Problem 126 - Chemistry The Molecular Science

Question

When \(12.6 \mathrm{~g}\) calcium carbonate (the principal component of chalk) is treated with \(63.0 \mathrm{~mL}\) hydrochloric acid (muriatic acid sold in hardware stores; density \(=1.096 \mathrm{~g} / \mathrm{mL}\) ), the calcium carbonate reacts with the acid, goes into solution, and carbon dioxide gas bubbles out of the solution. After all of the carbon dioxide has escaped, the solution weighs \(76.1 \mathrm{~g} .\) Calculate the volume (in liters) of carbon dioxide gas that was produced. (The density of the carbon dioxide gas is \(1.798 \mathrm{~g} / \mathrm{L}\).)

Step-by-Step Solution

Answer

3.086 liters

Step 1: Write the Balanced Equation

The chemical reaction is between calcium carbonate (\(\text{CaCO}_3\)) and hydrochloric acid (\(\text{HCl}\)). The balanced equation is:\[\text{CaCO}_3 + 2\text{HCl} \rightarrow \text{CaCl}_2 + \text{CO}_2 + \text{H}_2\text{O}\] Here, \(\text{CO}_2\) is the carbon dioxide gas that will bubble out of solution.

Step 2: Calculate Mass of Reactants

Calculate the mass of hydrochloric acid:\[m_{\text{HCl}} = \text{Volume} \times \text{Density} = 63.0\, \text{mL} \times 1.096 \frac{\text{g}}{\text{mL}} = 69.048 \text{ g}\]So, the total initial mass of the reactants is:\[m_{\text{total}} = m_{\text{CaCO}_3} + m_{\text{HCl}} = 12.6 \text{ g} + 69.048 \text{ g} = 81.648 \text{ g}\]

Step 3: Determine Mass of CO2 Produced

The final mass after the reaction is given as 76.1 g. Using the conservation of mass, the mass of \(\text{CO}_2\) produced is:\[m_{\text{CO}_2} = m_{\text{total}} - m_{\text{final}} = 81.648 \text{ g} - 76.1 \text{ g} = 5.548 \text{ g}\]

Step 4: Calculate Volume of CO2 at Given Density

Use the density of carbon dioxide to find its volume:\[\text{Volume of } \text{CO}_2 = \frac{m_{\text{CO}_2}}{\text{Density of } \text{CO}_2} = \frac{5.548 \text{ g}}{1.798 \frac{\text{g}}{\text{L}}} \approx 3.086 \text{ L}\]

Step 5: Conclusion

The volume of carbon dioxide gas produced in the reaction is approximately 3.086 liters.

Key Concepts

Calcium Carbonate

Calcium carbonate is a compound with the chemical formula \(\text{CaCO}_3\), and it is a major component of chalk, limestone, and marble. In this exercise, calcium carbonate acts as the reactant which reacts with hydrochloric acid to form carbon dioxide gas, water, and calcium chloride.
Calcium carbonate is often found in rocks and is also a key element in the shells of marine organisms, snails, and eggshells.
It is a common substance that finds its application in various fields:

• Construction: used in making cement and mortar.
• Environmental: employed in the treatment of water and soil.
• Healthcare: a dietary calcium supplement.

Understanding the role and significance of calcium carbonate helps clarify its necessity in the stoichiometry of chemical reactions.

Hydrochloric Acid

Hydrochloric acid, or \(\text{HCl}\), is a strong, corrosive acid commonly used in chemistry labs and industrial applications. In the given reaction, hydrochloric acid reacts with calcium carbonate to produce carbon dioxide gas, water, and calcium chloride.
This acid is found in stomach gastric acids where it helps break down food.
These are some key points to know about hydrochloric acid:

• Properties: It is a colorless to light yellow liquid with a pungent odor.
• Uses: Employed in the production of chlorides, fertilizers, and dyes as well as in the textile and rubber industries.
• Safety: Due to its highly corrosive nature, it must be handled with care.

Understanding the reaction and properties of hydrochloric acid is crucial in experimental chemistry and industrial processes.

Carbon Dioxide Gas

Carbon dioxide, \(\text{CO}_2\), is a colorless and odorless gas produced during the chemical reaction between calcium carbonate and hydrochloric acid.
In this exercise, calculating its formation helps elucidate stoichiometric principles and conservation of mass in chemical reactions.
Here are some important insights into carbon dioxide:

• Natural Occurrence: Exhaled by animals and used by plants in photosynthesis.
• Industrial Relevance: Utilized in carbonated beverages, fire extinguishers, and dry ice.
• Environmental Impact: A significant greenhouse gas contributing to climate change.

By understanding carbon dioxide's roles and characteristics, students can grasp its importance in both chemical and environmental contexts.

Balanced Chemical Equation

A balanced chemical equation is essential to accurately describe the stoichiometry of a chemical reaction. In this exercise, the balanced equation \(\text{CaCO}_3 + 2\text{HCl} \rightarrow \text{CaCl}_2 + \text{CO}_2 + \text{H}_2\text{O}\) shows the transformation of reactants into products.
Creating a balanced equation is crucial because:

• Mole Ratio: It provides the correct proportions of reactants needed to form products.
• Conservation of Mass: Ensures that no atoms are lost or gained during a reaction.
• Predicts Outcome: Helps in predicting the amounts of products made and reactants used.

Learning to balance equations is a fundamental skill in chemistry that enables students to understand and predict chemical reactions accurately.