Problem 105 - Chemistry: The Central Science

Question

A solid sample of \(\mathrm{Zn}(\mathrm{OH})_{2}\) is added to \(0.350 \mathrm{~L}\) of \(0.500\) \(M\) aqueous HBr. The solution that remains is still acidic. It is then titrated with \(0.500 \mathrm{M} \mathrm{NaOH}\) solution, and \(\mathrm{it}\) takes \(88.5 \mathrm{~mL}\) of the \(\mathrm{NaOH}\) solution to reach the equivalence point. What mass of \(\mathrm{Zn}(\mathrm{OH})_{2}\) was added to the HBr solution?

Step-by-Step Solution

Answer

The mass of the Zn(OH)₂ sample added to the HBr solution is approximately 6.50 g.

Step 1: Calculate the moles of \(\mathrm{H}^+\) ions left in the HBr solution

Using the volume and molarity of the \(\mathrm{NaOH}\) solution used for titration, we can calculate the moles of remaining \(\mathrm{H}^+\) ions in the HBr solution after reacting with \(\mathrm{Zn(OH)_2}\). Moles of NaOH = Molarity × Volume Moles of NaOH = 0.500 M × \(\frac{88.5 mL}{1000 mL/L}\) = 0.04425 moles Since the moles of NaOH and H⁺ react 1:1 to produce water (according to the neutralization reaction between a strong acid and a strong base), the moles of remaining H⁺ ions can be determined: Moles of H⁺ ions remaining in HBr solution = 0.04425 moles

Step 2: Calculate the moles of \(\mathrm{Zn(OH)_2}\) that reacted with HBr

Now we need to find out how many moles of H⁺ ions were in the HBr solution initially. Moles of H⁺ ions in HBr solution initially = Molarity × Volume Moles of H⁺ ions in HBr solution initially = 0.500 M × 0.350 L = 0.175 moles From this, we can determine the moles of H⁺ ions that reacted with Zn(OH)₂: Moles of H⁺ ions reacted with Zn(OH)₂ = Initial moles of H⁺ ions - Remaining moles of H⁺ ions Moles of H⁺ ions reacted with Zn(OH)₂ = 0.175 moles - 0.04425 moles = 0.13075 moles Each molecule of Zn(OH)₂ reacts with two H⁺ ions, so we can calculate the moles of Zn(OH)₂ that reacted with HBr: Moles of Zn(OH)₂ = Moles of H⁺ ions reacted with Zn(OH)₂ ÷ 2 Moles of Zn(OH)₂ = 0.13075 moles ÷ 2 = 0.065375 moles

Step 3: Calculate the mass of \(\mathrm{Zn(OH)_2}\)

Using the molar mass of Zn(OH)₂ (65.38 g/mol for Zn + 2×(15.999 g/mol for O + 1.008 g/mol for H) = 99.394 g/mol), we can calculate the mass of Zn(OH)₂: Mass of Zn(OH)₂ = Moles of Zn(OH)₂ × Molar mass of Zn(OH)₂ Mass of Zn(OH)₂ = 0.065375 moles × 99.394 g/mol ≈ 6.50 g The mass of the Zn(OH)₂ sample added to the HBr solution is approximately 6.50 g.

Key Concepts

Acid-Base Titration

In the chemistry lab, titration is a crucial analytical method used to determine the concentration of a known reactant. Acid-base titration, in particular, involves the gradual addition of an acid to a base (or vice versa) to neutralize the pH of the solution.

The point at which the acid completely neutralizes the base (or vice versa) is known as the equivalence point. It’s usually marked by a sudden change in the color of the indicator present in the solution, indicating that stoichiometrically equivalent amounts of acid and base have reacted.

When working acid-base titration problems, it’s important to remember the neutralization reaction typically is a 1:1 reaction, where one mole of acid reacts with one mole of base to produce salt and water. However, it is essential to consider the exact reaction taking place, as some acids and bases can react in different molar ratios. Always write out the balanced equation to guide your stoichiometric calculations.

Stoichiometry

Stoichiometry stems from the Greek words 'stoicheion' (element) and 'metron' (measure), and it's a section of chemistry that involves calculating the amounts of reactants and products in a chemical reaction.

It is the foundation for many procedures in chemistry, such as determining concentrations in titrations. Stoichiometry requires a balanced chemical equation to ensure that mass and charge are conserved and provides the framework to understand the relationship between different substances in a reaction.

The stoichiometry of a reaction can tell us how many moles of a reactant are needed to react with a certain amount of another reactant. We can use this information to find unknown concentrations, predict the amount of product formed, or in the case of our exercise, determine the amount of an acid necessary to neutralize a base, or vice versa.

Molar Mass Calculation

Molar mass is the mass of one mole of a substance (the Avogadro number of molecules), and it's expressed in grams per mole (g/mol). It's a bridge between the microscopic world of atoms and molecules and the macroscopic world of grams and liters that we interact with in the lab.

To calculate molar mass, you simply add up the atomic masses for each element in the molecule from the periodic table. For instance, zinc hydroxide, \( \mathrm{Zn(OH)_2} \), consists of one zinc atom, two oxygen atoms, and two hydrogen atoms.

The molar mass calculation is essential in stoichiometry calculations, as seen in the provided exercise. By knowing the molar mass, you can convert between mass and moles of a substance—enabling you to precisely measure out reactants for a reaction or, in the case of our zinc hydroxide sample, determine the mass of a substance given its quantity in moles.