Question

Malonic acid $\left({\mathrm{HO}}_2{\mathrm{CCH}}_2{\mathrm{CO}}_2\mathrm{H}\right)$ is a diprotic acid. In the titration of malonic acid with $\mathrm{NaOH}$, stoichiometric points occur at $\mathrm{pH}=3.9$ and 8.8. A 25.00-mL sample of malonic acid of unknown concentration is titrated with $0.0984M\mathrm{NaOH}$, requiring $31.50\mathrm{mL}$ of the $\mathrm{NaOH}$ solution to reach the phenolphthalein end point. Calculate the concentration of malonic acid in the unknown solution. (See Exercise $103.$ )

Short answer

The concentration of Malonic Acid in the unknown solution can be determined using the following steps: 1. Calculate moles of NaOH required to neutralize Malonic Acid: Moles of NaOH = 0.0984 M × 31.50 mL × (1 L / 1000 mL) 2. Calculate moles of Malonic Acid: Moles of Malonic Acid = Moles of NaOH / 2 3. Calculate concentration of Malonic Acid: Concentration of Malonic Acid = Moles of Malonic Acid / (25.00 mL × (1 L / 1000 mL))

Step-by-step solution

Calculate moles of NaOH required to neutralize Malonic Acid

First, we need to calculate moles of NaOH that were required to neutralize the Malonic Acid. To do so, we'll use the formula: Moles of NaOH = Molarity of NaOH × Volume of NaOH Moles of NaOH = 0.0984 M × 31.50 mL × (1 L / 1000 mL)

Calculate moles of Malonic Acid

Since Malonic acid is a diprotic acid, it will react with two moles of NaOH per mole of Malonic Acid. Hence, we can determine the moles of Malonic Acid as follows: Moles of Malonic Acid = Moles of NaOH / 2

Calculate concentration of Malonic Acid

Now that we have the moles of Malonic Acid, we can calculate its concentration in the initial solution by using the formula: Concentration of Malonic Acid = Moles of Malonic Acid / Initial volume in L Initial volume of Malonic Acid = 25.00 mL × (1 L / 1000 mL) Remember to convert the volume of Malonic Acid from mL to L before dividing.

Key concepts

Understanding Diprotic Acids

A diprotic acid is a type of acid that can donate two protons or hydrogen ions per molecule in solution. This characteristic results in unique behavior during chemical reactions, particularly in titration procedures. Malonic acid, as mentioned in the exercise, is a diprotic acid.
When malonic acid participates in a titration, each molecule has two available protons to react with a base like sodium hydroxide (NaOH). Therefore, this acid undergoes two ionization steps, each having its own equivalence point. This is why two distinct pH points, 3.9 and 8.8, are observed.
During a titration, as each proton is removed, the chemical species in the solution change, which can be detected by a pH indicator or a pH meter. Understanding the behavior of diprotic acids is beneficial in determining their concentration in titration experiments.

Neutralization Reaction in Titration

A neutralization reaction is a chemical reaction in which an acid and a base react to form water and a salt. In the case of titrating a diprotic acid like malonic acid with NaOH, neutralization occurs in two stages.

• In the first stage, the first proton is deprotonated, forming a salt and water.
• In the second stage, the second proton is removed, leading to another formation of salt and water.

In the exercise, malonic acid and NaOH react according to the stoichiometric ratios of the reaction. Since every molecule of malonic acid can donate two protons, a complete reaction with NaOH proceeds through this reaction:
1 mole of malonic acid neutralizes 2 moles of NaOH.
Using these stepwise neutralization reactions helps in determining the endpoints and ensuring proper titration methodology. Titration indicators like phenolphthalein can be used to signal these endpoints clearly.

Molarity Calculation in Titration

Molarity is an essential concept in titration as it defines the concentration of a solution. It is measured in moles of solute per liter of solution.
During a titration, you can calculate the molarity of an unknown solution by knowing the molarity and volume of the titrant, and the volume of the analyte. For this exercise, the titrant is NaOH, and the analyte is the unknown concentration malonic acid solution.

• First, calculate the moles of NaOH used: this is obtained by multiplying the molarity by its volume, ensuring the volume is in liters.
• Next, determine the moles of malonic acid using the relationship that one mole of the acid interacts with two moles of NaOH.
• Finally, determine the molarity of the malonic acid by dividing the number of moles by the initial volume of the solution, converted to liters.

Converting all units appropriately and using the stoichiometric relationships of the reaction allows for accurate concentration determination.