Solutions and Concentrations

When immersed in water, many solids break apart into particles (molecules or ions) surrounded by water molecules. This process of dissolution converts a heterogeneous mixture of solid and liquid into a single homogeneous mixture consisting of liquid water and dissolved solute particles. The dissolution process for sucrose can be written as a chemical equation using the solid and aqueous phase designators. The (aq) designator following a species implies that water molecules are surrounding and solvating that species.

Different solutions may contain different numbers of dissolved particles, and concentration is a measure that quantifies the density of solute particles within a solution. One fundamental measure of concentration is the mole fraction (x) of the solute: the number of moles of solute particles (n_solute) divided by the total number of moles of solution components (all solutes and solvent).

Multiplying the mole fraction by 10⁶ gives the parts per million (ppm) concentration, the number of solute particles per million particles of solution. The number of moles of solute per liter of solution, or molarity (M), is a second common measure of concentration.

Concentration may also be expressed as parts by mass, the fraction of the solution mass due to the solute.

Multiplying the parts by mass concentration by 100% gives the mass percent.

Finally, molality is a measure of concentration that uses the mass of the solvent, rather than the volume of the solution, as a measure of the “size” of the solution. Molality is the ratio of the number of moles of solute to the mass of the solvent in kilograms.

Precise and accurate preparation of a solution with a target molarity requires careful analytical technique. The solid solute must be carefully weighed and transferred quantitatively (completely) to a volumetric flask. The solvent can then be added carefully until the solution reaches the mark on the glassware. For best results, the solute should be allowed to dissolve completely in less than the total volume of solvent, and any remaining solvent should be added when no solid solute is visible.

Procedure step 1 creates 100 mL of a 0.0100 M sucrose solution. To convert to measures of concentration other than molarity, determine the mass of water used to prepare the solution. Although this can be measured accurately, in the absence of a measurement it can be assumed that the volume of dissolved solute particles is negligible (i.e., the volume of water used was 100 mL). Using the density of water…

The molality of sucrose in this solution is thus:

The parts by mass of sucrose is equal to:

The mole fraction of sucrose can be calculated by determining the number of moles in 100 g of water and dividing the amount of sucrose by the total amount of particles in the solution.

Procedure step 2 illustrates that the solubility of sucrose in water is temperature dependent. Upon heating, undissolved sucrose resting in a saturated solution dissolves, forming a saturated solution of higher concentration at higher temperature. When this solution cools, sucrose does not precipitate out of the solution. The resulting cooled solution is supersaturated with sucrose. Adding even a small amount of additional sucrose powder into this solution can trigger rapid recrystallization of all the dissolved sucrose.

Solid-liquid solutions are ubiquitous in chemistry. Most chemical reactions are run in solution because dissolved solutes are mobile enough to rapidly mix and bump into one another. Solutions can also be used to store small amounts of solutes in macroscopic and easily handled volumes. Solutions exhibit some interesting physical properties called colligative properties that can be attributed to the entropic effects of dissolving a solute in a solvent.

One may wonder why so many different measures of solution concentration exist. The answer lies in the many applications of solutions and the many orders of magnitude over which concentrations span. In samples of water from the environment, for example, concentrations of metal ions can be in the range of a few parts per million — it is impractical and potentially misleading to express this tiny concentration as a molarity or mole fraction. Although molarity is a convenient measure of concentration for stoichiometry calculations involving chemical reactions, molality is more appropriate in studies of certain colligative properties.

Perfecting the technique of solution preparation is important, because in many contexts, precise knowledge of concentration is essential. When running a chemical reaction, for example, use of too much or too little solute could result in wasted reactants or low product yields. Studies of empirical relationships involving concentration, such as Beer’s law, depend on precisely known concentrations. Oftentimes, imprecision in solution concentrations leads directly to uncertainty in calculated values, such as reaction enthalpies. Although it is impossible to completely eliminate imprecision, the use of analytical techniques for solution making ensures that uncertainty is minimized.