Problem 105 - Chemistry The Molecular Science

Question

An aqueous hydrochloric acid solution is \(37.0 \% \mathrm{HCl}\) by mass. The density of the solution is \(1.185 \mathrm{~g} / \mathrm{mL}\). Calculate the molarity of \(\mathrm{HCl}\) in this solution.

Step-by-Step Solution

Answer

The molarity of the HCl solution is 12.03 M.

Step 1: Understand the Given Information

We have a hydrochloric acid solution that is 37.0% HCl by mass with a density of 1.185 g/mL. We need to calculate the molarity of HCl, which is the number of moles of HCl per liter of solution.

Step 2: Calculate Mass of HCl in 1 L of Solution

Since the density of the solution is 1.185 g/mL, the mass of 1 L (or 1000 mL) of solution is \(1.185 \times 1000 = 1185 \text{ g}\). \(37.0\%\) of this mass is HCl, so the mass of HCl is \(0.37 \times 1185 = 438.45 \text{ g}\).

Step 3: Convert Mass of HCl to Moles

The molar mass of HCl is approximately 36.46 g/mol. To find the number of moles of HCl, divide the mass of HCl by its molar mass: \(\frac{438.45 \text{ g}}{36.46 \text{ g/mol}} = 12.03 \text{ moles HCl}\).

Step 4: Determine the Molarity of the Solution

The molarity is the number of moles of solute per liter of solution. Since we have calculated there are 12.03 moles of HCl in 1 L of solution, the molarity is 12.03 M.

Key Concepts

Hydrochloric Acid

Hydrochloric acid, abbreviated as HCl, is a strong, corrosive acid. It is commonly found in both industrial and laboratory settings due to its applications and properties. In aqueous solutions, it dissociates completely, meaning it releases hydrogen ions

• Strong acid: Dissociates fully in water.
• Pungent smell, clear liquid.
• Used in cleaning and pH regulation.

Hydrochloric acid plays a vital role in chemical reactions where it is used for breaking down substances, making laboratory solutions, and even in the digestive systems of animals.
In the context of calculating molarity, the concentration of hydrochloric acid is essential for further applications, such as titration or adjusting pH levels.

Density

Density is a measure of mass per unit volume. It helps determine how much mass is in a given space, which is crucial in chemical calculations. In the case of our HCl solution, the density is given as 1.185 g/mL.
To find out how much a liter of the solution weighs, we use the formula: \[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]

• Measurements such as 1,000 mL = 1 L are used.
• Aids in converting between volumes and masses.
• Crucial for accurate preparation of solutions.

Understanding density allows us to convert between the volume of the solution (1 L) and its mass (1,185 g). This conversion is used to understand how much HCl is present in the solution by mass.

Molar Mass

Molar mass is the mass of one mole of a substance, providing a bridge between mass and number of particles. For hydrochloric acid, it is about 36.46 g/mol.
You find molar mass by adding the atomic masses of hydrogen (approximately 1.01 g/mol) and chlorine (approximately 35.45 g/mol).

• Molar mass helps convert mass to moles.
• Calculated using the periodic table.
• Useful in stoichiometric calculations.

In our calculation, molar mass is used to convert 438.45 grams of HCl into moles, allowing us to determine the concentration of the solution in moles per liter, which is its molarity.

Aqueous Solution

An aqueous solution is one where water is the solvent. The term 'aqueous' signifies that the substance is dissolved in water. This is pertinent because water's properties influence the behavior of dissolved substances.

• HCl completely dissociates in water.
• Aqueous solutions can conduct electricity.
• Water's polarity aids in solubility.

In the exercise, you work with an aqueous solution of hydrochloric acid, which means that HCl is dissolved in water. This affects how HCl interacts with other substances and is a key factor when calculating properties like molarity. Understanding the nature of aqueous solutions helps predict and control the behavior of solutes within the solution.