Problem 45 - Chemistry The Central Science

Question

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

Step-by-Step Solution

Answer

The molality of the benzene solution is 4.6949 mol/kg and the molality of the sodium chloride solution is 0.2349 mol/kg.

Step 1: (a) Calculate the moles of benzene in the solution)

First, determine the molar mass of benzene: C6H6 \(C_{6}H_{6}\): (6 * 12.01 g/mol) + (6 * 1.008 g/mol) = 72.06 + 6.048 = 78.108 g/mol Now, we can calculate the moles of benzene in the solution: Moles of benzene = mass/molar_mass = \( \frac{8.66~g}{78.108~g/mol} \) = 0.1108 mol

Step 2: (a) Calculate the molality of the benzene solution)

To calculate the molality of the solution, we need the mass of carbon tetrachloride (solvent) in kilograms. Given the mass of solvent is 23.6 g, we can convert it to kilograms: Mass of solvent = \( \frac{23.6~g}{1000~g/kg} \) = 0.0236 kg Now, the molality of the solution can be calculated as: Molality = moles_of_solute / mass_of_solvent = \( \frac{0.1108~mol}{0.0236~kg} \) = 4.6949 mol/kg The molality of the benzene solution is 4.6949 mol/kg.

Step 3: (b) Calculate the moles of sodium chloride in the solution)

First, determine the molar mass of sodium chloride: NaCl \(NaCl\): (1 * 22.99 g/mol) + (1 * 35.45 g/mol) = 22.99 + 35.45 = 58.44 g/mol Now, we can calculate the moles of sodium chloride in the solution: Moles of sodium chloride = mass/molar_mass = \( \frac{4.80~g}{58.44~g/mol} \) = 0.0822 mol

Step 4: (b) Calculate the mass of water in the solution)

We are given the volume of water in the solution: 0.350 L. To convert this to mass, we need to use the density of water: Density of water = 1 g/mL or 1000 g/L Mass of water = volume * density = 0.350 L * 1000 g/L = 350 g Now, we convert it to kg: Mass of water = \( \frac{350~g}{1000~g/kg} \) = 0.35 kg

Step 5: (b) Calculate the molality of the sodium chloride solution)

Now, the molality of the solution can be calculated as: Molality = moles_of_solute / mass_of_solvent = \( \frac{0.0822~mol}{0.35~kg} \) = 0.2349 mol/kg The molality of the sodium chloride solution is 0.2349 mol/kg.

Key Concepts

Moles of solute

Moles of solute is a fundamental concept in chemistry that relates the mass of a certain substance to the amount of its constituent particles, typically atoms or molecules, which is measured in moles. To determine the moles of a solute, you need two primary pieces of information: the mass of the solute and its molar mass. The molar mass is the mass of one mole of a substance, usually given in grams per mole (g/mol). This can be calculated using the periodic table by adding up the atomic masses of the atoms in a compound.

For instance, in the exercise, you calculate the moles of benzene, (C₆H₆), by first determining its molar mass. Each carbon atom (C) has an atomic mass of approximately 12.01 g/mol, and hydrogen (H) has an atomic mass of 1.008 g/mol. Thus, the molar mass of benzene is (6 * 12.01 + 6 * 1.008 = 78.108) g/mol. To find the moles of benzene, you divide the given mass by the molar mass: \(\frac{8.66~g}{78.108~g/mol} = 0.1108~mol.\)

Understanding how to convert mass into moles is crucial for many chemistry calculations, as it allows you to work with actual quantities of atoms and molecules, which are otherwise too small to measure directly.

Mass of solvent

The mass of the solvent plays a key role in calculating molality, a measure of solution concentration. Molality is defined as the moles of solute per kilogram of solvent. This is distinct from molarity, which is based on the volume of the solution. Here, accurately finding the mass of the solvent is essential for precise calculations.

In the exercise, the solvent's mass is given for benzene as carbon tetrachloride and for sodium chloride as water. For benzene, the mass of the solvent is 23.6 g. Since molality is calculated using kilograms, you must convert grams to kilograms by dividing by 1000. Hence, for carbon tetrachloride:

• Mass of solvent in kg = \(\frac{23.6~g}{1000~g/kg} = 0.0236~kg\).

For the sodium chloride solution, where water is the solvent, you convert the volume of water into mass using its density (assuming it is 1 g/mL). For 0.350 L of water:

• Mass of water = 0.350 L * 1000 g/L = 350 g
• Convert grams to kilograms: \(\frac{350~g}{1000~g/kg} = 0.35~kg\)

By understanding how to correctly identify and convert the mass of the solvent, you can achieve an accurate measurement of molality.

Molar mass calculation

Molar mass calculation is pivotal in chemistry as it bridges the gap between the microscale of atoms and molecules and the macroscale amounts we measure in laboratories. To calculate molar mass, you need to sum the atomic masses of all atoms present in one molecule of a substance, typically using atomic masses found on the periodic table.

Consider the exercise involving sodium chloride, NaCl. The molar mass of sodium (Na) is approximately 22.99 g/mol, and that of chlorine (Cl) is 35.45 g/mol. Therefore, the molar mass of NaCl is the sum: (22.99 + 35.45 = 58.44) g/mol. This molar mass allows you to convert from mass to moles, a common necessity in chemical equations and solutions.

Molar mass serves as a conversion factor in calculations, such as determining how many moles are present in a given mass of sodium chloride. Given a mass of 4.80 g, you find the moles by dividing the mass by the molar mass:

• Moles of NaCl = \(\frac{4.80~g}{58.44~g/mol} = 0.0822~mol\).

By understanding molar mass, you can more precisely relate chemical quantities to the reactions they participate in, enhancing both calculations and experimental accuracy.