Problem 9 - Chemistry and Chemical Reactivity

Question

Hydrochloric acid is sold as a concentrated aqueous solution. If the molarity of commercial HCl is 12.0 and its density is \(1.18 \mathrm{g} / \mathrm{cm}^{3},\) calculate the following: (a) the molality of the solution (b) the weight percent of HCl in the solution

Step-by-Step Solution

Answer

(a) Molality is 16.16 m; (b) Weight percent is 37.08%.

Step 1: Understand the Given Information

We are given the molarity of the HCl solution as 12.0 M and the density of the solution as 1.18 g/cm³. We need to calculate the molality and the weight percent of HCl in the solution.

Step 2: Calculate the Total Mass of the Solution

First, we need to find the mass of 1 liter (1000 mL) of the solution, using the density. \[ \text{Mass of solution} = \text{Volume} \times \text{Density} = 1000 \text{ mL} \times 1.18 \text{ g/mL} = 1180 \text{ g} \].

Step 3: Calculate the Moles of HCl

Using the molarity and volume, find the number of moles of HCl in 1 liter of solution. \[ \text{Moles of HCl} = 12.0 \text{ mol/L} \times 1 \text{ L} = 12.0 \text{ moles} \].

Step 4: Calculate the Mass of HCl

Use the molar mass of HCl (approximately 36.46 g/mol) to find the mass of HCl. \[ \text{Mass of HCl} = 12.0 \text{ moles} \times 36.46 \text{ g/mol} = 437.52 \text{ g} \].

Step 5: Calculate the Mass of Water in the Solution

Subtract the mass of HCl from the total mass of the solution to find the mass of water. \[ \text{Mass of water} = 1180 \text{ g} - 437.52 \text{ g} = 742.48 \text{ g} \].

Step 6: Calculate the Molality of the Solution

Molality is defined as moles of solute per kilogram of solvent. Convert the mass of water to kilograms, then calculate molality. \[ \text{Molality} (m) = \frac{12.0 \text{ moles}}{0.74248 \text{ kg}} = 16.16 \text{ m} \].

Step 7: Calculate the Weight Percent of HCl

Weight percent is the mass of the solute divided by the total mass of the solution, multiplied by 100. \[ \text{Weight percent} = \left(\frac{437.52 \text{ g}}{1180 \text{ g}}\right) \times 100 = 37.08\% \].

Key Concepts

Molarity

Molarity is an important concept in chemistry that refers to the concentration of a solute in a solution. It's defined as the number of moles of solute per liter of solution. The formula is:

• Molarity (M) = moles of solute / liters of solution

Understanding molarity is crucial because it helps chemists and students alike understand how concentrated a solution is. If a solution has a molarity of 12.0 M, like our hydrochloric acid (HCl) solution, it means there are 12 moles of HCl in every liter of that solution. Molarity aids in making precise calculations during chemical reactions, enabling chemists to predict how substances will react when mixed. Molarity is especially useful in titration scenarios, where you need to know how much of a reactant will completely react with another substance.

Molality

Molality, unlike molarity, is a measure of the concentration based not on the volume of the solution but on the mass of the solvent. It is expressed in moles of solute per kilogram of solvent. The formula is:

• Molality (m) = moles of solute / kilograms of solvent

One of its advantages over molarity is that molality doesn't change with temperature, as it depends on mass rather than volume. In our problem, we find the molality of the HCl solution by calculating the moles of HCl and dividing by the mass of the water (solvent) in kilograms. This results in the molality of 16.16 mol/kg, indicating a highly concentrated solution. Molality is helpful in problems involving temperature changes, since it remains constant with fluctuations, unlike molarity.

Weight Percent

Weight percent, often expressed as percentage by mass, refers to the ratio of the mass of a component to the total mass of the mixture, multiplied by 100. It's a unit commonly used in chemistry to express concentration and purity. The formula is:

• Weight percent = (mass of solute / mass of solution) × 100

This concept helps in understanding how much of a solute is present in a mixture relative to the entire mixture, as seen in the calculation of 37.08% weight percent for HCl in the solution. Understanding weight percent is important for quality control in industries, where the purity of substances must be verified, and in academic settings, where precise chemical mixtures are needed.

Density

Density is a measure of how much mass is contained in a given volume and is expressed as grams per cubic centimeter (g/cm³) or grams per milliliter (g/mL) in the context of solutions. The formula to calculate density is:

• Density = mass / volume

In this context, density helps us find the mass of a solution when the volume is known. For instance, knowing the density of the HCl solution (1.18 g/cm³), we can calculate the mass of 1 liter of this solution. This density helps determine other aspects of the solution, like molality and weight percent, by providing a link between volume and mass. Density is fundamental in understanding how solutions will behave under different conditions and is a pivotal concept in various scientific fields, including chemistry, physics, and engineering.

HCl Solutions

Hydrochloric acid (HCl) is a common aqueous solution in labs, known for its strong acidic properties. Solutions of HCl vary in concentration, where commercial solutions are typically highly concentrated. These concentrations can be described in terms of molarity or weight percent, offering flexibility to chemists depending on the usage scenario. Commercial HCl solutions, like the one in our example with 12.0 M molarity, are used for industrial cleaning, pH control, and manufacturing of organic compounds. Safety is a big concern when handling HCl due to its corrosive nature; proper precautions and equipment are necessary. Understanding the concentration terms like molarity, molality, and weight percent aids in handling, storage, and application of HCl solutions safely and effectively.