Problem 77 - Chemistry: Principles and Reactions

Question

A sample of limestone weighing \(1.005 \mathrm{~g}\) is dissolved in \(75.00 \mathrm{~mL}\) of \(0.2500 \mathrm{M}\) hydrochloric acid. The following reaction occurs: $$ \mathrm{CaCO}_{3}(s)+2 \mathrm{H}^{+}(a q) \longrightarrow \mathrm{Ca}^{2+}(a q)+\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O} $$ It is found that \(19.26 \mathrm{~mL}\) of \(0.150 \mathrm{M} \mathrm{NaOH}\) is required to titrate the excess \(\mathrm{HCl}\) left after reaction with the limestone. What is the mass percent of \(\mathrm{CaCO}_{3}\) in the limestone?

Step-by-Step Solution

Answer

Answer: The mass percent of calcium carbonate (CaCO3) in the limestone sample is 78.97%.

Step 1: Calculate moles of HCl initially present

We are given the initial volume and concentration of the HCl solution, so we can calculate the initial moles of HCl. The moles of HCl (initial) = Volume (L) × Concentration (M) Moles of HCl (initial) = 0.075 L × 0.2500 M = 0.01875 mol.

Step 2: Calculate moles of NaOH used

We are given the volume and concentration of the NaOH solution, so we can calculate the moles of NaOH used. The moles of NaOH = Volume (L) × Concentration (M) Moles of NaOH = 0.01926 L × 0.150 M = 0.002889 mol.

Step 3: Calculate moles of HCl reacted with NaOH

In an acid-base reaction, moles of the acid (HCl) and base (NaOH) interact at a 1:1 ratio. Hence, the moles of HCl reacted with NaOH are equal to the moles of NaOH used. Moles of HCl reacted with NaOH = 0.002889 mol.

Step 4: Calculate moles of HCl reacted with CaCO3

To calculate the moles of HCl that reacted with the CaCO3, subtract the moles of HCl reacted with NaOH from the initial amount of HCl. Moles of HCl reacted with CaCO3 = Moles of HCl(initial) - Moles of HCl reacted with NaOH = 0.01875 - 0.002889 = 0.015861 mol

Step 5: Calculate moles of CaCO3

Using the balanced chemical equation, we know that 1 mole of CaCO3 reacts with 2 moles of HCl. Hence, we can calculate the moles of CaCO3 present. Moles of CaCO3 = Moles of HCl reacted with CaCO3 / 2 = 0.015861 / 2 = 0.0079305 mol.

Step 6: Calculate mass of CaCO3

To find the mass of CaCO3, multiply the moles by its molar mass (100.09 g/mol). Mass of CaCO3 = Moles of CaCO3 × Molar mass = 0.0079305 mol × 100.09 g/mol = 0.793194 g.

Step 7: Calculate mass percent of CaCO3

Now, we can calculate the mass percent of CaCO3 in the limestone sample. Mass percent of CaCO3 = (Mass of CaCO3 / Total mass of sample) × 100 Mass percent of CaCO3 = (0.793194 g / 1.005 g) × 100 = 78.97 % (rounded to two decimal places).

Key Concepts

Moles Calculation

Understanding moles is a fundamental concept in chemistry that helps in quantifying substances at the molecular level. The mole is a unit that measures the amount of substance, and the concept is essential when dealing with chemical reactions and equations. In a solution, moles can be calculated using the formula: \[ \text{Moles} = \text{Volume (L)} \times \text{Concentration (M)} \] This equation is critically important in titration experiments where we need to assess how much of a particular substance is present. For example, in the given problem, we calculated the moles of hydrochloric acid (\( \text{HCl} \)) and sodium hydroxide (\( \text{NaOH} \)) to understand how they interact in an acid-base titration. By multiplying the volume of the solution in liters by its concentration in molarity, we find the number of moles, which then helps us in further calculations and reactions.

Limestone Analysis

Limestone is mainly composed of calcium carbonate (\( \text{CaCO}_3 \)), and analyzing its composition involves determining what percentage of the limestone is made up of \( \text{CaCO}_3 \). This analysis is important for various industries and environmental studies. In the exercise, we discover the amount of \( \text{CaCO}_3 \) by first reacting our limestone with \( \text{HCl} \), and then using \( \text{NaOH} \) to titrate the leftover \( \text{HCl} \).

• Start by determining how much \( \text{HCl} \) reacts with the \( \text{CaCO}_3 \) using the balanced chemical equation.
• Subtracting the moles of \( \text{HCl} \) that react with \( \text{NaOH} \) reveals the moles that reacted with the \( \text{CaCO}_3 \).
• Using this information, you can calculate the mass of \( \text{CaCO}_3 \) in the original sample and determine its mass percent.

This procedure helps achieve accurate results in identifying the content of calcium carbonate in limestone, which is critical for quality control and environmental assessments.

Chemical Reaction Equation

A chemical reaction equation represents the transformation of reactants into products. It is a symbolic depiction of the chemical changes that occur. In the provided exercise, the reaction of calcium carbonate with hydrochloric acid is a perfect example of an acid-base reaction. The reaction can be shown as: \[ \text{CaCO}_3 (s) + 2 \text{H}^+ (aq) \rightarrow \text{Ca}^{2+} (aq) + \text{CO}_2 (g) + \text{H}_2\text{O} \]

• This equation shows that one mole of calcium carbonate reacts with two moles of hydrogen ions.
• It is balanced, meaning the number of each type of atom is the same on both sides of the equation, ensuring the conservation of mass.

Understanding this equation is crucial when calculating the amounts of reactants and products, which is why we use it to determine how much \( \text{CaCO}_3 \) was in the limestone. This balanced equation guides the stoichiometry calculations and is central to comprehending the interactions and transformations in the chemical process.