Chapter 2. Units, solutions, dialysis

by István Venekei

Table of Contents

2.1. About units
2.2. Numeric expression of quantities
2.2.1. The accuracy of numbers, significant figures
2.2.2. Expression of large and small quantities: exponential and prefix forms
2.3. About solutions
2.3.1. Definition of solutions and their main characteristics
2.3.2. Quantitative description of solutions, concentration units
2.3.3. Preparation of solutions
2.4. Dialysis
2.4.1. The principle of dialysis
2.4.2. Practical aspects and applications of dialysis

2.1. About units

Units/measures are used to specify quantities. Every unit has a well-defined standard basic value, which is used as a reference in measurements. The units used in scientific practice constitute a scientifically established system, SI (Système International). Although only SI units are “official”, numerous non-SI units are still widely used (calorie, Ångström, Celsius etc.).

We distinguish two types of quantities with two corresponding types of SI units. The base quantities cannot be derived from other quantities. Many of these are used in biochemistry (names of units and their symbols are given in brackets) to quantify the mass (gram, g), the length (meter, m), the time (second, s), the temperature (kelvin, K) and the charge (coulomb, C). Much larger is the group of derived quantities. Of these, the various units of concentration (to characterise the abundance of materials in solutions and other mixtures), volume and energy are the ones most frequently used in biochemistry.

It is important to note that the terms “mass” and “weight” are often used interchangeably as “alternatives”. Technically, however, they have different meanings. The mass is the total quantity of matter in an object, which comes from the mass of all of its protons and neutrons, although not simply additively. Weight is a measure of the gravitational force exerted on an object. As the mass of protons and neutrons is the unit mass, their total mass in an object (e.g. the mass of a molecule, the molar mass) is a unitless number (e.g. the molar mass of water is 18). In other words, the molar mass is a relative number that would reflect the number of protons and neutrons in an atom or molecule—if the masses of protons and neutrons were additive. We make mass measurable by expressing it in grams because this way we can handle it as weight and measure it with a balance, the device developed for this purpose. Thus, the measurement of weight means the measurement of mass of physical objects—not that of atoms or molecules, but e.g. that of 18 mL water. At the same time, this way we make the measured mass dependent on the place of measurement. (For example, 18 g of H2O is not the same amount (mL or mass) of water at the poles and the equator, although the difference cannot be demonstrated by a traditional lever-arm balance due to its principle of operation.) Thus the practical aspect of the relationship between mass and weight can be summarised as the following: we can measure mass only as weight, and weight is the effect of gravity exerted on mass. Weight is therefore determined by both the mass and gravitational forces, and an object can be weightless but never massless.

The mass unit to express the “size” of large molecules is Dalton (Da), used mainly in biochemistry. This shows how many times the mass of a macromolecule (e.g. a protein) is larger than the mass of a hydrogen atom (more precisely, a proton or a neutron).

An important quantity is the mole, which is special to chemistry. The atomic and molar masses expressed in grams correspond to one mole (e.g. 18 grams of water). One mole of a substance contains Avogadro’s number (6.022x1023) of particles (atoms, molecules, ions or even photons). Due to the definition of the mole, and because the unit of mass (“weight”) is the gram, we express atomic and molecular masses (“weights”) in grams. These are called atomic weight and molecular weight (gram atomic weight, gram molecular weight). We get the number of moles by dividing the quantity of material present by the atomic or molar mass, both expressed in grams (number of moles (m) = mass/molar mass).