Question

Lactic acid, \(\mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O}_{3}\), is the acid present in sour milk. A \(0.100-\mathrm{g}\) sample of pure lactic acid requires \(12.95 \mathrm{~mL}\) of \(0.0857 M\) sodium hydroxide for complete reaction. How many moles of hydroxide ion are required to neutralize one mole of lactic acid?

Short answer

Answer: 1 mole of hydroxide ion is required to neutralize one mole of lactic acid.

Step-by-step solution

Calculate the moles of lactic acid

Given the mass of lactic acid as 0.100 g, we first need to find its molar mass. The molar mass of lactic acid, \(\mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O}_{3}\), can be calculated as follows: Molar mass = (3 × 12.01) + (6 × 1.01) + (3 × 16.00) = 36.03 + 6.06 + 48.00 = 90.09 g/mol Now, we can find the moles of lactic acid by dividing the given mass by its molar mass: Moles of lactic acid = (mass of lactic acid) / (molar mass of lactic acid) = 0.100 g / 90.09 g/mol = 1.110 x 10^(-3) mol

Calculate the moles of sodium hydroxide

We are given the volume of sodium hydroxide solution (12.95 mL) and its molarity (0.0857 M). We can calculate the moles of sodium hydroxide using the formula: Moles of sodium hydroxide = (volume of NaOH solution) × (molarity of NaOH solution) To use appropriate units, convert the volume from mL to L: Volume of NaOH solution = 12.95 mL × (1 L / 1000 mL) = 0.01295 L Now, calculate the moles of sodium hydroxide: Moles of sodium hydroxide = 0.01295 L × 0.0857 mol/L = 1.110 x 10^(-3) mol

Find the moles of hydroxide ion required to neutralize one mole of lactic acid

We now have the moles of lactic acid and sodium hydroxide. Since complete reaction occurs, the ratio of moles of lactic acid to moles of sodium hydroxide should give us the moles of hydroxide ion required to neutralize one mole of lactic acid. Moles of hydroxide ion required = (moles of sodium hydroxide) / (moles of lactic acid) = (1.110 x 10^(-3) mol) / (1.110 x 10^(-3) mol) = 1 Thus, 1 mole of hydroxide ion is required to neutralize one mole of lactic acid.

Key concepts

Molar Mass Calculation

Understanding how to calculate the molar mass of a compound is a fundamental skill in chemistry. The molar mass is the weight of one mole of a substance, typically expressed in grams per mole (g/mol). It is the sum of the atomic masses of all the atoms in a molecule. For instance, lactic acid, with the chemical formula \(\mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O}_{3}\), has a molar mass calculated by adding the atomic masses of carbon (\(12.01 \text{g/mol}\)), hydrogen (\(1.01 \text{g/mol}\)), and oxygen (\(16.00 \text{g/mol}\)), weighted by the number of atoms of each present in the molecule.

Here's the breakdown:

• Carbon: 3 atoms × \(12.01 \text{g/mol}\) = \(36.03 \text{g/mol}\)
• Hydrogen: 6 atoms × \(1.01 \text{g/mol}\) = \(6.06 \text{g/mol}\)
• Oxygen: 3 atoms × \(16.00 \text{g/mol}\) = \(48.00 \text{g/mol}\)

Adding these together gives us the molar mass of lactic acid as \(90.09 \text{g/mol}\). Knowing this value allows us to determine how many moles of lactic acid are present in a given sample by dividing the mass of the sample by the molar mass of the compound.

Mole Concept

The mole concept is a bridge between the microscopic world of atoms and molecules and the macroscopic world that we can measure in the laboratory. One mole represents \(6.022 \times 10^{23}\) entities, whether they be atoms, ions, or molecules—this is known as Avogadro's number. In the context of our exercise, it helps us relate a tangible quantity of lactic acid (0.100 g) to an intangible number of lactic acid molecules.

Once the molar mass of lactic acid is known, you can calculate the number of moles contained in any given mass of lactic acid using the formula:
\[\text{Moles} = \frac{\text{mass of substance in grams}}{\text{molar mass}}\]
This calculation showed that a 0.100-gram sample of lactic acid is equivalent to \(1.110 \times 10^{-3}\) moles. This quantification is crucial for understanding how substances react in stoichiometry, as chemical reactions occur in proportions defined by moles.

Neutralization Reaction

A neutralization reaction occurs when an acid and a base react to form water and a salt. It is a specific type of double displacement reaction typically involving hydrogen ions (H+) from the acid and hydroxide ions (OH–) from the base combining to create water (H2O).

In the given problem, we investigate how many moles of hydroxide ion are necessary to neutralize one mole of lactic acid. Having calculated the moles of lactic acid and the moles of sodium hydroxide, we use the information that they react in a 1:1 ratio, as defined by the balanced chemical equation for the reaction. Hence, for each mole of lactic acid present, one mole of hydroxide ion is required for neutralization. This concept is vital in understanding titrations and can assist in determining the concentration of unknown solutions in analytical chemistry.