Question

Concentrated hydrochloric acid is usually available at a concentration of 37.7 percent by mass. What is its molar concentration? (The density of the solution is \(1.19 \mathrm{~g} / \mathrm{mL}\).)

Short answer

The molar concentration of the solution is approximately 12.3 M.

Step-by-step solution

Understand Given Data

We have a hydrochloric acid solution with a mass percentage of 37.7%. This means that there are 37.7 grams of HCl in every 100 grams of solution. The solution's density is given as 1.19 g/mL.

Calculate the Mass of the Solution

To find the molar concentration, we need to know how many grams of solution are in one liter (1000 mL). Using the density, we calculate: \[\text{Mass of the solution} = \text{density} \times \text{volume} = 1.19 \, \frac{\text{g}}{\text{mL}} \times 1000 \, \text{mL} = 1190 \, \text{g}\]

Find Grams of HCl in Solution

Now, using the mass percentage, calculate the mass of HCl in 1190 grams of solution:\[\text{Mass of HCl} = 1190 \, \text{g of solution} \times 0.377 = 448.63 \, \text{g}\]

Calculate Moles of HCl

Determine the number of moles of HCl using its molar mass (36.46 g/mol):\[\text{Moles of HCl} = \frac{448.63 \, \text{g}}{36.46 \, \text{g/mol}} \approx 12.3 \, \text{mol}\]

Determine Molarity

Molarity (M) is the number of moles of solute per liter of solution. So, in 1 L, we have approximately 12.3 moles of HCl.Thus, the molar concentration is:\[12.3 \, \text{M}\]

Key concepts

Hydrochloric Acid

Hydrochloric Acid (HCl) is a strong, corrosive acid that is commonly used in industrial and laboratory applications. It is formed when hydrogen chloride gas ( HCl ) is dissolved in water. Because it disassociates completely in water, it is considered a strong acid.

• Found in gastric acid, it aids digestion in the stomach.
• Used in various industrial processes such as metal refining and cleaning.
• It is usually handled carefully due to its corrosive nature.

Understanding its properties is crucial, especially when dealing with concentrated solutions, which are often used in chemical analysis and reactions.

Mass Percentage

Mass percentage is a way to express the concentration of a component in a mixture or solution. It represents the mass of a solute divided by the total mass of the solution, then multiplied by 100.

How to Calculate Mass Percentage

• Identify the mass of the solute.
• Measure the total mass of the solution.
• Use the formula: \[\text{Mass Percentage} = \left( \frac{\text{mass of solute}}{\text{total mass of solution}} \right) \times 100\]
• The result is given in percentage (%).

In the context of hydrochloric acid, a mass percentage of 37.7% means there are 37.7 grams of HCl per 100 grams of total solution.

Density

Density is a physical property that defines the mass of a substance per unit volume. It is often denoted in units such as grams per milliliter (g/mL). In solution chemistry, density is critical for calculating concentrations from mass percentage values.

Working with Density

The formula for density is:\[\text{Density} = \frac{\text{mass}}{\text{volume}}\]

• For the current problem, the density of the HCl solution is 1.19 g/mL.
• This means for each milliliter of the solution, there are 1.19 grams of material.
• By using this density value, you can convert the volume of the solution (e.g., in liters) into its mass.

Knowing the density helps in finding the exact amounts of each component in a given volume of solution.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is the sum of the atomic masses of all the atoms in a molecule.

Calculating Molar Mass

• For hydrochloric acid, the molecular formula is HCl.
• The molar mass of H (hydrogen) is about 1.01 g/mol and Cl (chlorine) is about 35.45 g/mol.
• Therefore, the molar mass of HCl is:\[1.01 \, \text{g/mol} + 35.45 \, \text{g/mol} = 36.46 \, \text{g/mol}\]

Using the molar mass, you can convert grams of HCl into moles, which allows for the calculation of molarity—the moles of solute per liter of solution.

Solution Chemistry

Solution chemistry involves understanding how substances dissolve and interact in solvent. It examines how solutes like hydrochloric acid can be measured and quantified within a solution.

• Solutions are homogenous mixtures of two or more substances.
• The solute is the substance that is dissolved, while the solvent is the substance in which the solute is dissolved.
• Molarity ( M ) is a key way to express solution concentration, defined as moles of solute per liter of solution.

In the example of HCl , knowing the density and mass percentage enables us to find the number of moles of solute and calculate its molarity. This allows for accurate preparation and use in various applications.