Problem 118 - General Chemistry

Question

A 0.239 -g sample of unknown organic base is dissolved in water and titrated with a \(0.135 \mathrm{M}\) hydrochloric acid solution. After the addition of \(18.35 \mathrm{~mL}\) of acid, a \(\mathrm{pH}\) of 10.73 is recorded. The equivalence point is reached when a total of \(39.24 \mathrm{~mL}\) of \(\mathrm{HCl}\) is added. The base and acid combine in a 1: 1 ratio.

Step-by-Step Solution

Answer

The molar mass of the base is approximately 45.13 g/mol.

Step 1: Calculate Moles of Acid

To find the moles of \(\text{HCl} \), we need to use the volume of \(\text{HCl} \) solution at the equivalence point:\[ V = 39.24 \, \text{mL} = 0.03924 \, \text{L} \]Using the molarity (\(M\)) of the acid:\[\text{Moles of } \text{HCl} = M \times V = 0.135 \, \text{mol/L} \times 0.03924 \, \text{L} = 0.0052974 \, \text{mol}\]

Step 2: Determine Molar Mass of the Base

The moles of the base will equal the moles of \(\text{HCl}\) as they react in a 1:1 ratio. Using the mass of the base sample and the calculated moles, we can determine its molar mass:\[\text{Molar mass} = \frac{\text{mass of sample}}{\text{moles}} = \frac{0.239 \, \text{g}}{0.0052974 \, \text{mol}} \approx 45.13 \, \text{g/mol}\]

Step 3: Verify the Calculation using pH

The \(\text{pH}\) value is provided at a point before the equivalence where the solution is basic. At a \(\text{pH} = 10.73\), the \(\text{pOH}\) can be calculated by:\[\text{pOH} = 14 - \text{pH} = 3.27 \]Therefore, \(\text{[OH}^-\text{]} = 10^{-3.27} \, \text{M}\), confirming that base is present before equivalence.

Key Concepts

Molarity Calculation

Molarity is a fundamental concept in chemistry that helps us understand the concentration of a solution. It is defined as the number of moles of solute per liter of solution. In the context of acid-base titration, molarity allows us to determine how much reagent is required to reach the equivalence point. To calculate molarity, use the formula:

• \( ext{Molarity} (M) = \frac{n}{V} \)

where \( n \) is the number of moles of the solute and \( V \) is the volume of the solution in liters.During the titration of the organic base with hydrochloric acid (HCl), we found that at the equivalence point, a total of 0.0052974 moles of HCl had been added. This was determined by multiplying the molarity of the HCl (0.135 M) by the volume of the HCl solution used at the equivalence point (39.24 mL or 0.03924 L).Understanding molarity allows chemists to precisely gauge how much acid is necessary to neutralize or interact with a given base. This precise measurement is key in reactions where the amount of reactant is directly related to the outcome.

Equivalence Point

The equivalence point in a titration is a critical concept, marking the stage where the quantity of titrant added exactly neutralizes the reactant present in the flask. At this juncture, the amount of acid and base are stoichiometrically equivalent. In the provided exercise, the equivalence point was reached with the addition of 39.24 mL of hydrochloric acid. The base and acid reacted in a 1:1 ratio, meaning that for every mole of base, one mole of acid was required to achieve neutrality. Reaching the equivalence point is essential for determining the concentration of an unknown sample.

• It allows us to calculate the molar mass of the unknown base.
• By knowing the moles of HCl needed, we deduced the moles of the organic base.

These moles were used with the mass of the base sample to compute its molar mass, which was about 45.13 g/mol. The concept of the equivalence point is pivotal in analytical chemistry. It provides insights into the properties and quantities required for reactions to proceed to completion.

pH and pOH Relationship

The relationship between pH and pOH is central to understanding the nature of acidic and basic solutions. pH is a scale used to specify the acidity or basicity of an aqueous solution, while pOH represents the concentration of hydroxide ions in the solution.The formula connecting pH and pOH is:

• \( ext{pH} + ext{pOH} = 14 \)

In the titration exercise, reading a pH of 10.73 at a point before equivalence indicated a basic solution. Using the relationship, we calculated the pOH:

• \( ext{pOH} = 14 - 10.73 = 3.27 \)

This value confirmed the presence of excess base and highlighted that the resolution of acid had not yet neutralized the base entirely.The complementary nature of pH and pOH helps chemists determine the point of neutrality or the presence of excess acids or bases in a solution.
These calculations verify the status of the reaction at different stages, ensuring accuracy and understanding in titrations and broader chemical analysis.