Concentration is a fundamental concept in chemistry used to describe the amount of a dissolved substance within a mixture. Most people are familiar with molarity, which is a measure of concentration based on the volume of the solution. Molality is a less commonly encountered measure of concentration, yet it holds a distinct advantage in specific scientific applications. Understanding how to find molality involves focusing on mass, a property that remains constant regardless of external conditions, rather than volume.
Defining Molality and Its Components
Molality is defined as the ratio of the moles of solute to the mass of the solvent, measured in kilograms. To understand this definition, it is helpful to first distinguish between the two primary components of any solution. The solute is the substance that is dissolved, such as salt or sugar. The solvent is the substance that does the dissolving, which is often water but can be any liquid.
In a molality calculation, the amount of the solute must be expressed in moles. Conversely, the amount of the solvent must be expressed by its mass, specifically in kilograms. This reliance on mass for the solvent is the defining feature of molality, setting it apart from other concentration units like molarity, which uses the total volume of the final solution. Because mass is not affected by changes in temperature or pressure, molality provides a measure of concentration that remains fixed, making it particularly useful in precise thermodynamic studies.
The Molality Formula and Required Units
The molality (\(m\)) is calculated by dividing the number of moles of solute by the mass of the solvent in kilograms. The formula is written as: \(m\) = moles of solute / kilograms of solvent. This simple relationship requires adherence to specific units for the calculation to be accurate.
The resulting unit for molality is moles per kilogram (mol/kg). When presenting the final concentration, this unit can also be abbreviated simply as a lowercase \(m\), which is often read aloud as “molal.” The use of kilograms for the solvent mass is standard because the unit mol/kg is the standard way to express this concentration. Any measurement of the solvent taken in grams or milliliters must first be converted into the required kilograms before the division is performed.
Step-by-Step Calculation Guide
The first step involves determining the moles of solute, which is typically given to the chemist as a mass in grams. To convert this mass into moles, the mass of the solute is divided by its molar mass. The molar mass is the total mass of one mole of a chemical compound, found by summing the atomic masses of all the atoms in its chemical formula.
The second critical step is to determine the mass of the solvent and convert it into kilograms. Often, the solvent is measured in grams, so this conversion requires dividing the mass in grams by 1,000. If the solvent is measured by volume, such as in milliliters, the density of the solvent must be used to first calculate its mass. The mass of the solvent in kilograms is the denominator in the molality equation.
Once the moles of solute and the mass of solvent in kilograms have been calculated, the final step is to apply the molality formula. The moles of solute are divided by the mass of the solvent in kilograms. This division yields the final molality value, which represents the concentration of the solution. Careful attention to these unit conversions is necessary, as they are the most common source of error in molality calculations.
Applying the Calculation (Worked Examples)
Consider a scenario where 15.0 grams of potassium chloride (KCl) are dissolved in 250.0 grams of water. The first step requires converting the mass of the solute (KCl) into moles. The molar mass of KCl is approximately 74.55 grams per mole. Dividing the 15.0 grams of KCl by its molar mass yields approximately 0.201 moles of solute.
The next step is converting the mass of the solvent (water) from grams to kilograms. The 250.0 grams of water is divided by 1,000 to convert the mass to the required unit. This conversion results in a solvent mass of 0.2500 kilograms. The mass of the solvent is used directly, as molality considers only the solvent mass and not the total solution mass.
The final step is to divide the calculated moles of solute by the mass of the solvent in kilograms. Dividing 0.201 moles of KCl by 0.2500 kilograms of water gives a result of 0.804. Therefore, the molality of the solution is 0.804 mol/kg, or \(0.804\ m\).