A 0.5895-g sample of impure magnesium hydroxide is dissolved in 100.0 mL of 0.2050 M HCl solution. The excess acid then needs 19.85 mL of 0.1020 M NaOH for neutralization. Calculate the percentage by mass of magnesium hydroxide in the sample, assuming that it is the only substance reacting with the HCl solution.

Verified step by step guidance

1. Calculate the moles of HCl initially present using the concentration and volume: \( \text{moles of HCl} = 0.2050 \, \text{M} \times 0.1000 \, \text{L} \).
2. Calculate the moles of NaOH used in the neutralization of excess HCl: \( \text{moles of NaOH} = 0.1020 \, \text{M} \times 0.01985 \, \text{L} \).
3. Since NaOH neutralizes the excess HCl in a 1:1 ratio, the moles of excess HCl are equal to the moles of NaOH used.
4. Subtract the moles of excess HCl from the initial moles of HCl to find the moles of HCl that reacted with magnesium hydroxide.
5. Use the stoichiometry of the reaction \( \text{Mg(OH)}_2 + 2\text{HCl} \rightarrow \text{MgCl}_2 + 2\text{H}_2\text{O} \) to find the moles of \( \text{Mg(OH)}_2 \) that reacted, then calculate the mass of \( \text{Mg(OH)}_2 \) and determine the percentage by mass in the sample.

Key Concepts

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions based on the balanced chemical equation. It allows us to determine the amount of a substance consumed or produced in a reaction. In this question, stoichiometry is essential for relating the moles of HCl reacted with magnesium hydroxide to the moles of NaOH used for neutralization.

Molarity

Molarity is a measure of concentration defined as the number of moles of solute per liter of solution. It is crucial for calculating the amount of acid and base involved in the reaction. In this problem, the molarity of HCl and NaOH solutions is used to find the moles of each reactant, which are necessary for determining the mass percentage of magnesium hydroxide.

Mass Percentage

Mass percentage is a way of expressing the concentration of a component in a mixture, calculated as the mass of the component divided by the total mass of the mixture, multiplied by 100. In this scenario, calculating the mass percentage of magnesium hydroxide involves determining the mass of magnesium hydroxide that reacted with HCl and comparing it to the total mass of the impure sample.