SI Units and Fundamental Constants

SI UNITS AND FUNDAMENTAL CONSTANTS SI PREFIXES AND THEIR SYMBOLS 621... 

Presented in this appendix are a list of basic and derived SI units, some fundamental constants frequently required by inorganic chemists, and some useful conversion factors. 

Many non-Sl units are now defined exactly in terms of SI some can only be related to SI units via fundamental constants, and the relationship is therefore restricted by the precision to which the constants are known. Factors for converting some non-Sl units into their SI equivalents are listed in ... 

The process of validation checks, using appropriate tests (see above), that the functional relation (Equation[10.1j) above is adequate under a stated range of conditions ( (m+i) )- tlii validation check is found to be obeyed to within an acceptable level of uncertainty, Y is then said to be traceable to (Xj... x ). Then, to demonstrate complete traceability for Y, it is necessary to show that aU the values (Xj-Xj) are themselves either traceable to reference values (and via these, ultimately to the SI standards), or are defined values (i.e., unitconversion factors, mathematical constants like IT, or the values of constants used to relate some SI units to fundamental physical constants). An example would involve calibration of a semi-microbalance against a set of weights that have been certified relative to a national mass standard that has in turn been calibrated against the... 

Most equations that we must evaluate involve a mixture of variables and fundamental constants (i.e., consider PV = nRT, where P, V, n, and T are variables and I is a fundamental constant). When plugging numbers into such equations, the units that are used for the variables should be consistent with the units used for the fundamental constants. The simplest way to ensure this consistency is to use SI units for... 

Units, Conversion Factors and Fundamental Constants in the SI System... 

Section 2 combines the former separate section on Mathematics with the material involving General Information and Conversion Tables. The fundamental physical constants reflect values recommended in 1986. Physical and chemical symbols and definitions have undergone extensive revision and expansion. Presented in 14 categories, the entries follow recommendations published in 1988 by the lUPAC. The table of abbreviations and standard letter symbols provides, in a sense, an alphabetical index to the foregoing tables. The table of conversion factors has been modified in view of recent data and inclusion of SI units cross-entries for archaic or unusual entries have been curtailed. 

Other SI electrical units are determined from the first four via the fundamental constants eo and tiQ, the permittivity and permeability of free space respectively. The ampere is defined in terms of the force between two straight parallel infinitely long conductors placed a metre apart, and once this has been defined the coulomb must be such that one coulomb per second passes along a conductor if it is carrying a current of one ampere. 

Electrical units. The fundamental SI unit is the unit of current which is called the ampere (A), and which is defined as the constant current which, if maintained in two parallel rectilinear conductors of negligible cross-section and of infinite length and placed one metre apart in a vacuum, would produce between these conductors a force equal to 2 x 10 7 newton per metre length. 

NEW The Fact Sheet at the back of the book provides students with a single source for most of the information they need to solve problems. The fact sheet includes a list of key equations for each chapter the periodic table and tables of the elements, SI prefixes, fundamental constants, and relations between units. 

All equations given in this text appear in a very compact form, without any fundamental physical constants. We achieve this by employing the so-called system of atomic units, which is particularly adapted for working with atoms and molecules. In this system, physical quantities are expressed as multiples of fundamental constants and, if necessary, as combinations of such constants. The mass of an electron, me, the modulus of its charge, lei, Planck s constant h divided by lit, h, and 4jt 0, the permittivity of the vacuum, are all set to unity. Mass, charge, action etc. are then expressed as multiples of these constants, which can therefore be dropped from all equations. The definitions of atomic units used in this book and their relations to the corresponding SI units are summarized in Table 1-1. 

A list of some non-SI units, together with their SI values, and a table containing the best values of some fundamental physical constants are given in appendix A. 

According to the modern convention, measurable quantities are expressed in SI (System Internationale) units and replace the centimetre-gram-second (cgs) system. In this system, the unit of length is a metre (m, the unit of mass is kilogram (kg) and the unit of time is second (s). All the other units are derived from these fundamental units. The unit of thermal energy, calorie, is replaced by joule (1 J = 107 erg) to rationalize the definition of thermal energy. Thus, Planck s constant... 

