Entry by Haifei Zhang, AP 225, Fall 2009
What is concentration
Concentration is the measure of how much of a given substance there is mixed with another substance. This can apply to any sort of chemical mixture, but most frequently the concept is limited to homogeneous solutions, where it refers to the amount of solute in the solvent. To concentrate a solution, one must add more solute, or reduce the amount of solvent (for instance, by selective evaporation). By contrast, to dilute a solution, one must add more solvent, or reduce the amount of solute. Unless two substances are fully miscible there exists a concentration at which no further solute will dissolve in a solution. At this point, the solution is said to be saturated. If additional solute is added to a saturated solution, it will not dissolve (except in certain circumstances, when supersaturation may occur). Instead, phase separation will occur, leading to either coexisting phases or a suspension. The point of saturation depends on many variables such as ambient temperature and the precise chemical nature of the solvent and solute. Analytical concentration includes all the forms of that substance in the solution.
Often in informal, non-technical language, concentration is described in a qualitative way, through the use of adjectives such as "dilute" for solutions of relatively low concentration and of others like "concentrated" for solutions of relatively high concentration. Those terms relate the amount of a substance in a mixture to the observable intensity of effects or properties caused by that substance. For example, a practical rule is that the more concentrated a chromatic solution is, the more intensely colored it is (usually).
For scientific or technical applications, a qualitative account of concentration is almost never sufficient; therefore quantitative measures are needed to describe concentration. There are a number of different ways to quantitatively express concentration; the most common are listed below. They are based on mass, volume, or both. Depending on what they are based on it is not always trivial to convert one measure to the other, because knowledge of the density might be needed to do so. At times this information may not be available, particularly if the temperature varies.
Mass versus volume
Units of concentration — particularly the most popular one, molarity — require knowledge of a substance's volume, which unlike mass is variable depending on ambient temperature and pressure. In fact (partial) molar volume can even be a function of concentration itself. This is why volumes are not necessarily completely additive when two liquids are added and mixed. Volume-based measures for concentration are therefore not to be recommended for non-dilute solutions or problems where relatively large differences in temperature are encountered (e.g. for phase diagrams). Unless otherwise stated, all the following measurements of volume are assumed to be at a standard state temperature and pressure (for example 0 degrees Celsius at 1 atmosphere or 101.325 kPa). The measurement of mass does not require such restrictions. Mass can be determined at a precision of < 0.2 mg on a routine basis with an analytical balance and more precise instruments exist. Both solids and liquids are easily quantified by weighing. The volume of a liquid is usually determined by calibrated glassware such as burettes and volumetric flasks. For very small volumes precision syringes are available. The use of graduated beakers and cylinders is not recommended as their indication of volume is mostly for decorative rather than quantitative purposes. The volume of solids, particularly of powders, is often difficult to measure, which is why mass is the more usual measure. For gases the opposite is true: the volume of a gas can be measured in a gas burette, if care is taken to control the pressure, but the mass is not easy to measure due to buoyancy effects.
Molality (mol/kg, molal, or m) denotes the number of moles of solute per kilogram of solvent (not solution). For instance: adding 1.0 mole of solute to 2.0 kilograms of solvent constitutes a solution with a molality of 0.50 mol/kg. Such a solution may be described as "0.50 molal". The term molal solution is used as a shorthand for a "one molal solution", i.e. a solution which contains one mole of the solute per 1000 grams of the solvent. Following the SI system of units, the National Institute of Standards and Technology, the United States authority on measurement, considers the unit symbol m to be obsolete, and suggests instead the term 'molality of substance B' (mB) with units mol/kg or a related unit of the SI. This recommendation has not been universally implemented in academia yet. Note: molality is sometimes represented by the symbol (m), while molarity by the symbol (M). The two symbols are not meant to be confused, and should not be used as symbols for units. The SI unit for molality is mol/kg. (The unit m means meter.) Like other mass-based measures, the determination of molality only requires a good scale, because masses of both solvent and solute can be obtained by weighing, and molality is independent of physical conditions like temperature and pressure, providing advantages over molarity. In a dilute aqueous solution near room temperature and standard atmospheric pressure, molarity and molality will be very similar in value. This is because 1 kg of water roughly corresponds to a volume of 1 L at these conditions, and because the solution is dilute, the addition of the solute makes a negligible impact on the volume of the solution. However, in all other conditions, this is usually not the case.
The mole fraction Χ, (also called molar fraction) denotes the number of moles of solute as a proportion of the total number of moles in a solution. For instance: 1 mole of solute dissolved in 9 moles of solvent has a mole fraction of 1/10 or 0.1. Mole fractions are dimensionless quantities. (The mole percentage or molar percentage, denoted "mol %" and equal to 100% times the mole fraction, is sometimes quoted instead of the mole fraction.) This measure is used very frequently in the construction of phase diagrams. It has a number of advantages: the measure is not temperature dependent (such as molarity) and does not require knowledge of the densities of the phase(s) involved a mixture of known mole fraction can be prepared by weighing off the appropriate masses of the constituents the measure is symmetrical: in the mole fractions Χ=0.1 and Χ=0.9, the roles of 'solvent' and 'solute' are reversed. As both mole fractions and molality are only based on the masses of the components it is easy to convert between these measures. This is not true for molarity, which requires knowledge of the density.