Question

What will be the molality of chloroform in the water sample which contains 15 ppm chloroform by mass? (a) \(1.25 \times 10^{-4} \mathrm{~m}\) (b) \(2.5 \times 10^{-4} \mathrm{~m}\) (c) \(1.5 \times 10^{-3} \mathrm{~m}\) (d) \(1.25 \times 10^{-5} \mathrm{~m}\)

Short answer

1.256 \times 10^{-4} \mathrm{~m}

Step-by-step solution

Understand Molality

Molality (\(m\)) is a concentration term for a solution that is defined as the number of moles of solute per kilogram of solvent. The formula for molality is \( m = \frac{n_{solute}}{m_{solvent(kg)}} \) where \( n_{solute} \) is the number of moles of the solute and \( m_{solvent(kg)} \) is the mass of the solvent in kilograms.

Convert ppm to Mass Fraction

Parts per million (ppm) measures the mass of the solute in parts per million parts of the solution. To convert ppm to a mass fraction, we use the relationship \( 1 ppm = \frac{1 mg}{1 kg} \) or \( \frac{1 g}{10^6 g} \) of solution. Given that chloroform is 15 ppm in the water sample, the mass fraction of chloroform is \( \frac{15 mg}{1 kg} \) of solution or \( \frac{15 g}{10^6 g} \) of solution.

Calculate the Mass of Chloroform

The mass of chloroform in grams can be calculated by converting the mass fraction into grams, which is \( \frac{15 g}{10^6 g} = 15 \times 10^{-6} g \) of chloroform per gram of solution.

Calculate the Number of Moles of Chloroform

The number of moles (\( n \) of chloroform is calculated using the molar mass of chloroform (\( CHCl_3 \) with molar mass \( 119.38 gm/mol \) and the mass of chloroform in grams. \( n = \frac{mass}{molar~mass} = \frac{15 \times 10^{-6} g}{119.38 g/mol} = 1.256 \times 10^{-7} mol \) of chloroform.

Calculate the Mass of Water in Kilograms

Since we are considering a 1 kg sample of the solution, and assuming the rest of the solution is all water, the mass of water is approximately 1 kg (because the mass of chloroform is negligible compared to the mass of the water).

Calculate the Molality of the Solution

Use the molality formula with the number of moles of chloroform and the mass of water in kilograms. \( m = \frac{1.256 \times 10^{-7} mol}{1 kg} = 1.256 \times 10^{-7} mol/kg = 1.256 \times 10^{-4} m \) (molality).

Key concepts

Mole Concept

The mole concept is a fundamental principle in chemistry that provides a bridge between the microscopic world of atoms and molecules and the macroscopic world we experience daily. A mole is simply a unit that denotes a specific number of particles, typically atoms or molecules, and that number is Avogadro's number, which is approximately 6.022 x 10²³. One mole of any substance will contain this many atoms or molecules. This allows chemists to count atoms by weighing out a certain mass of a substance, as every element or compound has a corresponding molar mass (the mass of one mole of that substance).

For instance, when we say we have 1 mole of chloroform (CHCl₃), we mean that we have 6.022 x 10²³ molecules of chloroform. The molar mass of chloroform, which is the mass of a single mole of chloroform, is crucial for converting between the mass of a substance and the number of moles present – a step that is often used in molality calculations.

Parts per Million (ppm)

Parts per million (ppm) is a unit of measurement used to describe small concentrations of substances. One ppm represents one part of solute per one million parts of the solution, and it is commonly used to quantify contamination levels, for example, in water or air quality studies. It can be expressed in terms of mass, as milligrams of solute per kilogram of solution (mg/kg), which is equivalent to micrograms of solute per gram of solution (µg/g).

Understanding ppm is critical when dealing with very dilute solutions, where the solute's mass is much smaller compared to the solution's mass. This is where the conversion to mass fractions becomes handy, as it simplifies calculations for concentration-related problems. It's essential for accurately determining concentrations in cases such as the given chloroform water sample, where the concentration of chloroform is very low.

Solution Concentration

Solution concentration is a measure of the amount of solute that is dissolved in a given quantity of solvent. It can be expressed in various ways, including molarity, molality, and mass percentage, among others. Molality, in particular, is a concentration term that considers the moles of solute per kilogram of the solvent, not affected by changes in temperature or pressure. It is expressed as moles of solute per kilogram of solvent (mol/kg).

Molality is particularly useful in colligative properties calculations, which include boiling point elevation and freezing point depression, because these properties depend on the number of particles of solute in a solution rather than the type of particles.

Exercise Improvement Advice

For students, it is beneficial to use visualization techniques such as diagrams and flowcharts to illustrate the step-by-step conversion from ppm to molality. Additionally, providing real-world examples and practice problems related to daily life can help in better understanding the relevance of the concept of solution concentration.

Molar Mass

Molar mass is the mass of one mole of a particular substance and is expressed in grams per mole (g/mol). It serves as a connection between the microscopic world (number of molecules) and the macroscopic world (mass). This physical property is determined by the atomic mass of each element as listed on the periodic table and accounts for the average atomic mass of all isotopes of an element as they naturally occur.

Knowing the molar mass of chloroform (119.38 g/mol) allows us to convert from mass to moles, an essential step for calculating the molality of a solution. Whenever a problem involves the quantity of a substance in a reaction or a solution, molar mass will be an indispensable tool for the conversion between mass and moles.

To aid in clarity, it may be helpful to include a brief example demonstrating how to calculate the molar mass of a compound, such as chloroform, by summing the molar masses of each constituent atom.