For thermal conductivity, the SI units are W/(m K). In laminar flow, the thermal conductivity, A, and the diffiisivity, D, are constant with respect to their respective gradients. Eqn. (3.4-3) indicates that the diffusion flux of solute [mol A/(m2 s)] is proportional to the transverse concentration gradient, with D as the proportionality constant. The dimensions of D are length2/ time, and its units are m2/s in the SI. Eqn. (3.4-2) states that the heat flux [in J/ (m2.s) = W/m2] is proportional to the temperature gradient, with a constant a = A/(p cp) that is called the thermal diffusivity. Its dimensions are length2/time and its SI units are m2/s. Thus, it is not unexpected that the coefficient v = p/p has the same dimensions and units, m2/s. The coefficient v is called the kinematic viscosity, and it clearly has a more fundamental significance than the dynamic viscosity. The usual unit for kinematic viscosity is the Stokes (St) and submultiples such as the centistokes (cSt). In many viscometers, readings... 

Determination of the amount of substance is thus in direct relation to basic units of the SI system and does not need a RM for comparison. The Faraday constant is one of the fundamental constants (it can be expressed as the product of the electron charge and the Avogadro constant). It enables the attainment of high precision and accuracy and is independent of the atomic weights of the elements in the sample. Its drawback is lower selectivity, a feature common to titration methods. This makes coulometry especially suitable for determination of relatively pure substances used as standards by other (relative) methods. The Faraday constant has been proposed as an ultimate standard in chemistry [3],... 

Certain units not part of the SI are so widely used that it is impractical to abandon them (e.g., liter, minute, and hour) or are so well established that the International Committee on Weights and Measures has authorized their continued use (e.g., bar, curie, and angstrom). In addition, quantities that are expressed in terms of the fundamental constants of nature, such as elementary charge, proton mass, Bohr magneton, speed of light, and Planck constant, are also acceptable. However, broad terms such as atomic units are not acceptable, although atomic mass unit, u, is acceptable and relevant to chemistry. 

The relation of atomic units to the corresponding SI units involves the values of the fundamental physical constants, and is therefore not exact. The numerical values in the table are based on the estimates of the fundamental constants given in chapter 5. The numerical results of calculations in theoretical chemistry are frequently quoted in atomic units, or as numerical values in the form (physical quantity)/(atomic unit), so that the reader may make the conversion using the current best estimates of the physical constants. 

The importance of atomic units lies in the fact that ab initio calculations in theoretical chemistry necessarily give results in atomic units (i.e. as multiples of me, e, ft, Eh and a0). They are sometimes described as the natural units of electronic calculations in theoretical chemistry. Indeed the results of such calculations can only be converted to other units (such as the SI) by using the current best estimates of the physical constants me, e, ft, etc., themselves expressed in SI units. It is thus appropriate for theoretical chemists to express their results in atomic units, and for the reader to convert to other units as and when necessary. This is also the reason why atomic units are written in italic (sloping) type rather than in the roman (upright) type usually used for units the atomic units are physical quantities chosen from the fundamental physical constants of electronic structure calculations. There is, however, no authority from CGPM for designating these quantities as units , despite the fact that they are treated as units and called atomic units by workers in the field. 

Before we consider topics such as the design of an assay, calculation of drug purity, and so on, it is useful to revise the units and terms chemists use for amount of substance and concentration. The fundamental unit of quantity or amount of substance used in chemistry is the mole. The mole is the amount of a substance (either elements or compounds) that contains the same number of atoms or molecules as there are in 12.0000 g of carbon-12. This number is known as the Avogadro number (after Amedeo Avogadro, an Italian chemist) or Avogadro s constant, and has the value 6.02 X 1023. When this amount of substance is dissolved in solvent (usually water) and made up to 1 litre, a 1 molar (1 m) solution is produced. In a similar way, if one mole of substance were made up to 2 litres of solvent, a 0.5 m solution would result, and so on. The litre is not the SI unit of volume but, along with the millilitre (mL), is still used in the British Pharmacopoeia. 

Interpretation of the most precise measurements in atomic physics with the best ah initio theories leads to values of the fundamental constants, which reflect relations between phenomena in the different realms of physics, and which can be regarded as the ultimate base units of physical measurement. In the past decades, a revolution has occurred in our system of measurements, whereby the accuracy of many of the fundamental physical constants, especially of the atomic constants (such as the Rydberg constant), has caught up with our ability to realise the definitions of many of the SI units [2, 3]. 

---