Question

A sample of peanut oil weighing \(2 \mathrm{~g}\) is added to \(25 \mathrm{~mL}\) of \(0.40 \mathrm{M} \mathrm{KOH}\). After saponification is complete, \(8.5 \mathrm{~mL}\) of \(0.28 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}\) is needed to neutralize excess of \(\mathrm{KOH}\). The saponification number of peanut oil is : (saponification number is defined as the milligrams of KOH consumed by \(1 \mathrm{~g}\) of oil) (a) \(146.72\) (b) \(223.44\) (c) \(98.9\) (d) None of these

Short answer

The saponification number of peanut oil is approximately 213.8 mg/g, which doesn't match any of the given options (a) 146.72, (b) 223.44, (c) 98.9, so the answer is (d) None of these.

Step-by-step solution

Determine molarity and volume of remaining KOH after saponification

The excess KOH after saponification is neutralized by H2SO4. Since it takes 8.5 mL of 0.28 M H2SO4 to neutralize the KOH, we can calculate the number of moles of H2SO4, which will be equal to the moles of unreacted KOH because H2SO4 has 2 acidic hydrogens (dihydrogen sulfate) and KOH has a 1:1 reaction ratio with H2SO4.Moles of H2SO4 = Molarity of H2SO4 (M) * Volume of H2SO4 (L)Moles of H2SO4 = 0.28 mol/L * 8.5 mL * 1L/1000mLMoles of H2SO4 = 0.28 * 8.5/1000Moles of H2SO4 = 0.00238 mol

Calculate the moles of KOH originally added

Calculate the total moles of KOH originally added to react with the peanut oil.Moles of KOH = Molarity of KOH (M) * Volume of KOH (L)Moles of KOH = 0.40 mol/L * 25 mL * 1L/1000mLMoles of KOH = 0.40 * 25/1000Moles of KOH = 0.010 mol

Calculate the moles of KOH that reacted with the peanut oil

Determine the moles of KOH that reacted with the peanut oil by subtracting the moles of excess KOH (which we calculated from the moles of H2SO4 used to neutralize it) from the original moles of KOH added.Moles of KOH reacted = Moles of KOH originally added - Moles of excess KOHMoles of KOH reacted = 0.010 mol - 0.00238 molMoles of KOH reacted = 0.00762 mol

Calculate the milligrams of KOH that reacted

Convert the moles of KOH that reacted into milligrams. The molar mass of KOH is approximately 56.11 g/mol.Milligrams of KOH reacted = Moles of KOH reacted * Molar mass of KOH (g/mol) * 1000 mg/gMilligrams of KOH reacted = 0.00762 mol * 56.11 g/mol * 1000 mg/gMilligrams of KOH reacted = 427.5982 mg

Determine the saponification number

The saponification number is defined as the milligrams of KOH consumed by 1 g of oil. Thus, divide the milligrams of KOH that reacted by the weight of the oil sample in grams to find the saponification number.Saponification number = Milligrams of KOH reacted / Weight of the oil (g)Saponification number = 427.5982 mg / 2 gSaponification number = 213.7991 mg/g

Key concepts

Chemical Stoichiometry

Understanding chemical stoichiometry is essential when delving into the process of saponification and calculating the resulting saponification number. Chemical stoichiometry refers to the quantitative relationship between reactants and products in a chemical reaction. For any given chemical process, it involves balancing the equation and calculating the amounts of substances required or produced.

For example, in the exercise given, stoichiometry helps us determine the amount of potassium hydroxide (KOH) that has reacted with the peanut oil during saponification. By recognizing the reaction ratio between KOH and sulfuric acid (H2SO4), we can calculate the moles of KOH that remained unreacted and accordingly, those that reacted with the oil. The balanced equation and the mole concept serve as the foundation for these calculations. This balancing act is a central component of chemical stoichiometry and is paramount for understanding chemical reactions in practical scenarios such as saponification.

Titration

Titration is a laboratory technique used to determine the concentration of a known reactant in a solution. During a titration, a solution of known concentration (the titrant) is added to a solution containing the substance of unknown concentration until a chemical reaction is completed. The point at which the reaction is completed is often determined by a noticeable change in the solution, such as a color change with the use of an indicator.

In the context of our saponification exercise, titration is critical for finding the amount of excess KOH after saponification. By using sulfuric acid (H2SO4) as the titrant, the amount of KOH that did not react can be established. This value is necessary for calculating the saponification number. Understanding the theory behind titration, including end-point determination and the stoichiometric relationship between the titrant and analyte, is crucial for students to interpret the implications of the titration results accurately.

Molarity Calculation

The concept of molarity calculation plays a vital role in the quantitative analysis of solutions. Molarity, defined as the number of moles of solute per liter of solution, gives us the concentration of a solution. To calculate molarity, one divides the number of moles of the solute by the volume of the solution in liters.

In our exercise, the molarity calculation allows us to quantify the amount of KOH and H2SO4 used in the saponification and titration processes, respectively. By knowing the initial molarity and the volume of the solutions used, we can calculate the number of moles of the reagents. These calculations lead us to understand the amount of KOH that reacted with the peanut oil, which is an essential step in determining the saponification number. Grasping molarity calculations is fundamental for students not only to solve this problem but also to master solution preparation and analysis in chemistry.