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The international system of units and its particular application to chemistry1

S. J. Thien and J. D. Oster2

ABSTRACT sentiality of adopting SI in its journals. Using SI in ASA journals would aid communication among scientists The International System of Units (SI) brings uni- within agronomic disciplines as well as among these and form style and terminology to world-wide com- other disciplines, especially internationally and in the munication of . Because the Ameri- pure sciences. Scientists will find that SI does not differ can Society of Agronomy (ASA), Crop Science So- ciety of America (CSSA) and Soil Science Society greatly from the now used, and it in- of America (SSSA) are international, they should creases understanding of the units the authors use. adopt SI in their communications. This paper sum- The General Conference on Weights and Measures marizes SI units, definitions, symbols, and rules of (CGPM) adopted the International System of Units in usage. Discussions of applying SI to agronomic 1960. The International Bureau of Weights and Meas- parameters are included where new concepts are ures (BIPM) and, in the USA, the National Bureau of introduced. Tables of recommended units and Standards (NBS) published rules on its use (2). SI guide- conversion factors are presented so use of SI can lines, besides being used in many foreign countries and begin immediately. It is proposed that a 2 to 3- international societies, are followed by several Ameri- adaptation period begin with this printing, with authors beginning to use SI and including tradi- can societies and college textbooks (1). ASA members tional units, as desired, in parenthesis. are not expected to adopt this new system immediately. Rather, the ASA SI Units committee (ACS 321.4) Additional index words: Metric, Conversion table, recommends adoption over 2 to 3 after these Publication style, . guidelines are published. During the interim, it is strongly recommended that authors begin now to use SI 'Contribution No. 81-483-j from the Agronomy Dep., Kansas E Systeme International d'Unites (SI) is being Agric. Exp. Stn., Kansas State Univ., Manhattan, KS 66506 and the U.S. Salinity Laboratory, AR-SEA, USDA, 4500 Glenwood Drive, L adopted aiound the world. Its purpose is to bring Riverside, CA 92501. Current address of the junior author is Dep. of uniformity of style and terminology in communicating Soil and Environmental Sciences, Univ. of California, Riverside, CA measurements. The world-wide impact of American 92521. Society of Agronomy (ASA) dictates the logic and es- 2 Research soil scientist, and soil and specialist, respectively. SI UNITS IN SOIL 63

Table I. BaseSI Units (2) Table 4. Examplesof SI derived units expressed by meansof special names(2) Quantity Unit Symbol meter m Expression kg in terms of s Quantity Name Symbol SI base units A Dynamicviscosity second Paos m-~okgos-~ Thermodynamic K Momentof force meter N.m m~.kg.s-2 Amount-of-substance mol Surface tension newton per meter N/m kg.s-~ Luminousintensity cd , density, per square ~ -3 Table 2. Examplesof SI derived units expressed irradiance meter W/m kg.s , per kelvin J/K m2.kg.s-2.K-~ in termsof baseunits (2) , joule per kilogram specific entropy kelvin J/(kg.K) m~.s-~.K-t SI Unit Specific joule per kilogram J/kg m2.s-~ " watt per meter kelvin W/(m.K) m.kg.s-3.K-’ Quantity Name Symbol e joule per cubic meter j/m m-~.kg.s-2 °’ square meter m~ Electric strength per meter V/m m.kg.s-3.A density coulombper cubic cubic meter m ~ Speed, velocity meter per second m/s meter C/m m-~.s.A meter per second squared 2 Electric flux density per square Acceleration m/s 2 Wave number 1 per meter meter C/m m-~.s.A -3. -~. ~ Density, mass density kilogram per cubic meter ~ Permittivity per meter F/m m kg s’- A kg/m -’ Current density ampere per square meter A/m2 Molar energy joule per mole J/mol m~.kg.s-2.mol Molar entropy, molar Magnetic field strength ampere per meter A/m * heat capacity joule per mole kelvin J/(mol.K) m~.kg.s-~.K-’.moF (of ) mole per cubic meter mol/m’ Exposure (x and coulomb per 3,rays) kilogram C/kg kg-~,s.A cubic meter per kilogram m~Jkg -~ Luminance candela per square meter cd/m2 Absorbed dose rate per second Gy/s m2*s

