Problem 25 - General Chemistry: Principles and Modern Applications

Question

What is the molality of para-dichlorobenzene in a solution prepared by dissolving \(2.65 \mathrm{g} \mathrm{C}_{6} \mathrm{H}_{4} \mathrm{Cl}_{2}\) in \(50.0 \mathrm{mL}\) benzene \((d=0.879 \mathrm{g} / \mathrm{mL}) ?\)

Step-by-Step Solution

Answer

The molality of the solution is \(0.410 \, mol/kg\).

Step 1: Calculate the molar mass of para-dichlorobenzene

The molar mass of para-dichlorobenzene (\(C_{6}H_{4}Cl_{2}\)) can be calculated as follows: \(6(12.01 \mathrm{g/mol}) + 4(1.008 \mathrm{g/mol}) + 2(35.45 \mathrm{g/mol}) = 146.98 \mathrm{g/mol}\).

Step 2: Calculate the number of moles of para-dichlorobenzene

The number of moles of para-dichlorobenzene can be calculated by dividing the given mass by the molar mass: \((2.65 \mathrm{g}) / (146.98 \mathrm{g/mol}) = 0.0180 \mathrm{mol}\).

Step 3: Convert the volume of benzene to mass

The volume of benzene can be converted to a mass by multiplying it by the given density: \((50.0 \mathrm{mL}) \times (0.879 \mathrm{g/mL}) = 43.95 \mathrm{g}\). Then convert the mass of benzene from grams to kilograms: \((43.95 \mathrm{g}) / (1000 \mathrm{g/kg}) = 0.04395 \mathrm{kg}\).

Step 4: Calculate the molality of the solution

Molality is calculated by dividing the number of moles of the solute by the mass of the solvent in kilograms: \((0.0180 \mathrm{mol}) / (0.04395 \mathrm{kg}) = 0.410 \mathrm{mol/kg}\).

Key Concepts

Molar Mass

Molar mass is a crucial concept in chemistry that refers to the mass of a given substance (element or compound) divided by the amount of substance. It gives you an understanding of how much one mole of a substance weighs. The molar mass is expressed in grams per mole (g/mol) and is derived by summing up the atomic masses of all the atoms present in the molecular formula.
For the compound para-dichlorobenzene ( C_{6}H_{4}Cl_{2} ), calculating the molar mass involves adding up the atomic masses of carbon, hydrogen, and chlorine.

• Carbon ( C): 6 atoms x 12.01 g/mol = 72.06 g/mol
• Hydrogen ( H): 4 atoms x 1.008 g/mol = 4.032 g/mol
• Chlorine ( Cl): 2 atoms x 35.45 g/mol = 70.90 g/mol

The total molar mass of para-dichlorobenzene is 146.98 g/mol. Understanding this value is essential as it allows you to transform the mass of a substance into moles, which is used later in various calculations, such as determining molality.

Density and Mass Conversion

Converting volume to mass is a fundamental process in chemistry, especially when you need to determine how much a liquid substance weighs. This is done using the concept of density, which is defined as mass per unit volume and typically expressed in g/mL for liquids.
To find the mass of benzene using its density:

• Benzene has a given density of 0.879 g/mL.
• If you have 50.0 mL of benzene, the mass is calculated by multiplying the volume and density: 50.0 mL x 0.879 g/mL = 43.95 g.

To get the right units for molality, which requires the solvent's mass in kilograms, you need to convert grams to kilograms by dividing by 1000. So, convert 43.95 g to kg, yielding 0.04395 kg.
This process highlights the importance of understanding when and how to transition between different units in chemistry calculations seamlessly.

Solution Chemistry

In solution chemistry, the term 'molality' refers to a measure of the concentration of a solute in a solution. It is calculated as the number of moles of solute per kilogram of solvent. Unlike molarity, which depends on the volume of the solution, molality is volume-independent because it deals with mass, making it more practical in situations where temperature and pressure change, as these do not affect mass.
To find the molality of the solution:

• First, determine how many moles of para-dichlorobenzene you have. This was found to be 0.0180 moles from the given mass and molar mass.
• Next, calculate the mass of the benzene solvent in kilograms, which is 0.04395 kg as per the previous conversion.
• Molality is then calculated using the formula: molality = moles of solute/mass of solvent in kg.
• For this exercise, molality = 0.0180 mol/0.04395 kg, resulting in 0.410 mol/kg.

Understanding solution chemistry and the concentration measures, like molality, is fundamental for studying reactions in a solution, especially for reactions sensitive to changes in concentration.