Molarity and Molality

FIELDS OF STUDY: Physical Chemistry

ABSTRACT

The characteristics of molarity and molality are discussed, and the methods of calculating both the molarity and the molality of a solution are described. Molarity is the number of moles of solute per volume of a solution, and molality is the number of moles of solute per mass of the solvent.

The Concept of the Mole

The mole is a fundamental tool of calculation in chemistry. It directly relates mass quantities of atoms or molecules to the mass of the individual atom or molecule. Based on experimental observations of the behavior of gases, Italian scientist Amadeo Avogadro (1776–1856) theorized that equal volumes of gases, at the same temperature and pressure, contain the same number of "particles" (a viable theory of atomic structure did not exist at that time). The key to this conclusion was that the mass of a specific volume of any gas, under identical conditions of temperature and pressure, was found to be directly related to the mass of the particles that composed that gas, or what is known now as the molecular mass. From the point of view of the modern theory of atomic structure, this is easy to understand. Because atoms interact only at the level of their outermost, or valence, electrons, only whole atoms are involved in compounds and chemical transformations. Accordingly, an individual atom has a specific atomic mass that does not change. A molecule composed of any number of atoms therefore has a molecular mass that is the sum of the mass of its component atoms.

The mole was developed as a unit of measure to describe atoms and molecules in amounts large enough to work with in the laboratory. Originally, scientists sought to determine the number of hydrogen atoms in one gram of hydrogen, which has an atomic mass of 1. This number, approximately 6.022 × 10²³, was eventually named Avogadro’s number (now also called the Avogadro constant) and corresponds to one mole. The mass in grams of one mole of any element or compound—its molar mass—is numerically the same as its atomic or molecular mass; thus, oxygen has an atomic mass of 16, and one mole of oxygen has a mass of sixteen grams. Ways of calculating Avogadro’s number have changed over time, and the modern standard is the number of atoms in twelve grams of the pure isotope carbon-12.

Moles in Solution

The use of weights and measures in science, especially in the practice of chemistry, requires the scientist to know what quantities of material are being used. For solid materials, this is not a great problem, as such materials are easily weighed. But for materials in solution, the quantities cannot be so easily measured, and it may be necessary to know how much of a specific material is present in a specific amount of the solution. This amount is called the concentration of the solution.

A solution is prepared by dissolving a given amount of a material, or solute, in an amount of a fluid, or solvent. Many characteristic behaviors of solutions, and of materials in solutions, are found to be related to the amount of solute per unit volume of the solution; this is called the molarity of the solution. Other properties are found to be related to the amount of solute per unit mass of the solvent, which is called the molality of the solution.

Molarity versus Molality

The important distinction between molarity and molality is that molarity is defined as the number of moles of a solute per liter of solution (called molars, abbreviated M), while molality is defined as the number of moles of a solute per kilogram of solvent (originally called molal, now given in units of moles per kilogram, abbreviated m). To comprehend this difference, it is helpful to visualize the preparation of two solutions, each containing one mole of a particular solute. To prepare the one-molar (1 M) solution, one mole of the solute is added to a quantity of solvent significantly less than one liter in volume and dissolved. Next, additional solvent is added to increase the volume of the solution to one liter. This produces a solution that contains one mole of solute per liter of solution. To prepare a solution with a molality of one mole per kilogram (1 m), the mole of solute is added directly to an amount of solvent weighing one kilogram and dissolved. This produces a solution that contains one mole of solute per kilogram of solvent.

For low concentrations of solute in an aqueous solution (that is, a solution in which water is the solvent), there may be little difference between the values of molarity and the molality, and the properties of an aqueous solution with a molarity of one mole per liter will be only very slightly different from those of the same solution with a molality of one mole per kilogram. As concentrations increase, however, the difference between molarity and molality increases as well. A one-mole-per-kilogram solution of acetone in water, for example, will have a volume of 1.0733 liters and a molarity of 0.932 molar, but a four-mole-per-kilogram solution of acetone in water will have a volume of 1.293 liters and a corresponding molar concentration of just 3.094 molars.

Calculating Molarity and Molality

The calculation of molarity uses the general formula

For example, 0.25 gram of sodium hydroxide (NaOH) is dissolved in 20 milliliters of water, and the final volume is brought up to 25 milliliters by the addition of the necessary amount of water. The molecular weight of sodium hydroxide is 40 grams per mole, so the number of moles of sodium hydroxide is 0.25 divided by 40, or 0.00625 mole. The concentration of the solution is therefore 0.00625 mole divided by 0.025 liter, which is 0.25 mole per liter, or 0.25 molar. It is common when dealing with small quantities such as these to state the moles as "millimoles" (mmol) and keep the volume in milliliters, thus eliminating the need to convert to moles and liters. In the above example, 0.00625 mole of sodium hydroxide is the same as 6.25 millimoles. The calculation using this value and the volume in milliliters also yields a molar concentration of 0.25 molar (6.25 divided by 25).

The calculation of molality uses the general formula

For example, if the same 0.25 gram of sodium hydroxide, or 0.00625 mole, were added directly to 25 milliliters of water and dissolved, the molality of the solution would be 0.00625 mole divided by 0.025 kilogram, or 0.25 moles per kilogram. The same use of millimoles is appropriate for the calculation of molality; 6.25 millimoles divided by 25 grams also equals 0.25 moles per kilogram. The mass of the solvent is determined from its density, which is dependent on both the temperature and the pressure. For aqueous solutions, except when very precise measurements are required, a density of 1 gram per milliliter is sufficient. For other solvents, however, the density can vary considerably with temperature, and the mass of the solvent must be adjusted accordingly.

Solid and Gaseous Solutions

The fluid component of a solution is most commonly a liquid, but can also be a gas or even a solid. Metal alloys, for example, are also known as solid solutions, having solidified after being prepared in the liquid state from molten components. Solutions of gases, commonly though incorrectly called gas mixtures, are very well known, the atmosphere of the planet being one such combination. Both solid and gaseous solutions have the same component relationships as liquid solutions.

PRINCIPAL TERMS

• Avogadro’s number (NA): 6.02214129 × 10²³, often rounded to 6.022 × 10²³; the number of particles (atoms or molecules) that constitute one mole of any element or compound, the mass of which in grams is numerically equal to the atomic or molecular weight of the material.
• concentration: the amount of a specific material present in a given volume of a mixture.
• density: the amount of a material contained within a particular space, usually expressed as mass per unit volume.
• mole: the amount of any pure substance that contains as many elementary units (approximately 6.022 × 10²³) as there are atoms in twelve grams of the isotope carbon-12.
• solute: any material that is dissolved in a liquid or fluid medium, usually water.
• solvent: any fluid, most commonly water, that dissolves other materials.

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