Problem 42 - Chemistry: Principles and Reactions

Question

Analysis of an unknown acid shows that \(24.55 \mathrm{~mL}\) of \(0.128 \mathrm{M} \mathrm{NaOH}\) are required to react completely with \(0.566 \mathrm{~g}\) of the acid. The equation for. the reaction is $$ \mathrm{HB}(a q)+\mathrm{OH}^{-}(a q) \longrightarrow \mathrm{H}_{2} \mathrm{O}+\mathrm{B}^{-}(a q) $$ What is the molar mass of the acid?

Step-by-Step Solution

Answer

Based on the given information and solution steps, here is a short answer question for students: Question: A 0.566 g sample of an unknown acid, HB, was neutralized by 24.55 mL of 0.128 M NaOH solution. Calculate the molar mass of the unknown acid.

Step 1: Determine the moles of OH- in the NaOH solution.

We are given the volume and molarity of NaOH solution. We can calculate the moles of OH- in the solution by multiplying the volume by the molarity: Moles of OH- = Volume x Molarity We have the volume in mL, so we need to convert it to L first: \(24.55\ \mathrm{ mL} = 24.55 / 1000 = 0.02455\ \mathrm{ L}\) Now, we can find the moles of OH-: Moles of OH- = \((0.02455\ \mathrm{L})({0.128\ \mathrm{M\:NaOH}})\)

Step 2: Determine the moles of HB.

Since the reaction equation shows that there is a 1:1 ratio between the moles of HB and the moles of OH-, the moles of HB are equal to the moles of OH-. Moles of HB = Moles of OH- from Step 1

Step 3: Calculate the molar mass of the acid HB.

We can find the molar mass of the acid HB by dividing the mass of the acid (given in grams) by the moles of HB (calculated in Step 2): Molar mass of HB = \(\frac{Mass\ of\ HB}{Moles\ of\ HB}\) Substitute the known values into the equation and calculate the molar mass of HB: Molar mass of HB = \(\frac{0.566\ \mathrm{g}}{Moles\ of\ HB}\) Remember to calculate and substitute the moles of OH- from Step 1 and use it as the moles of HB in the formula.

Key Concepts

Acid-Base Titration

An acid-base titration is a laboratory method used to determine the concentration of an acid or base in a solution. In this method, a solution of known concentration, called the titrant, is added to a solution of unknown concentration until the chemical reaction between the two is complete. The point at which this reaction is complete is known as the equivalence point.
In the given problem, the titration process involves an unknown acid reacting with a sodium hydroxide (NaOH) solution. The NaOH serves as the titrant with a known concentration. When it is added to the acidic solution, a neutralization reaction occurs, forming water and a conjugate base. The volume of NaOH used to reach the equivalence point helps determine the original concentration of the acid.
The key to understanding titration is knowing that the number of moles of base and acid must be equal at the equivalence point, which allows the calculation of the unknown quantity through stoichiometric relationships.

Chemical Reaction Equations

Chemical reaction equations are symbolic representations of chemical reactions. They show the reactants and products involved in the reaction as well as their stoichiometric relationships.
For example, in the problem's reaction: \[ \text{HB (aq) + OH}^{-} \text{ (aq)} \rightarrow \text{H}_2\text{O} + \text{B}^-(\text{aq}) \] This equation tells us that one mole of the acid HB reacts with one mole of hydroxide ions (OH-) to produce one mole of water and one mole of the base B-.
Understanding chemical equations is crucial for solving problems related to chemical reactions, as they provide the information needed to calculate the amounts of reactants consumed and products formed. Such information is vital in titration and stoichiometric calculations.

Mole Concept

The mole concept is a fundamental principle in chemistry that provides a way to quantify the amount of substance. One mole of any substance contains Avogadro's number of entities, which is approximately \(6.022 \times 10^{23}\). This concept helps bridge the gap between the atomic scale and the scale of laboratory measurements.
In the context of the exercise, the mole concept allows us to calculate the number of moles of hydroxide ions that reacted with the acid. We use the volume and the molarity of the NaOH solution to determine moles using the formula: \[ \text{Moles} = \text{Volume (L)} \times \text{Molarity} \]
This calculation is essential for determining the moles of the acid, enabling us to assess how much of the acid is present, thereby allowing us to find the molar mass of the acid.

Stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions. It uses the balanced chemical equation to derive the relationships between the quantities of reactants and products.
In the given problem, stoichiometry plays a key role in determining the moles of the unknown acid. The chemical equation shows that the reaction involves a one-to-one molar relationship between the acid (HB) and hydroxide ions (OH-).
This one-to-one ratio simplifies the calculation: the moles of the base used in the reaction equal the moles of the acid present. From here, dividing the mass of the acid by the number of moles gives the molar mass, a crucial piece of information from the exercise. Understanding stoichiometry ensures accurate quantitative analysis of chemical reactions, making it invaluable in laboratory experiments and chemical synthesis.