Question

Lactic acid is a common by-product of cellular respiration and is often said to cause the "burn" associated with strenuous activity. A 25.0 -mL sample of 0.100$M$ lactic actid $({\mathrm{HC}}_3{\mathrm{H}}_3{\mathrm{O}}_3$ $\mathrm{p}{K}_{\mathrm{a}}=3.86)$ is titrated with 0.100 $\mathrm{M}$ NaOH solution. Calculate the pH after the addition of $0.0\mathrm{mL},4.0\mathrm{mL},8.0\mathrm{mL},12.5\mathrm{mL},$ $20.0\mathrm{mL},24.0\mathrm{mL},24.5\mathrm{mL},24.9\mathrm{mL},25.0\mathrm{mL},25.1\mathrm{mL}$ $26.0\mathrm{mL},28.0\mathrm{mL}$ , and 30.0 $\mathrm{mL}$ of the NaOH. Plot the results of your calculations as $\mathrm{pH}$ versus milliliters of NaOH added.

Short answer

In this titration, the initial moles of $0.100\mathrm{M}$ lactic acid are $0.00250\mathrm{mol}$. For each given point of NaOH volume added, calculate the moles of NaOH and determine the pH, considering whether the point is before, at, or after the equivalence point: - Calculate moles of NaOH using the given volume and concentration. - For points before the equivalence point, use the concentration of lactic acid and its $p{K}_a$ value to find the pH. - At the equivalence point, determine pH based on the concentration of the formed salt. - After the equivalence point, calculate the concentration of excess ${\mathrm{OH}}^{-}$ ions and find the pH. Finally, plot milliliters of NaOH added (x-axis) against the pH (y-axis) to illustrate the titration curve.

Step-by-step solution

Initial moles of lactic acid

Calculate the initial moles of lactic acid in the $25.0\mathrm{mL}$ solution by using the given information that it has $0.100\mathrm{M}$ concentration: Moles of lactic acid (acid) = Initial Volume of the solution (in liters) × Initial Concentration of lactic acid (in $\mathrm{M}$) Moles of lactic acid (acid) = $0.025\times 0.100$ Moles of lactic acid (acid) = $0.00250\mathrm{mol}$

Calculating moles of NaOH added at each point

Recall that the NaOH concentration is $0.100\mathrm{M}$. Moles of NaOH will be calculated as follows: Moles $\mathrm{NaOH}$ = Volume of NaOH added (in liters) × Concentration of NaOH (in $\mathrm{M}$) Calculate the moles of NaOH for each given point: $0.0\mathrm{mL},4.0\mathrm{mL},8.0\mathrm{mL},12.5\mathrm{mL},20.0\mathrm{mL},24.0\mathrm{mL},24.5\mathrm{mL},24.9\mathrm{mL},25.0\mathrm{mL},25.1\mathrm{mL},26.0\mathrm{mL},28.0\mathrm{mL}$, and $30.0\mathrm{mL}$.

Calculating $\mathrm{pH}$ for each point

For each point in the titration, determine whether it occurs before the equivalence point, at the equivalence point, or after the equivalence point. - If before the equivalence point (i.e., moles of $\mathrm{NaOH}$ < moles of lactic acid), we have to calculate the concentration of lactic acid (acid) and use its $\mathrm{p}{K}_{\mathrm{a}}$ value to find the $\mathrm{pH}$. - At the equivalence point (i.e., moles of $\mathrm{NaOH}$ = moles of lactic acid), the $\mathrm{pH}$ is determined by the concentration of the produced salt. - After the equivalence point (i.e., moles of $\mathrm{NaOH}$ > moles of lactic acid), we have to calculate the concentration of the excess ${\mathrm{OH}}^{-}$ ions and use it to find the $\mathrm{pH}$. Calculate the pH accordingly for each given point.

Plotting the results

After calculating the pH at each given point, create a plot with milliliters of NaOH added (x-axis) against pH (y-axis). This will result in a titration curve that shows how the pH changes as more $0.100\mathrm{M}$ NaOH is added to the lactic acid solution.

Key concepts

Lactic Acid

Lactic acid is an organic compound commonly found in the body. It plays a crucial role in cellular respiration and energy production. During intense exercise, our bodies produce more lactic acid, leading to a burning sensation in the muscles as it accumulates. This compound can donate a proton (H+) making it an acid, and its chemical formula is ${\text{HC}}_3{\text{H}}_3{\text{O}}_3$. Lactic acid is a weak acid, which means it doesn't completely dissociate into ions in solution. The strength of an acid is often expressed using the acid dissociation constant, $K_a$. For lactic acid, $p{K}_a$ is 3.86, which gives an idea of its acidity. A lower $p{K}_a$ value generally indicates a stronger acid. In the context of titration, understanding the properties of lactic acid helps in anticipating how it will react with a base like NaOH.

pH Calculation

The pH of a solution is a measure of its acidity or basicity. In a titration, pH calculation is essential to understand how the solution's acidity changes as a titrant is added. To calculate the pH at various points during a titration, we need to take into account the moles of acid and base present.

• Before Equivalence Point: The pH depends on the remaining unreacted lactic acid. You can use the initial concentration of lactic acid and the $p{K}_a$ to calculate it using the Henderson-Hasselbalch equation.


• At Equivalence Point: All the lactic acid is neutralized, and the pH is determined by the properties of the resulting salt.


• After Equivalence Point: Excess ${\text{OH}}^{-}$ determines the pH, and you calculate it based on the concentration of leftover NaOH.

These calculations enable us to construct a detailed picture of the solution's composition at various stages of titration.

Equivalence Point

During a titration, the equivalence point is a critical concept. It is when the amount of titrant (NaOH in this case) added is stoichiometrically equal to the amount of lactic acid initially present. At this juncture, the acid has completely reacted with the base. For a weak acid like lactic acid, the equivalence point does not necessarily occur at $pH=7$. Instead, it depends on the nature of both the acid and the base. The pH at the equivalence point can be calculated by considering the ions formed and the concentrations of products. It's important to distinguish between the equivalence point and the endpoint. The endpoint is where a physical change indicates that the titration should stop. Ensuring that students grasp these distinctions helps avoid confusion during lab exercises and chemical experiments.

Titration Curve

A titration curve graphically represents the change in pH of the solution as titrant is added. It plots the pH of the solution against the volume of titrant added. This curve for a weak acid-strong base titration, such as lactic acid and NaOH, typically shows a steep rise near the equivalence point. The different sections of the curve offer valuable information:

• Initial region: There's a slow rise in pH as the added base begins to neutralize the lactic acid.


• Buffer region: The slope of the graph levels off indicating the formation of a buffer system comprising both weak acid and its conjugate base.


• Near Equivalence Point: A rapid increase in pH shows the swift transition from acidic to basic conditions.


• Post-equivalence region: The pH slowly increases as excess NaOH determines the solution's basicity.

Understanding this visual change assists greatly in interpreting the titration process and the chemical dynamics occurring at each stage.