Table 5. SupplementarySI Units (2) Table 3. SI derived units with special names(2) Quantity Unit Symbol SI unit Plane angle rad Expression Expression Solid angle sr in terms in terms Sym- of other of Sl base Quantity Name bol units units Frequency Hz s-t Sl UNITS -2 Force newton N m.kg.s ~ -~ , stress pascal Pa N/m m-’. kg ¯ s SI units are divided into three classes: base units, de- Energy, work, quantity of heat joule J N.m m2.kg.s-~. Power, radiant, flux watt W J/s m~.kg.s-3 rived units and supplementary units. Quantity of electricity, Base units are seven, well-defined units which by con- electric charge coulomb C A.s s.A vention are regarded as dimensionally independent: the Electric potential, potential difference, electromotive meter, the kilogram, the second, the ampere, the kelvin, force volt V W/A m2.kg.s-3.A-’ ~ the mole, and the candela (Table 1). Note that lower Capacitance farad F C/V m-~.kg-t.s’.A case is used for unit symbols except where the symbol is Electric resistance i~ V/A m2.kg.s-~.A-~ Conductance S A/V m-2.kg-~.s~.A~ derived from a proper name, then a capital is used (un- temperature abbreviated units are not capitalized). Symbols do not celsius °C K Luminous flux lm cd. sr~" change in the plural and are not followed by a period. Illuminance Ix lm/m~ m-~.cd.sr~" Derived units are expressed in algebraic terms of base Activity (of a radionuclide) Bq s-’ units (Table 2). Some have been given special names and Absorbed dose, imparted, kerma, absorbed symbols (Table 3), which may be used to express other dose index gray Gy J/kg-~ m~.s derived units (Table 4). ~" In this expressionthe steradian (st) is treated as a . Supplementary units are those not yet classified as either base units or derived units. This class now con- and include traditional units, as desired, in parentheses. tains onIy two units, radian and steradian (Table 5). Each scientific discipline presents unique circum- Punctuation of Derived Units. The product of two or stances regarding unit expressions. Hence, there may more units is preferably indicated by a dot midway in appear cases in crop or soil sciences where strict use of relation to symbol height. The dot may be dispensed SI appears unsuitable. This paper addresses some of with when there is no risk of confusion with another those considerations and the committee intends to symbol, remain active to consider future problems. This paper is one of a series being prepared by mem- for example: Nom or N m bers of the SI Units committee. It first describes SI in general and then discusses its particular application to A solidus (oblique stroke, /), a horizontal line, or ASA publications and the soil science discipline with negative powers may be used to express a derived unit emphasis on soil chemistry. formed from two others by division, 64 JOURNALOF AGRONOMICEDUCATION, VOL. 10, 1981

m for example: m/s, ~-, or m.s-’. Table6. SI Prefixes(2) Multiplication factor Pref’Lx Symbol Only one solidus may be used in combinations of 1~ 000000000000000000 = 10 exa E units unless parentheses are used to avoid ambiguity, 1~’ 000000000000000= 10 peta P 1’2 000000000000 = 10 tera T 1 000000000 = 109 giga G for example: mokg/s3oA, or l~ 000000 = 10 mega M 1~ 000 = l0 kilo k mokg°s-3°A-1, 100 = 102 hecto h 10 = 10’ deka da but not, m°kg/s3/A. 0.1-I = 10 deci d 0.01-2 = 10 centi c -3 Application of SIPrefixes. The prefixes and symbols 0.001 = 10 milli m 0.00001-6 = 10 micro listed in Table 6 are used to indicate orders of magni- 0.000000001 = 10-" nano n tude of SI units. Amongthe base units, the unit of mass 0.0000001300001-1~ = 10 pico p 0.000000000000001 = 10-" femto f (kilogram) is the only one whose name, for historical -1~ 0.0130000000000000001 = 10 atto a reasons, already contains a prefix. Names of decimal multiples and sub-multiples of the unit of mass are formed by attaching prefixes to the word "", for Table7. Unitsin usewith S! (2) example rag, but not gkg because compound prefixes Quantity Unit Symbol Definition are not allowed. Time rain 1 min = 60 s Prefixes should be chosen to reduce nonsignificant h 1 h = 60 min = 3,600 s digits or leading zeros in decimal fractions. A prefix pre- d 1 d = 24 h = 86,400 s ~ -J ~ ferably should be chosen so that the numerical value lies Volume liter L 1 L = 1 dm = 10 m Mass metric ton () t 1 t = 10~ kg = Mg between 0.1 and 1000 and the same unit, multiple, or Area ha 1 ha = 1 hm~ =~ 10’ m submultiple should be used throughout a text, including its tables and graphs. Exponential expression of num- Table8. Units