given. First, convert the volume to liters and then use the molarity to find the moles of KOH. The molarity (M) is 0.050 M.

- Convert volume to moles of KOH

Use the formula: \[ \text{moles of KOH} = \text{Molarity} \times \text{Volume} \] for each volume: 19.60 mL, 19.80 mL, and 20.00 mL.

- Calculate moles of oleic acid reacted

Since one mole of KOH reacts with one mole of oleic acid, the moles of oleic acid will be equal to the moles of KOH used.

- Calculate the mass of oleic acid

Using the molar mass of oleic acid (282.47 g/mol), convert the moles of oleic acid to grams using: \[ \text{mass} = \text{moles} \times \text{molar mass} \]

- Calculate mass percentage of oleic acid

Convert the mass of oleic acid to a mass percentage using the initial mass of the oil sample (10.00 g). Use the formula: \[ \text{mass percentage} = \frac{\text{mass of oleic acid}}{\text{mass of sample}} \times 100 \]

- Correct volume of KOH for temperature change

Adjust the volume of KOH for the thermal expansion effect. The temperature correction factor is given (0.00104 /°C). Calculate the corrected volume for each titration.

- Determine actual mass percentage

Recalculate the mass percentage of oleic acid using the corrected KOH volume.

- Analyze error type

Examine if the differences in acidity (from the original titration volumes) show random variation or a consistent pattern (systematic error).

- Summarize findings and explanations

Provide an explanation for the variation and describe how you would demonstrate the actual acidity value, considering any systematic errors.

Key concepts

Free Fatty Acids (FFAs)

Free fatty acids (FFAs) are simply the fatty acids that are not bound to any other molecule, such as glycerol in triglycerides. Over time, the presence of FFAs in fats and oils increases due to hydrolysis and oxidation processes, leading to rancidity. Rancidity is the unpleasant odor and taste resulting from the breakdown of fats.

In the given exercise, oleic acid (an example of FFA) is measured to determine the rancidity level in olive oil. FFAs are measured because their increase signals fat deterioration. The more FFAs present, the more rancid the oil is.

To measure FFAs, we use a technique called titration. By knowing the amount of a titrant (in this case, KOH in ethanol) used to neutralize the FFAs in a sample, we can calculate the FFA content. This is a crucial step in the control and quality assurance of edible fats and oils.

Titration

Titration is a common laboratory method used to determine the concentration of an analyte (the substance being measured) in a solution. It involves the slow addition of a titrant (a solution of known concentration) to a solution containing the analyte until the reaction reaches its endpoint.

In the case of measuring FFAs, the titrant is ethanolic KOH, and the analyte is oleic acid in olive oil. Since KOH is a strong base, it neutralizes the oleic acid, forming water and a salt.
The titration process:

• Prepare the KOH solution of known concentration.
• Add it slowly to the oil sample solution containing FFAs.
• Observe the reaction until the endpoint is reached, indicating all FFAs have been neutralized.

The volume of KOH used tells us the amount of oleic acid in the sample. This is then converted to a percentage to express the FFAs present in the oil.

Molarity

Molarity is the measure of the concentration of a solution, represented as moles of solute per liter of solution, symbolized as M. It's essential for calculating the amount of reactants in titration experiments.

In this exercise, we know the molarity of the KOH solution is 0.050 M. This means there are 0.050 moles of KOH in every liter of the solution.

To find out how many moles of KOH are used, we'll use the formula: \[ \text{moles of KOH} = \text{Molarity} \times \text{Volume in liters} \]

For instance, if 19.60 mL (or 0.01960 L) of KOH is used, the calculation is: \[ 0.050 \times 0.01960 = 0.00098 \text{ moles of KOH} \] This allows us to determine the moles of oleic acid, as one mole of KOH neutralizes one mole of oleic acid.

Temperature Effect on Volume

Temperature fluctuations can significantly impact the accuracy of volumetric measurements in titration. Liquids expand when heated and contract when cooled; this volume change must be corrected for accurate results.

In the solved problem, it's noted that the KOH solution was prepared and stored at different temperatures. The KOH solution was initially prepared at 25°C, stored at 0°C, and then used at another temperature during titration.

The volume correction factor given is 0.00104 /°C. This factor helps calculate the volume change due to temperature variations. For instance, if the solution warmed up by 5°C, the volume correction would be: \[ \text{Volume} \times (1 + \text{Temperature change} \times \text{correction factor}) \]

Adjusting the volume before calculating the acidity ensures accurate and reliable results, leading to correct experimental conclusions.