Problem 46 - Chemistry The Central Science In Si Units

Question

(a) What is the molality of a solution formed by dissolving 1.12 mol of KCl in 16.0 mol of water? (b) How many grams of sulfur \(\left(S_{8}\right)\) must be dissolved in \(100.0 \mathrm{~g}\) of naphthalene \(\left(\mathrm{C}_{10} \mathrm{H}_{8}\right)\) to make a \(0.12 \mathrm{~m}\) solution?

Step-by-Step Solution

Answer

(a) The molality of the KCl solution is 3.885 m. (b) 3.079 g of \(S_8\) are needed for the solution.

Step 1: Understanding Molality

The molality (m) of a solution is defined as the number of moles of solute per kilogram of solvent. It's important to note that molality uses kilograms of the solvent, not the solution.

Step 2: Calculating Molality for KCl in Water

Given: 1.12 mol of KCl and 16.0 mol of water. First, convert moles of water to mass. Water has a molar mass of approximately 18.02 g/mol. Thus, 16.0 mol of water: \(16.0 \text{ mol} \times 18.02 \, \text{g/mol} = 288.32 \, \text{g} \). Convert grams to kilograms: 288.32 g = 0.28832 kg. Molality = moles of solute / kilograms of solvent = \( \frac{1.12}{0.28832} = 3.885 \, m \).

Step 3: Understanding Molality for the Second Part

For the sulfur in naphthalene, you need to find the amount of solute required to achieve a specific molality. Given the desired molality, we find how much solute is needed using grams of solvent.

Step 4: Using Molality Formula to Find Grams for S in Naphthalene

Given: Desired molality (m) = 0.12 m, mass of naphthalene = 100.0 g = 0.1 kg, formula of sulfur \(S_8\). The formula connects molality with moles and kilograms of solvent: \(m = \frac{\text{moles of } S_8}{0.1} \). Therefore, moles of \(S_8 = 0.12 \times 0.1 = 0.012 \). Next, find the mass of \(S_8\): Molar mass of \(S_8\) = \(8 \times 32.07 = 256.56 \) g/mol. Thus, mass of \(S_8 = 0.012 \times 256.56 = 3.07872 \) grams.

Key Concepts

Solute

In chemistry, a solute is the substance that is dissolved in a solvent to form a solution. The solute is present in a smaller proportion compared to the solvent. The essence of a solution revolves around how the solute interacts with the solvent.

When calculating the molality of a solution, the solute's amount, given in moles, plays a crucial role. For example, if you have a solution of potassium chloride (KCl) in water, KCl is the solute.

• The formula for molality involves the molar amount of the solute.
• In our exercise, 1.12 moles of KCl were the moles of solute used to measure molality.
• The importance lies in ensuring the solute amount is accurately calculated in moles for precise solution concentration.

Understanding and calculating the moles of your solute is foundational to solving many chemistry problems.

Solvent

The solvent is the component in a solution that dissolves the solute. It is generally present in a larger amount compared to the solute. In a solution, the solvent's primary role is to disperse the solute particles.

In the context of molality, solvent mass directly impacts the calculation:

• Molality is determined by dividing the moles of solute by the mass of solvent in kilograms.
• In the first part of the exercise, water acts as the solvent, with 16.0 moles translating to 288.32 grams (0.28832 kilograms).
• Keeping track of the mass in kilograms is crucial because molality is expressed per kilogram of solvent, not per the entire solution.

Remember, understanding the characteristics of your solvent helps in achieving accurate and meaningful molarity or molality values.

Moles

Moles are a fundamental unit of measurement in chemistry, representing a quantity of chemical entities (atoms, molecules, etc.). The concept of moles simplifies dealing with chemical reactions and solutions.

When discussing solutions and molarity or molality, knowing how to convert between moles and other units is vital:

• In the exercise, moles were used to measure both the solute (KCl and sulfur, \(S_8\)) and the solvent (water).
• The conversion from moles to grams (and vice versa) is important, especially when dealing with molar mass. For instance, 16.0 moles of water is converted to grams using its molar mass, 18.02 g/mol.
• Similarly, the exercise required calculating moles of sulfur based on desired molality, which was then converted to grams using sulfur's molar mass.

Having a solid grasp of calculating moles and using them in formulae ensures successful outcomes in chemistry problem-solving.