A 1.248-g sample of limestone rock is pulverized and then treated with 30.00 mL of 1.035 M HCl solution. The excess acid then requires 11.56 mL of 1.010 M NaOH for neutralization. Calculate the percentage by mass of calcium carbonate in the rock, assuming that it is the only substance reacting with the HCl solution.

Verified step by step guidance

1. Calculate the moles of HCl initially added using the formula: \( \text{moles of HCl} = M \times V \), where \( M \) is the molarity and \( V \) is the volume in liters.
2. Calculate the moles of NaOH used to neutralize the excess HCl using the formula: \( \text{moles of NaOH} = M \times V \).
3. Determine the moles of excess HCl by using the stoichiometry of the neutralization reaction: \( \text{moles of excess HCl} = \text{moles of NaOH} \).
4. Subtract the moles of excess HCl from the initial moles of HCl to find the moles of HCl that reacted with calcium carbonate.
5. Use the stoichiometry of the reaction between calcium carbonate and HCl (\( \text{CaCO}_3 + 2\text{HCl} \rightarrow \text{CaCl}_2 + \text{CO}_2 + \text{H}_2\text{O} \)) to find the moles of calcium carbonate, then calculate its mass and determine the percentage by mass in the rock.

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 calcium carbonate (CaCO3) to the mass of CaCO3 in the limestone sample.

Acid-Base Neutralization

Acid-base neutralization is a chemical reaction where an acid reacts with a base to produce water and a salt. In this scenario, HCl (an acid) reacts with NaOH (a base) to determine the amount of excess HCl after reacting with CaCO3. Understanding this concept is crucial for calculating how much HCl was consumed by the limestone and how much remains for neutralization.

Percentage by Mass

Percentage by mass is a way to express 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 problem, calculating the percentage by mass of calcium carbonate in the limestone involves determining the mass of CaCO3 that reacted with HCl and comparing it to the total mass of the limestone sample.