temporarilyin usewith SI (2) bers is acceptable. The prefix should only be attached to a unit in the numerator. An exponent attached to a Quantity Unit Symbol Definition symbol containing a prefix indicates that the unit with Energy kilowatt hour kWh 1 kWh = 3.6 MJ its prefix is raised to the power expressed by the ex- Pressure bar bar 1 bar = 10~ Pa ponent, Activity (of radionuclide) curie Cr 1 Cr = 3.7 x 10~°Bq Exposure (X and for example: 1 cm-3 = (10-2m)3 =~ 10-~m gamma rays) roentgen 1 R = 2.58 × 10-~ C/kg Absorbed dose rad rd 1 rd = 0.01 Gy 1 mm2/s = (10-~m)2/s = 10"6m2/s 1 ns-1 = (10-gs)-’ =-1 109s. Kilogram: The kilogram is the unit of mass equal to the mass of the international prototype of the kilogram Units from Different Systems. To preserve the ad- in the custody of the Bureau International des Poids et vantage of SI as a system, it is advisable to minimize its Mesures at Sevres, France (2). use with units from other systems. The American So- Second: The second is the duration of 9 192 631 770 ciety for Testing and Materials (ASTM)(3) recommends periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of that such use be limited to the units listed in Table 7. Another set of units whose use is temporarily acceptable the cesium - 133 (2). with SI are given in Table 8. Ampere: The ampere is that current which, if main- tained in two straight parallel conductors of infinite Punctuation. Periods are not used after any SI unit length, of negligible circular cross section, and place 1 symbol, except at the end of a sentence, nor are plurals meter apart in a vacuum, would produce between these used. For example, write 5 kg and not 5 kg. or 5 kgs. conductors a force equal to 2 x 10-~ newton per meter When writing numbers less than one, a zero should be of length (2). written before the decimal. Use spaces instead of Kelvin: The kelvin, unit of thermodynamic tempera- commas to group numbers into threes (thousands) ture, is the fraction 1/273.16 of the thermodynamic counting from the decimal point toward the left and the temperature of the triple point of water (2). right. For four-digit numbers, the space is not necessary Mole: The mole is the amount of substance of a sys- except for uniformity in tables. tem which contains as manyelementary entities as there are in 0.012 kilogram of 12. In use, the Examples: 2.141 596 73 722 7372 0.1335 elementary entities must be specified and maybe atoms, , , , other particles, or specified Definitions of Base Units. Meter: The meter is the groups of such particles (2). length equal to 1 650 763.73 wavelengths in vacuum of Candela: The candela is the , in the the radiation corresponding to the transition between perpendicular direction, of a surface of 1/600 000 the levels 2p,0 and 5d~ of the krypton - 86 atom (2). square meter of a blackbody at the temperature of freez- SI UNITS IN SOIL CHEMISTRY 65 ing platinum under a pressure of 101 325 newtons per square meter (2). Mass--Base and Derived Units The kilogram is the unit of mass, equal to the mass of the international prototype of the kilogram. In the USA, the commonlyused term for mass is weight, but ADAPTING Sl TO SOIL CHEMISTRY that now should be avoided in technical communica- tions. The weight of an object is a force (f), representing Length--Base and Derived Units the product of its mass (m) and the acceleration due gravity (a) in the equation: f = ma. A properly cali- Soil scientists should find little difficulty in working brated balance, with a set of standards of knownmass, with the base unit of length, meter (m). In derived units, measures mass because the effect of acceleration due to meter is the preferred unit to be used in the denominator. gravity (which varies with altitude, longitude, and lati- For long distances, kilometer is preferred; but cm or tude) is accounted for by calibration. mmis acceptable for short associated with re- Soil scientists should find little difficulty in meeting search measurements and line drawings. The familiar SI standards of usage for expressing mass. As the base term, micron, is no longer acceptable, being replaced by unit already contains a prefix, rememberto form names micrometer (/zm -- 10-6m). Interatomic distances are of decimal multiples and sub-multiples by attaching pre- adequately described by either nanometer (nm -- 10-gm) fixes to the word "gram". Thus, we do not, for ex- or picometer~ (pm = 10-1~m). Another familiar term, ample, refer to a kilokilogram (kkg) or to a millikilo- Angstrom (A = 10-1°m), is unacceptable because gram (mkg) but to a megagram(Mg) or a gram does not fit into a multiple-of-three exponent incre- Kilogram in the denominator of derived units is the ment. accepted form, but it is the only instance when units Area is a derived unit of the base unit for length ex- containing a prefix are allowed. pressed as m’ (Table 2), with z and mm2 al so re com- A potentially confusing use involving SI expression of mended. Hectare (ha -- hm2) is an acceptable unit, and mass centers on the term ton. A metric ton (or tonne), although m2 is preferred in the denominator of an ex- denoted by the symbol "t", equals 103 kg (or mega- pression, ha also may be used. Thus, readers may find gram, Mg) in SI. But that definition does not equal the yields or application rates given in kg/ha easier to grasp commonly understood meaning of ton (1 ton = 2000 because they are closely related to pounds per . Al- pounds) in the USA.In written communication, spelling though acreage is an acceptable, commonlyused noun tonne avoids ambiguity, but in verbal communication in the English system, hectareage is not a word. The SI megagram(1 t = 1 Mg)is suggested. system uses the word area under such conditions. Volume, expressed as m3, is another derived unit of the base unit for length (Table 2). However, other ac- Time--Base and Derived Units cepted expressions of volumes include: cm3, liter (L -- dm3), mL(cm3), and #L (10-9m3). Use of liter (L) The base unit of time is the second (s), but equally ac- denominator of a derived unit will be permitted, al- 3 ceptable units in SI are minute (60 s), hour (3 600 s), though m is often more convenient when manipulating day (86 400 s). Units of time that could vary in length units. This can be demonstrated in the conversion of should be avoided, for example, month or growing amount-of-substance concentration in irrigation water season. to amount-of-substance applied: Because plant growth phenomena have diurnal phases, it is acceptable to use day in the denominator of (10 mol/m3) × (1,000 m~/ha) = (10’mol/ha), some agronomic expressions, for example, growth rate as opposed to (mm/d) or evapotranspiration rate (cm/d). (10 mmol/L) x (1,000 mVha) x (1,000 3) ThermodynamicTemperature--Base and + (1,000 mmol/mol) = (10’ mol/ha) Derived Units (Note that mol "3 is n umerically equal t o mmol L-~) The base unit used to express thermodynamic temperature and temperature intervals is kelvin (K). Acre-furrow slice is a quasi-volumetric relationship However, temperature intervals also may be expressed with no direct counterpart in SI because compoundex- in degrees Celsius (C). The kelvin scale is set by assign- pressions such as hectare furrow slice, hectare-meter, or ing the origin at absolute zero and 273.16 (exactly) hectare-centimeter are unacceptable units. Instead, soil the triple point of water (the temperature and pressure volume in this context is described in multiples or sub- of water at which ice, liquid, and vapor are all in multiples of m~. Thus, whereas an acre-furrow slice (0.5 equilibrium in the absence of air). The ice point (the ft. deep) of 21 780 ft 3 becomes 618 m~, the temperature at which ice and water are in equilibrium in volumetric concept in SI for a hectare would be O. 15 m the presence of air and at one atmosphere) is zero on the x3. 100 m x 100 m, or 1500 m Celsius scale (273.15 K). Thus Celsius temperature (C) 66 JOURNALOF AGRONOMICEDUCATION, VOL. 10, 1981 related to thermodynamic temperature (K) by the equa- In a simple case of a pure substance composed of tion: atoms, say Na÷, the is determined as follows: C = K - 273.15. M(Na÷) = (mass of an atom of Na÷/ Amountof Substance--Base and Derived Units mass-~ of an atom of ~2C) x 0.012 kg mol ÷) The base unit for amount-of-substance is the mole. M(Na = (22.99/12) x 0.012 Any amount-of-substance that contains 6.02 x 1053 en- M(Na÷) =-~ 0.02299. kg mol tities is a mole. This number, known as Avogadro’s number, is the number of ’2C atoms in 0.012 kg of car- For molecules and compounds, a summation proce- bon 12. Whenthe mole is used, elementary entities must dure of the above example for the separate constituents be specified; they maybe atoms, molecules, ions, elec- yields the molar mass. trons, other particles, or specified groups of such parti- Whenmolar mass is expressed in units of g mol-~, it is cles. Examplesof type of entities used to describe a mole numerically identical to relative , or relative include: . 