Problem 45 - Chemistry The Central Science

Question

Calculate the molality of each of the following solutions: (a) 8.66 g of benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)\) dissolved in 23.6 \(\mathrm{g}\) of carbon tetrachloride \(\left(\mathrm{CCl}_{4}\right),(\mathbf{b}) 4.80 \mathrm{g}\) of NaCl dissolved in 0.350 \(\mathrm{L}\) of water.

Step-by-Step Solution

Answer

The molality of the first solution (benzene in carbon tetrachloride) is 4.70 mol/kg, and the molality of the second solution (NaCl in water) is 0.235 mol/kg.

Step 1: Calculate the moles of benzene

To find the moles of benzene, we need to divide the mass of benzene by its molar mass. The molar mass of benzene (C6H6) is: (6 × 12.01 + 6 × 1.01) g/mol = 78.12 g/mol. moles of benzene = \(\frac{8.66}{78.12}\) moles of benzene = 0.1109 moles

Step 2: Convert the mass of carbon tetrachloride to kg

Since molality is expressed in terms of moles of solute per kg of solvent, we need to convert the given mass of carbon tetrachloride (23.6 g) to kg. mass of carbon tetrachloride = 23.6 g = 0.0236 kg

Step 3: Calculate the molality of benzene in carbon tetrachloride

Now, we can calculate the molality of benzene in carbon tetrachloride using the formula: molality (m) = \(\frac{moles \, of \, benzene}{mass \, of \, carbon \, tetrachloride \, (kg)}\) molality (m) = \(\frac{0.1109}{0.0236}\) molality (m) = 4.70 mol/kg The molality of benzene in carbon tetrachloride is 4.70 mol/kg. **Solution (b):**

Step 1: Calculate the moles of NaCl

To find the moles of NaCl, we need to divide the mass of NaCl by its molar mass. The molar mass of NaCl is (22.99 + 35.45) g/mol = 58.44 g/mol. moles of NaCl = \(\frac{4.80}{58.44}\) moles of NaCl = 0.0822 moles

Step 2: Convert the volume of water to mass (in kg)

We are given the volume of water (0.350 L) and need to convert it to mass (in kg) because molality is expressed in terms of mass. Since the density of water is 1 g/mL (or 1 kg/L), we can directly convert the volume to mass. mass of water = 0.350 L × 1 kg/L = 0.350 kg

Step 3: Calculate the molality of NaCl in water

Now, we can calculate the molality of NaCl in water using the formula: molality (m) = \(\frac{moles \, of \, NaCl}{mass \, of \, water \, (kg)}\) molality (m) = \(\frac{0.0822}{0.350}\) molality (m) = 0.235 mol/kg The molality of NaCl in water is 0.235 mol/kg.

Key Concepts

Molar Mass

The concept of molar mass is fundamental in chemistry, as it connects the mass of a substance to the amount of its particles, expressed as moles. Molar mass is the mass of one mole of a given substance, typically measured in grams per mole (g/mol).
For example, benzene \(C_{6}H_{6}\) has a molar mass calculated by summing the atomic masses of all the atoms in its molecular formula:

• Carbon (C) has an atomic mass of approximately 12.01 g/mol.
• Hydrogen (H) has an atomic mass of approximately 1.01 g/mol.

Thus, the molar mass calculation for benzene is: \(6 (12.01) + 6 (1.01) = 78.12\) g/mol.Understanding the correct molar mass is essential for determining how many moles of a substance are present in a sample.

Moles of Solute

The concept of moles relates the amount of chemical substance to its mass in grams. Calculating the moles involves dividing the mass of the substance by its molar mass, which results in the number of moles.
For instance, if you have 8.66 g of benzene, and you know its molar mass is 78.12 g/mol, the calculation would be:\(\text{moles of benzene} = \frac{8.66}{78.12} = 0.1109\) moles.This resource helps you to find out how moles give a quantitative description of a substance, allowing for practical applications in stoichiometry and chemical equations.

Mass Conversion

Converting mass units is a practical skill needed in chemistry, especially when dealing with solution concentrations like molality, which requires the mass of the solvent in kilograms.
For instance, when converting 23.6 g of carbon tetrachloride into kilograms, you divide by 1000 (since there are 1000 grams in a kilogram):\(23.6\, \text{g} = 0.0236\, \text{kg}\).This conversion is crucial for consistent and accurate calculations of solution concentrations.

Density of Water

Density is a property that describes how much mass of a material is contained in a given volume, often used to convert between mass and volume. For water, this value is typically 1 g/mL or 1 kg/L.
This constant density allows for easy conversions from liters to kilograms. For example, if you have 0.350 L of water, converting to mass would be:\(0.350\, \text{L} \times 1\, \text{kg/L} = 0.350\, \text{kg}\).Using the known density aids in calculating solution properties when mass or volume is involved, an important aspect in many chemistry experiments and calculations.

Solution Chemistry

Solution chemistry involves the study of solutes dissolved in solvents, creating solutions. Understanding the properties like molality indicates how concentrated the solute is within the solvent.
The formula for molality is the moles of solute per kilogram of solvent. This unit remains unchanged by temperature, making it highly reliable for diverse laboratory conditions.For example, the molality of a solution with 0.1109 moles of benzene in 0.0236 kg of carbon tetrachloride is calculated as:\(\text{molality (m)} = \frac{0.1109}{0.0236} = 4.70\, \text{mol/kg}\).This type of calculation helps chemists to describe how the solute interacts with the solvent on a molecular level.