Calculating the concentration of a chemical solution is a fundamental practice in chemistry. Molality, symbolized by a lowercase \(m\), offers a specific advantage by basing its measurement on mass rather than volume. This approach provides a temperature-independent measure of concentration, which is useful in precise laboratory settings where temperature fluctuations might change the volume of a liquid. Calculating molality requires understanding the constituent parts of a solution and applying a straightforward mathematical relationship.
Defining Solute, Solvent, and Units
To begin any concentration calculation, differentiate between the two components that form a solution: the solute and the solvent. The solute is the substance being dissolved, such as salt or sugar, and is typically present in the lesser amount. Conversely, the solvent is the substance doing the dissolving, usually a liquid like water, which constitutes the majority of the solution’s mass.
The quantity of the solute is measured using the mole, the standard international unit for the amount of a substance. To find the moles of solute from a measured mass, one must first determine the molar mass, which is the mass in grams of one mole of a specific chemical compound. This value is calculated by summing the atomic masses of all atoms present in the compound’s chemical formula, sourced from the periodic table.
The quantity of the solvent must be expressed in kilograms (kg) for the molality calculation. Even if the solvent is initially measured in grams, it must be converted to kilograms by dividing the mass by 1,000. This adherence to kilograms for the solvent and moles for the solute is required for accurately determining the molality of the solution.
The Fundamental Molality Formula
The definition of molality is mathematically expressed as the moles of solute divided by the mass of the solvent in kilograms. This relationship is written as \(m = frac{text{moles of solute}}{text{kilograms of solvent}}\), yielding a unit of moles per kilogram, often abbreviated as \(text{mol/kg}\) or simply \(m\).
This formula establishes a direct ratio between the amount of the dissolved substance and the mass of the dissolving medium. The numerator, representing the solute, expresses the count of particles present, while the denominator, representing the solvent, provides a consistent, temperature-stable measure of the medium. Employing the correct units is important, as using grams instead of moles for the solute or grams instead of kilograms for the solvent will produce an incorrect concentration value.
Step-by-Step Example Calculation
A comprehensive example illustrates the process of finding molality, such as dissolving 15 grams of sodium chloride (\(text{NaCl}\)) into 500 grams of water (\(text{H}_2text{O}\)). The first step involves determining the molar mass of the solute, \(text{NaCl}\). Sodium (\(text{Na}\)) has an atomic mass of approximately \(22.99\) grams per mole, and chlorine (\(text{Cl}\)) has an atomic mass of \(35.45\) grams per mole, resulting in a molar mass of \(58.44\) grams per mole for \(text{NaCl}\).
This molar mass is then used to convert the mass of the solute into moles, which is the required numerator for the molality equation. Dividing the initial 15 grams of \(text{NaCl}\) by its molar mass of \(58.44\) grams per mole results in approximately \(0.2567\) moles of \(text{NaCl}\). This value quantifies the particle count of the solute.
The next step focuses on preparing the solvent measurement for the denominator. Since the solvent, water, was measured as 500 grams, it must be converted to kilograms by dividing by \(1,000\), which yields \(0.500\) kilograms of water. This conversion ensures the concentration is expressed in the standard units of moles per kilogram.
With the moles of solute (\(0.2567\) moles) and the kilograms of solvent (\(0.500\) kg) determined, insert these values into the molality formula. Dividing \(0.2567\) moles by \(0.500\) kilograms results in a molality of \(0.5134\) \(text{mol/kg}\), or \(0.5134m\). This ensures an accurate calculation of the solution’s concentration.
Molality Compared to Molarity
While molality (\(m\)) measures the concentration based on the mass of the solvent, molarity (\(M\)) is based on the total volume of the solution. Molarity is defined as the moles of solute divided by the total volume of the solution in liters, written as \(M = frac{text{moles of solute}}{text{liters of solution}}\). The distinction between solvent mass and solution volume is the primary difference between these two terms.
The choice of using molality over molarity is often dictated by the need for consistency, especially when temperature is a variable. Volume measurements, which are used in molarity, change slightly with temperature due to thermal expansion or contraction of the liquid. Mass, however, remains constant regardless of temperature fluctuations, making molality a fixed concentration value under varying conditions.
This stability makes molality the preferred unit when studying colligative properties. These properties of solutions depend only on the ratio of the number of solute particles to the number of solvent particles. Colligative property calculations, such as freezing point depression and boiling point elevation, rely on the precise, temperature-independent ratio provided by molality. Therefore, in applications requiring high precision across a range of temperatures, molality offers a scientific advantage over molarity.