1 mole of... ¯ . .NaCl has 6.02 x 1023 molecules and a mass of For example: M(Caz÷) = 40.08 g mol-’; 58.44 g, A~ (Ca2.) = 40.08; M(CaSO,-2H20)= 172.18 g mol-’; . . .Caz÷ has 6.02 x 1023 ions and a mass of 40.08 g, ¯ . . ½ Caz÷ has 6.02 x 10’3 ½ Ca~÷ units and a mass Mr (CaSO,.2H20) = 172.18. of 20.04 g, .. ¯positive charges (protons, p÷) has 6.02 x ~3 DERIVED UNITS positive charges and a charge of 96.49 kC, ¯ . .electrons (e-) has 6.02 x 1023 electrons, a mass Pressure 548.6 #g and a charge of -96.49 kC, or ¯ . ¯photons (T) has 6.02 x ’3 particles wh ose fr e- The SI unit for pressure is the pascal (Pa), which quency is 104 Hz and an energy of 39.90 kJ. the pressure produced by a force of one newton on an The emphasis in these examples is that the mole con- area of one square meter. A standard atmosphere is cept can refer to any specified particle, or grouping of equal to the pressure required to support 0.76 m of particles (for example, ½ Ca~÷), convenient to fit the mercury at 0 C at a point on the earth where the ac- situation. Thus, the term mole in SI is not entirely celeration of gravity is 9.806 m s-~. As the density of synonymous with older terminologies¯ Many have mercuryat 0 C is 13.595 x 103 kg m-3, the unit force ex- learned to regard the mole as a definite mass; i.e. one erted by a standard atmosphereis calculated as follows: mole of NaOHas one gram molecular weight (40 g) sodium hydroxide, but now when describing an 1 atm = 0.76m x 13.595 x 103 kgm-3 x-~ 9.806m s amount-of-substance, mole requires a more precise de- -~ scription. 1 atm = 101 300 N m Somebasic chemical relationships restated in SI con- Thus a pressure of one atmosphere equals 101 300 N text follow: m-2 = 101 300Pa = 101.3 kPa = 0.1013 MPa = 1.013 Relative atomic mass (At), formerly atomic weight, bar. the average mass of one atom of the element (in its Pa, kPa, and MPa are recommended units, but bar, natural isotopic condition) compared to 1/12 of the although temporarily acceptable, is strongly discour- mass of an atom of carbon 12, aged. for example: Ar (Ca~÷) = 40.08. Amountof Substance Concentration Ar values are unitless, being a ratio formed from two physical quantities of the same unit. will normally be using the amount-of- Relative molecular mass (Mr), formerly molecular substance concept (symbol n) in a concentration con- weight, is the average mass per formula of the constitu- text. Amount-of-substance concentration (symbol c) ent atoms (in their natural condition) compared then is correct terminology to describe the amount-of- to 1/12 of the mass of an atom of carbon 12. Mr values substance divided by the volume of solution. SI base likewise are unitless, unit for this concept is mol m-~ where the molar mass (M) is known,and kg -~ (in u se, g -~) where it is not. for example: Mr (CaSO,-2H~O)= 172¯ 18. Equally acceptable is the practical unit mol L-’ (-- mol dm-J). The "amount-of-substance concentration" con- Molar mass (M) is the mass divided by the amount-of- cept can be replaced with "concentration" without substance and has SI base units of kg mo1-3, but the creating confusion. Examples of correctly expressing practical unit g mol-’ is also used. concentration include: SI UNITS IN SOIL CHEMISTRY 67

-~ Thus, c(HCI) = 0.1 mol L (= 0.1 MHCI) and H~PO, + KOH = KH,PO, + H~O -~ c(H~PO,-) = 2.1 mol (= 2.1 mmol L-~). n(KOH) = n(H~PO,). Note the acceptability of referring to the concentra- Whereas for tion 0.1 tool L-~ as a 0.1 M solution. While the concept and useage of molarity as previously used has been re- H~PO, + 2KOH = KzHPO, + 2H~O [4] placed by the amount-of-substance concentration con- n(KOH) = n(½ H~PO,). cept, the descriptive symbol(M) is still permitted (7). -~ Note, also, mmolL (numerically identical to the base And for unit mol m-3) nicely describes low solute often encountered in soil environments. H~PO, + 3AgOH = Ag~PO,(s) + 3H~O Thus, molarity is discarded in SI because the "amount-of-substance concentration" concept makes it n(AgOH) = n(1/3 H~PO,). redundant, but (mol kg-~) remains the pre- ferred unit for precise, nonisothermal conditions be- Now, consider the reaction cause molality, but not concentration, is independent of temperature (5). H2SO, + Ca(OH), = CaSO, + 