Question

Lactic acid, \(\mathrm{HC}_{3} \mathrm{H}_{5} \mathrm{O}_{3},\) is a monoprotic acid that forms when milk sours. An \(18.5 \mathrm{~mL}\) sample of a solution of lactic acid required \(17.25 \mathrm{~mL}\) of \(0.155 \mathrm{M} \mathrm{NaOH}\) to reach an end point in a titration. (a) How many moles of lactic acid were in the sample? (b) How many grams of lactic acid were in the sample?

Short answer

(a) There were approximately 0.002673 moles of lactic acid in the sample. (b) There were approximately 0.2407 grams of lactic acid in the sample.

Step-by-step solution

Calculate the moles of NaOH used in the titration

First, calculate the moles of sodium hydroxide (NaOH) that were used to neutralize the lactic acid. Use the formula: moles = concentration (M) * volume (L). The concentration of NaOH is given as 0.155 M and the volume used in the titration is 17.25 mL, which must be converted to liters.

Write the balanced chemical equation

Write the balanced chemical equation for the neutralization reaction between lactic acid (HC3H5O3) and NaOH. Since lactic acid is monoprotic, it donates one hydrogen ion (H+) which reacts with hydroxide ion (OH-) from NaOH to form water (H2O). The reaction is: HC3H5O3 + NaOH -> NaC3H5O3 + H2OThis tells us that the reaction ratio of lactic acid to NaOH is 1:1.

Calculate the moles of lactic acid neutralized

Since the reaction ratio is 1:1, the moles of NaOH used is equal to the moles of lactic acid neutralized. The moles of NaOH calculated in Step 1 are the same as the moles of lactic acid.

Calculate the mass of lactic acid in the sample

To find the mass of lactic acid, use the formula: mass = moles * molar mass. The molar mass of lactic acid (HC3H5O3) can be calculated by adding the atomic masses of its constituent atoms. It is approximately 90.08 g/mol.

Convert the moles of lactic acid to grams

Using the moles of lactic acid calculated in Step 3 and the molar mass determined in Step 4, calculate the mass of lactic acid in the sample.

Key concepts

Lactic Acid

Lactic acid, with the chemical formula \(\mathrm{HC}_{3} \mathrm{H}_{5} \mathrm{O}_{3}\), is an organic compound prevalent in dairy products when milk sugars are fermented, typically during the souring process. Most commonly known for its presence in soured milk, lactic acid is also produced in our muscles during intense exercise when oxygen levels are low. This monoprotic acid exhibits the characteristic properties of carboxylic acids, such as the ability to donate a proton (\(\mathrm{H}^{+}\)) to a base during a reaction. In the context of a titration exercise, understanding that lactic acid can only donate one hydrogen ion is essential, as this detail directs the stoichiometry of the reaction that occurs.

When lactic acid reacts with a strong base, it forms lactate (the conjugate base of lactic acid) and water, which fits the general behavior of an acid reacting with a base. Learning about lactic acid not only serves a purpose in titration exercises but also provides insights into biochemical pathways and food science, where its ability to act as a preservative is valued.

Molarity Calculation

Molarity, indicated by the symbol \(M\), refers to the concentration of a solution and is expressed as moles of solute per liter of solution. When calculating molarity, one must always pay close attention to units, ensuring that the volume is in liters, not milliliters or any other unit. The formula for molarity calculation is:\[M = \frac{\text{moles of solute}}{\text{volume of solution in liters}}\]

This concept is fundamental when conducting titrations, as the molarity of a titrant (a solution of known concentration) and the volume used are crucial in determining the amount of the substance being analyzed. By mastering molarity calculations, students can confidently approach various chemistry problems that involve solution concentration and can apply these skills in lab practices where precise measurements and understanding of concentration are essential.

Stoichiometry

Stoichiometry is a section of chemistry that deals with the quantitative aspect of chemical reactions. It provides the relationship between the reactants and products of a chemical reaction. A balanced chemical equation is central to stoichiometry, as it gives the mole ratio of reactants to products involved in the reaction.

In the case of acid-base titrations, stoichiometry tells us how a specific quantity of an acid reacts with a certain amount of a base. For a monoprotic acid like lactic acid, the reaction with sodium hydroxide (NaOH) proceeds on a 1:1 mole basis (one mole of lactic acid reacts with one mole of NaOH). Hence, stoichiometry is essential for understanding the exact proportions in which chemicals react and is a fundamental tool in determining the unknown concentration or quantity of a substance in a chemical reaction. With proper stoichiometric calculations, students can predict the outcomes of reactions and design experiments accordingly.

Molar Mass

Molar mass is a physical property defined as the mass of a given substance (chemical element or chemical compound) divided by its amount of substance. The unit for molar mass is grams per mole (\(\text{g/mol}\)). It is calculated by summing the standard atomic weights of the atoms that make up the molecule. For instance, the molar mass of lactic acid (\(\mathrm{HC}_{3} \mathrm{H}_{5} \mathrm{O}_{3}\)) involves the addition of the atomic masses of hydrogen, carbon, and oxygen found in its structural formula.

Knowing the molar mass allows chemists to convert between the mass of a substance and the number of moles, facilitating quantitative analysis and chemical reaction design. When participating in titration exercises or analyzing substances, the molar mass serves as a pivotal factor for converting moles to grams and vice versa, enabling precise determination of the quantity of reactants and products in a chemical equation. Understanding how to calculate and apply molar mass is an essential skill in the study of chemistry and various applications involving calculations of substance amounts.