Problem 90 - Chemistry The Central Science

Question

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 \(\mathrm{mL}\) of 1.010 \(\mathrm{M}\) 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.

Step-by-Step Solution

Answer

The percentage by mass of calcium carbonate (CaCO3) in the limestone rock sample is approximately 98.4%. This value was obtained by considering the stoichiometry of the involved chemical reactions, calculating the moles of HCl that reacted with CaCO3, determining the moles of CaCO3 in the rock sample, and finally computing the mass and percentage of CaCO3 in the sample.

Step 1: Write down the balanced chemical equations involved in the reactions

First, we have the reaction between calcium carbonate and hydrochloric acid: CaCO3 (s) + 2 HCl (aq) → CaCl2 (aq) + H2O (l) + CO2 (g) Next, we have the reaction between the excess hydrochloric acid and sodium hydroxide: HCl (aq) + NaOH (aq) → NaCl (aq) + H2O (l)

Step 2: Calculate the moles of HCl reacted with CaCO3 and NaOH

We can calculate the moles of HCl that reacted with the CaCO3 and NaOH. First, let's find the moles of HCl added initially: moles of HCl = volume (L) × concentration (M) moles of HCl = 0.03 L × 1.035 mol/L = 0.03105 mol Next, let's find the moles of HCl that reacted with the NaOH: moles of HCl = volume (L) × concentration (M) moles of HCl = 0.01156 L × 1.010 mol/L = 0.0116736 mol

Step 3: Calculate the moles of HCl that reacted with CaCO3

By subtracting the moles of HCl that reacted with NaOH from the moles of HCl added initially, we can determine the moles of HCl that reacted with the CaCO3: moles of HCl reacted with CaCO3 = total moles of HCl - moles of HCl reacted with NaOH moles of HCl reacted with CaCO3 = 0.03105 mol - 0.0116736 mol ≈ 0.0193764 mol

Step 4: Calculate the moles of CaCO3 in the rock sample

By keeping the stoichiometry of the reaction between CaCO3 and HCl in mind, we can calculate the moles of CaCO3 in the rock sample: CaCO3 (s) + 2 HCl (aq) → CaCl2 (aq) + H2O (l) + CO2 (g) 1 mole of CaCO3 reacts with 2 moles of HCl. Therefore, moles of CaCO3 = moles of HCl reacted with CaCO3 / 2 moles of CaCO3 ≈ 0.0193764 mol / 2 ≈ 0.0096882 mol

Step 5: Calculate the mass of CaCO3 in the rock sample

Now, we can find the mass of CaCO3 in the rock sample: mass of CaCO3 = moles of CaCO3 × molar mass of CaCO3 mass of CaCO3 ≈ 0.0096882 mol × (40.08 + 12.01 + 3 × 16.00) g/mol ≈ 1.228 g

Step 6: Calculate the percentage of CaCO3 in the rock sample

Finally, we can calculate the percentage by mass of CaCO3 in the rock sample: percentage of CaCO3 = (mass of CaCO3 / mass of rock sample) × 100% percentage of CaCO3 ≈ (1.228 g / 1.248 g) × 100% ≈ 98.4% The percentage by mass of calcium carbonate in the rock sample is approximately 98.4%.

Key Concepts

Limestone Analysis

Limestone analysis involves determining the composition of a limestone sample, commonly focusing on the amount of calcium carbonate present. This is crucial for various industries, as calcium carbonate is used in construction, manufacturing, and even agriculture. The first step in analyzing limestone is to take a representative sample from the rock. In our example, a 1.248-gram sample was used, which ensures that the results are applicable to the entire rock source.

One of the most reliable methods for limestone analysis is an acid-base titration. By reacting the limestone with an acid, any calcium carbonate present will dissolve, allowing for its quantity to be measured indirectly. This is achieved through a series of chemical reactions where the limestone sample is dissolved in hydrochloric acid and the excess acid is neutralized with sodium hydroxide.

• Take a precise weight of the limestone sample.
• React it with a known concentration and volume of hydrochloric acid.
• Determine the unreacted hydrochloric acid by titration with sodium hydroxide.
• Calculate the calcium carbonate percentage by using the stoichiometry of the reactions involved.

This method provides an accurate assessment of the composition of limestone, potentially revealing the purity of the sample.

Acid-Base Titration

Acid-base titration is a fundamental laboratory method used to measure the concentration of an unknown acid or base. It involves the gradual addition of a known concentration of base (or acid) to react with the acid (or base) in your sample, allowing for precise calculation of concentration and purity.

In the context of limestone analysis, the reaction of calcium carbonate with hydrochloric acid is pivotal. This process can be broken down into two key reactions: initially, calcium carbonate reacts with the hydrochloric acid, followed by titrating the leftover hydrochloric acid with a sodium hydroxide solution.

• The release of carbon dioxide gas when CaCO3 and HCl react is a visible indication of the reaction occurring.
• Once the excess HCl is determined through titration with NaOH, you can determine how much HCl reacted initially with the limestone.
• The method hinges on using a balanced equation to interpret the quantities of substances involved accurately.

Proper execution of the titration is crucial, as it directly influences the accuracy of the calcium carbonate determination. Given the complexity, practice and familiarity with titration techniques are needed for reliable results.

Chemical Stoichiometry

Chemical stoichiometry is the study of the relationships between quantities of reactants and products in chemical reactions, providing a framework for predicting reaction outcomes. Stoichiometry is essential when calculating proportions of reactants like in the limestone analysis exercise, where calcium carbonate reacts with hydrochloric acid.

Each chemical equation in stoichiometry must be balanced. This means that the number of atoms for each element in the reactants side must equal the number on the products side. For limestone's decomposition reaction, the equation is:
CaCO3 (s) + 2 HCl (aq) → CaCl2 (aq) + H2O (l) + CO2 (g)

• One mole of calcium carbonate reacts with two moles of hydrochloric acid.
• Understanding this ratio allows for the calculation of how much of each reactant you will need to react completely without any leftover.
• By knowing this proportion, we can also deduce the amount of calcium carbonate in a given sample.

In practical measurements, stoichiometry guides the conversion from moles to grams, using substances' molar masses. This connection between mathematical formulation and chemical reactions is what allows chemists to measure and predict outcomes accurately.