2H,O. [6] The unit mole replaces such terms as gram-, gram-atom and gram equivalent, and has led to a re- Then, at the -base end point, evaluation of the concept of an equivalent and the cor- responding amount of substance concentration, n(H,SO,) = n (Ca(OH)0 [71 normality (5). The equivalent is defined (5) as that entity which in a specified reaction would combine with or be and the equivalence factor for H~SO,would appear to in any other appropriate way equivalent in he 1 instead of ½ as was the case for reaction [1]. Re- (a) an acid-base reaction to one entity of titratable calling that the definition refers to titratable hydrogenit ions, H÷ or should be clear that the equivalence factor is ½. An- (b) a redox reaction to one entity of electrons, e-. other way of stating this definition would be to sub- Thus: stitute the statement "the exchange between the reac- 1 equivalent of Cl- would be stated as 1 mole of Cl-; tants of one mole of protons" for the statement "one 1 equivalent of H2SO,could be stated as 1 mole of entity of titratable hydrogenions." ½H,SO,; A solution in which the amount of substance concen- 1 equivalent of AP÷ could be stated as 1 mole of 1/3 tration of the reagent is 1 mol L-~ is a normal solution, Al~+; symbol N. Thus for reaction [2], if c(½ H~SO,)equals 1 equivalent of MnO~-could be stated as 1 mole of mol L-’, the concentration of this 1 N solution of sul- 1/5 MnO~-. phuric acid is 0.049 kg L-1 [M (H2SO,) = 0.098 Use of terms like 1/3 AP÷, ½H2SO~and 1/5 MnO4-is mol-q. Likewise for reaction [4] if c(½ H~PO,)equals possible because the definition of the mole permits mol L-’, the concentration of a 1 N solution of phos- reference to any specified entity; a mole refers to 6.02 x phoric acid is also 0.049 kg L-t[M (H~PO,) = 0.098 102~ units of that entity. The fractions ½, 1/3, and 1/5 mol-~]. Because confusion may exist when a reagent has in these examples are called equivalence factors (for Cl different equivalence factors depending on the specific it is l) and represent the entity of substance in question reaction involved, any statements of solution concentra- reacting with one entity of titratable hydrogen ions (or tion in terms of normality must include the equivalence equivalent) at the equivalence point or one entity of factor, e.g., electrons, e’, in a redox reaction. The concept of equivalence factors is illustrated as 0.05 N(H~PO,); 4.9 g -1 of H~PO, follows: For the reaction 0.10 N(½H~PO,); 4.9 g -~ of H~PO, 2 NaOH + H,SO, = Na,SO, + 2HzO [1] 0.15 N(1/3 H~PO,); 4.9 g -~ of H~PO,.

However, note that in each case the normality of the one entity of H,SO, reacts with two of NaOHallowing solution is being expressed on a molar basis e.g., 0.15N the reaction to be rewritten as (1/3 H~PO,) = 0.15 M (1/3 H~PO,). It follows normality and the amount of substance concentration NaOH + ½ H2SO, = ½ Na~SO, + H,O [2] formerly referred to as molarity, are the same. This is a direct consequence of the definition of a mole. Conse- making the two reactants equal when n (NaOH) = n quently, we strongly recommend that amount of sub- H,SO,), where n represents the number of moles. The stance concentrations expressed as normality be aban- equivalence factor varies with the nature of the reaction. doned. 68 JOURNALOF AGRONOMICEDUCATION, VOL. 10, 1981

Redox Reactions. Since the mole can refer to any soil. The exchangeable cation composition and total specified entity, it is convenient for redox reactions to cation exchange capacity (CEC) would be: relate the amount of reactant to the numberof electrons 40-1, mmol(K÷).kg per mole that it combineswith or releases. To arrive at the appropriate equivalence factor, one must consider 40 mmol (½ Ca2÷)°kg-~, and the of the overall redox reaction. For the 80 mmol(+) ¯ -~, respectively. reaction: As another example, consider that isomorphism (sub- 10FeSO, + 2KMnO, + 8H2SO~ = K2SO, stituting of AI3÷ for Si4÷ and Mg2÷ or Fe~÷ for AI3÷) in Up- + 2MnSO, + 5Fe2(SO,)3 + 8H20 [81 ton, Wyomingmontmorillonite with a molecular mass of 0.7295 kg mol-~ results in 1 mole of excess electrons the equivalent factor for KMnO,is 1/5, and for FeSO, (6.02 x 10"3) per mole of clay (4, p. 578) or a specific it is 1. One mole of KMnO,is equivalent to 5 moles of charge density of FeSO, because, according to reaction [8], five moles of Fe2÷ are oxidized for each mole of Mn7÷ that is reduced: [ 1 mol (-)/mol (clay)] [mol(clay)/0.7295 =-I 1.37 mol(-).kg MnO,- + 8H÷ + 5e = Mn2÷ + 4H~O [9] This charge is neutralized by cations whose positive 5Fe~÷ -~÷ 5e. = 5Fe [I0] charges sum to an equal number 0.37) (6.02 Consequently, the CECis 1.37 mol( ÷ ) -~. L.ikewise for the reaction involved in the biological oxi- This reasoning lends readily apparent stoichiometry dization of sulfur to CECcalculations and has been demonstrated as a 2S + 302 = 2SO3 [11] workable approach to teaching soil chemistry (6). CECis determined by the single- saturation tech- n(1/6S) = n(¼00, nique, then the ion used should be specified. If the CEC n(2/3S) = n(O0 for the Upton, Wyomingmontmorillonite, in the ex- ÷, because ample above, was determined using Na its CECshould be expressed as 1.37 mol(Na÷).kg-~. Likewise,2÷ if Mg S~÷ - 6e = S [121 were used, the expression would be 1.37 mol(½ kg-I. Onereason for specifying the saturating ion is that O, + 4e = 202-. [13] it can influence the CECmeasured. Converting CECto surface charge density requires In summary, the recommended definition of the terms for specific surface area (m2 kg-t) and molar equivalent is as follows: the equivalent of a species X is charge, i.e., quantity of electrical charge per mole of the entity that in a specified reaction would combine charge entities [C.mol(-)-q, which is the Faraday con- with, or be in any other appropriate way, equivalent in: stant. The surface charge density of the electrons in the (a) an acid-base reaction to one entity of titratable hydrogen ions, H÷ or protons; or (b) a redox reaction sample of 1~ pton, Wyomingmontmorillonite is one entity of electrons, e-. In both instances, the equiva- [1.37 mol(-)/kg] [kg/(766 x 10~m~)] lent can be established from a knowledge of the equiva- lence factor and the of the species. [(9.6485 x 10~C)/mol(-)] = 0.17 -~ For a more detailed discussion of determining equiva- The surface charge density of the exchangeable lence factors, see (5). cations would also be expressed as 0.17 C m-’. Cation Exchange Capacity Conductivity Historically, the soil scientist has expressed cation ex- The SI unit of electrical conductance is siemens (S), change capacity (CEC) in "equivalents per 100g". electrical conductivity of solutions is nowexpressed as SI, the unit becomes "specific amount-of-substance". S m-~. To obtain a numerical value equal to that previ- "Specific" implies on a per-mass basis, and "amount- ously reported in units of mmhocm -’ and still retain of-substance" selected as either plus charges (protons, base units in the denominator, it is recommendedto p÷) or negative charges (electrons, e-). In SI base units, report values in units of dS m-~ (1 dS -~ =1 mScm-1 charges per unit mass becomes mol (p÷)okg-’ in refer- = 1 mmhocm-l). The equivalent expression for #mho ence to cationic charges neutralizing exchange sites, or cm-’ would be 10-3 dS m-~ (10-’ mS m-~), but because mol (e-)okg-i in reference to the negatively charged ex- symbol for a prefix of 10-4 is not defined in SI, using change sites. Values would be numerically equal because tzmho cm-~ is unacceptable. one proton (p÷), or its electrochemical equivalent, neutralizes one negatively charged exchange site. For ex- Radioactivity ample, let us assumea soil is reported to contain 4 milli- equivalents each of exchangeable K÷ and Ca2÷ per 100 g SI uses the derived unit bequerel (Bq) to express SI UNITS IN SOIL CHEMISTRY 69 radioactivity instead of the unit curie (Tables 3 and 8). 1 curie = 3.7 x 10’° Bq The bequerel is expressed with the basic SI unit of time, Thus a solution previously described as labelled with the second. 30/zCr p32, now is correctly described as labelled with sBqP3". Table 9. Examples of preferred units for expressing 1.11 x l0 physical quantities in ASAjournals SUMMARY Quantity Application Unit Symbol Area Specificsurface square meterper The SI Units committeeof the ASAis recommending areaof soil kilogram m2 ¯ kg-’ Pot area square centimeter cm~ adoptionof SI in its journals. It is expectedthat SI Leaf area square meter m2 usage will expandinto textbooks and classrooms as Landarea hectare ha well. Tables of recommendedunits (Table 9) and con- Cation exchange capacity Soil mole per kilogram mol.kg-~ versionfactors (Table10) are includedso use of SI can ConcentrationS" In liquid media begin immediately. Membersare encouragedto begin molecularwt. using SI and include