Problem 41 - 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 each solution is: (a) 5.08 mol/kg for benzene in carbon tetrachloride and (b) 0.235 mol/kg for sodium chloride in water.

Step 1: Calculate the number of moles of solute for each solution.

To calculate the number of moles of solute, we need to use the molar mass of the solute and the mass given in the problem. The molar mass of benzene is \(\mathrm{C_6H_6}\) and the molar mass of sodium chloride is \(\mathrm{NaCl}\). For benzene, the molar mass is: \(6(\mathrm{C}) + 6(\mathrm{H}) = 6(12.01 \mathrm{g/mol}) + 6(1.01 \mathrm{g/mol}) = 72.12 \ \mathrm{g/mol}\) For sodium chloride, the molar mass is: \(\mathrm{Na} + \mathrm{Cl} = 22.99 \mathrm{g/mol} + 35.45 \mathrm{g/mol} = 58.44 \ \mathrm{g/mol}\) Now we can calculate the moles of solute for each solution using the mass given. (a) Benzene: \(\frac{8.66 \mathrm{g}}{72.12 \ \mathrm{g/mol}} = 0.120 \ \mathrm{mol}\) (b) Sodium Chloride: \(\frac{4.80 \mathrm{g}}{58.44 \ \mathrm{g/mol}} = 0.0822 \ \mathrm{mol}\)

Step 2: Convert the mass of solvent to kilograms and calculate molality.

Now that we have the number of moles of solute for each solution, we need to convert the mass of solvent to kilograms and calculate molality. (a) Mass of carbon tetrachloride: 23.6 g = 0.0236 kg (b) Mass of water: First, we need to calculate the mass of water knowing the density of water is about 1 g/mL. 0.350 L = 350 mL 350 mL * 1 g/mL = 350 g 350 g = 0.350 kg Now, we can calculate the molality for each solution. (a) Molality of benzene in carbon tetrachloride: \(\frac{0.120 \ \mathrm{mol}}{0.0236 \ \mathrm{kg}} = 5.08 \ \mathrm{mol/kg}\) (b) Molality of sodium chloride in water: \(\frac{0.0822 \ \mathrm{mol}}{0.350 \ \mathrm{kg}} = 0.235 \ \mathrm{mol/kg}\) So, the molality of each solution is: (a) 5.08 mol/kg for benzene in carbon tetrachloride. (b) 0.235 mol/kg for sodium chloride in water.

Key Concepts

Molar Mass

Molar mass is a crucial concept in chemistry that helps in relating the mass of a substance to the amount of substance in moles. It is essentially the mass of one mole of a particular element or compound. To calculate molar mass, add up the atomic masses of the elements that make up the compound. For instance, when calculating the molar mass of benzene, C\(_6\)H\(_6\), each carbon atom weighs 12.01 g/mol and each hydrogen atom weighs 1.01 g/mol. Multiply these by their respective counts and add them together: 6(12.01 g/mol) + 6(1.01 g/mol) = 72.12 g/mol. You would repeat this process for any compound, like NaCl, where you sum up the atomic masses of sodium and chlorine. The molar mass plays a pivotal role in converting the given mass of a compound to moles, which we will cover next.

Solute

In a solution, the solute is the substance that is dissolved. It is typically present in smaller quantities compared to the solvent. The solute can be a solid, liquid, or gas. In the exercises given, benzene and sodium chloride (NaCl) are the solutes.

• Benzene, C\(_6\)H\(_6\), is the solute in carbon tetrachloride.
• Sodium chloride is the solute when dissolved in water.

The main job of the solute is to be spread uniformly throughout the solvent, forming a homogeneous mixture. Understanding the role of the solute is essential for determining molality, where the amount of solute in terms of moles is used.

Solvent

The solvent is the component of a solution that dissolves the solute. It is usually present in larger amounts than the solute. A wide variety of substances can be solvents, typically depending on the solute that needs to be dissolved. In the provided exercises:

• Carbon tetrachloride acts as the solvent with benzene as the solute.
• Water is the solvent for sodium chloride, a common combination in many household and laboratory scenarios.

The solvent is vital for the dissolution process, facilitating the solute particles to spread out evenly, which is essential for calculating properties like molality.

Moles

Moles are a fundamental unit in chemistry, used to express the amount of a chemical substance. The concept of a mole allows chemists to count entities like atoms, ions, or molecules in a given mass of a substance. To calculate the number of moles, use the formula:\[\text{Moles} = \frac{\text{mass}}{\text{molar mass}}\]Using the given exercises as examples:

• Benzene: With a given mass of 8.66 g, and a molar mass of 72.12 g/mol, the moles of benzene is calculated by dividing the mass by the molar mass, which equals 0.120 mol.
• Sodium Chloride: For a mass of 4.80 g and a molar mass of 58.44 g/mol, the moles of sodium chloride is calculated as 0.0822 mol.

Understanding moles is key to quantifying the solute in a solution and finding properties like molality.

Mass Conversion

Mass conversion is a necessary step in many chemistry problems, especially those concerning molality. It involves converting mass into different units such as from grams to kilograms. This is crucial since molality is defined as moles of solute per kilogram of solvent.

• Converting g to kg: To convert grams to kilograms, simply divide the mass in grams by 1000. This is necessary as a prerequisite to calculate molality.
• In the exercise, for benzene, converting 23.6 g of carbon tetrachloride results in 0.0236 kg.
• Similarly, the 350 g of water becomes 0.350 kg.

Once mass is converted, you can use it to find the molality of the solution by dividing the moles of solute by the solvent mass in kilograms.