traditional units, if desired, in known moleper liter mol. L-’ molecularwt. parenthesis.Problems arising with SI usageare solicited unknown gramper liter g. L-’ by the SI Units committeeso that the systemwill be of In plant material molecularwt. greatestutility to oursociety. known moleper kilogram mol.kg-’ molecularwt. Table10. Factorsfor convertingnon-SI units to unknown gramper kilogram g.kg-’ (mg-kg-’) ion uptake moleper liter moI.L-’-~) (mol.m acceptableSI units, withparenthetic reference Fertilizer kilogramper to Sl baseunits where needed hectare kg.ha-’ gramper cubic Non-S!Units SI Units meter g ¯ m-J (me¯ -~) Osmoticpotential jouleper kilogram J.kg-’ Multiply By To obtain Osmoticpressure pascal Pa acre 4047 square~ meter, m Density Soil bulk density megagramper 2) -~ acre 0.405 hectare, ha (IlY cubic meter Me. m acre 4.05-~ x 10 square kilometer, km~ (106 ~) Electrical Angstromunit 10 nanometer,nm (10-’ m) conductivity Salt tolerance decisiemenper atmosphere 0.101 megapascal,MPa (10’ Pa) meter dS.m- bar 10-* megapascal,MPa (10 * Pa) Evapotranspira- British thermalunit 1054 joule, j tion rate Plant meter per second m.s-’ 4.19 joule, J millimeterper day mm.d-’ cubicfeet 0.028 cubic~ meter, m Growthrate Plant meter per second m- cubicfeet 28.3 liter, L (10-~ m~) millimeterper cubicinch 1.64-s x 10 cubic~ meter, m second mm.s-’ cubicinch 16.4 cubiccentimeter, cm ~ (10-~ m~)l meter per day re.d-’ curie 3.7~0 x 10 becquerel, Bq Ion transport Ion uptake mole per square degrees(angle) 1.75-* x 10 radian, rad meter second mol- m -I dyne I0" new’ton,N Velocity moleper second mol.s erg 10"~ joule,J Leaf area ratio Plant square meterper foot 0.305 meter,m kilogram m foot- 1.356 joule,J Length Soil depth meter m gallon 3.785 liter, L (10-~ m’) centimeter cm gallon per acre 9.35 liter, per hectare,L-ha-’ Photosynthetic milligramper square -~ CO,mass flux -’ gramper cubic centimeter 1.00 megagramper cubic meter, Mgom rate density meter second mg.m-~.s inch 25.4 millimeter, mm(10 -~ m) CO~amount of micromoleper micron 1.00 micrometer,~m (10 -6 m) substanceflux square meter mile 1.61 kilometer, km(10 ~ m) density second #mol.m-2.s miles per hour 0.477 meterper second,m. s-’ Radiation Light hertz millimhosper centimeter 1.00 decisiemenper meter, dS.m-’ Wavenumber per meter m-’ ounce 28.4 gram,g (10-~ kg) Wavelength nanometer nm ounce(fluid) 2.96-~ × 10 liter, L (10-~ m’) lrradiance watt per square -~ pint (liquid) 0.473 liter, L (10 meter W.m pound 453.6 -J Photonflux moleper square gram,g (10 kg) -’ poundper acre 1.12 kilogram-~ per hectare, kg oha density meter second mol.m-2.s poundper acre 1.12-~ x 10 megagramper hectare, Me.ha-’ Resistance Stomatal secondper meter s.m-’ poundsper cubic foot 16.02 -~ Transpiration H20mass flux milligramper square kilogramper cubic meter, kgom -t poundsper cubic inch 2.77 x 10’ kilogram"~ per cubic meter, kg°m rate density meter second mg-m-a.s poundsper 47.88 pascal, Pa Waterrelations Potential joule per kilogram J. poundsper square inch 6.90x I0’ pascal,Pa Pressure pascal Pa quart(liquid) 0.946 liter,L (I0 -~m’) Yield Grainor forage megagramper quintal(metric) 10~ kilogram,kg yield hectare Mgoha-’ solidangle 12.57 steradian,sr gramper square ~. -~ squarecentimeter pergram 0.I squaremeter per kilogram, m kg-’ meter g.m squarefeet 9.29-~ x 10 square~ meter, m Mass of plant or gram {gramper squareinch 645.2 squaremillimeter, mm~ (10 -6m~) plant part plant or per g(g.plant-’; squaremile 2.59 square’ kilometer, km plant part)~/ g ¯ kernel-’) squaremillimeters pergram 10-~ squaremeter per kilogram, m’¯ kg-" If percentis used, the basis mustbe specified. temperature(°F) - 32 0.5555 temperature, C Herethe use of a non-basicunit in the denominatoris an acceptablealterna- temperature (°C) + 273 1 temperature, °K tive. For exampleone can write either "the averageyield per plant was100 g" ton (metric) 10~ kilogram, kg or "the average yield was 100 g.plant." Probably the latter usage wouldbe ton (2000lb) 907 kilogram, kg restricted to table headings. tons (2000lb) per acre 2.24 megagramper hectare, Me.ha-’ 70 JOURNAL OF AGRONOMIC EDUCATION, VOL. 10, 1981

ACKNOWLEDGMENTS The authors are greatly appreciative of the laborious review talents and many helpful suggestions of Dr. Jan van Schilf- gaarde. Likewise, we acknowledge the learned efforts of the entire ASA SI Units committee (ACS 321.4) to inform society members on this topic.