LECTURE 4 - Units Used in Measurements Note: Slide numbers refer to the PowerPoint presentation which accompanies the lecture. Units, slide 1 here Introduction Geochemical measurements may be expressed in a variety of ways. All scientific measurements are based on the metric system. Units, slide 2 here The metric system, universally used in science, was actually two systems, the MKS (Meter-kilogramsecond) system derived from the system introduced in France in 1791, and the CGS (centimetergram-second) system adopted by the British Association for the Advance of Science in 1874. In an effort to resolve differences between the system, the Tenth General Conference on Weights and Measures adopted the International System of Units in 1954. This system is abbreviated SI, for the French Système International d Unitès. There are seven basic units in the SI system, from which other units are derived. They are shown in Table 4-1. (IUPAC, Names and symbols for the SI base units, Section 1.4.2, 2002) Units, slide 3 here Table 4-1 SI Base Units Physical Quantity Name Symbol Length Meter m Mass Kilogram kg Time Second s Temperature Kelvin K Amount of Substance Mole mol Electric Current Ampere A Luminous Intensity Candela cd 1
Many other units can be derived from the seven basic SI units. Some examples of these are shown in Table 4-2. Units, slide 4 here Note that some derived units may be expressed in term of other derived units. A joule, the unit for energy, heat, or work, is a Nm. Pressure, in Pascals, is Nm -2. The Pascal unit is often inconvenient in geology, where many measurements at done at 1 atmosphere ambient pressure. The atmosphere equals 101,325 pascals. A more convenient unit is the bar, which equals 100,000 pascals. Since 1 bar = 0.987 atm, the difference is often ignored. Another derived unit is the megapascal, equal to 10 6 Pascals, or 10 bars. A unit still very much in use is the calorie, which comes from the older CGS system. A calorie is defined as the quantity of heat necessary to raise 1 gram of water from 14.5 C to 15.5 C, is equal to 4,184 J. (Misra, 2012) Table 4-2 SI Derived Units Physical Quantity Name Symbol SI Base Units Electric charge Coulomb C A s Electric Conductance Electric Potential Difference Siemens S m -2 kg -1 s 3 A 2 Volt V m 2 kg s -3 A -1 Energy (work, heat) Joule J m 2 kg s -2 Force Newton N m kg s -2 Frequency Hertz Hz s -1 Power Watt W m 2 kg s -3 Pressure (stress) Pascal Pa m -1 kg s -2 Volume Liter L or l 10-3 m 3 From IUPAC, SI derived units with special names and symbols, Sect. 1.4.3, 2002 Units, slide 5 here Temperature deserves special mention. The SI unit is the Kelvin, K, not K, often mistakenly seen in the literature. The Kelvin scale is an absolute temperature scale, where 0K is 2
absolute zero. At absolute zero, molecules have no thermal energy, neither rotational, translational, nor vibrational. The Kelvin is defined as 1/273.16 of the triple point of water. On the Celsius scale, the triple point of water is 0.01 C. The ice point (point at which water melts at 1 atmosphere) is 0 C, or 273.15K. Units, slide 6 here Thus the Kelvin and Celsius scales are related by T( K) t( C) 27315. Eq. 4-1 In thermodynamics, all temperatures must be expressed in Kelvin. Both the SI base units and derived units may be modified by prefixes. These are used to signify decimal multiples and submultiples of SI units. Table 4-3 lists the common SI prefixes. Units, slide 7 here Table 4-3 SI Prefixes Submultiple Prefix Symbol Multiple Prefix Symbol 10-1 deci d 10 deca da 10-2 centi c 10 2 hecto h 10-3 milli m 10 3 kilo k 10-6 micro μ 10 6 mega M 10-9 nano n 10 9 giga G 10-12 pico p 10 12 tera T 10-15 femto f 10 15 peta P 10-18 atto a 10 18 exa E 10-21 zepto z 10 21 zetta Z 10-24 yocto y 10 24 yotto Y From IUPAC, Prefixes, Sect. 1.4.5, 2002 Units, slide 8 here 3
Classification of physico-chemical quantities into extensive and intensive quantities A quantity whose magnitude is additive for subsystems is called extensive. Examples include mass m, volume V, Gibbs energy G. A quantity whose magnitude is independent of the extent of the system is called intensive; examples include temperature T, pressure p, density ρ, and chemical potential (partial molar Gibbs energy) µ. The latter two are examples of quantities made intensive by dividing one extensive variable by another. (i.e. ρ = m/v) Units, slide 9 here The adjective specific before the name of an extensive quantity is often used to mean divided by mass. When the symbol for the extensive quantity is a capital letter, the symbol used for the specific quantity is often the corresponding lower case letter. Example: Heat capacity at constant pressure, C p Specific heat capacity at constant pressure, c p = C p /m (IUPAC, Classification of physico-chemical quantities into extensive and intensive quantities, section 1.2, 2002) Concentration in Liquid Solution Units, slide 10 here Many of the units used in geochemistry involve concentration of solutes in a solution. The solution may be a liquid, a gas, or a fluid above the critical point. There are a number of ways of expressing concentration. Each may be useful in certain situations, and less useful or inappropriate in others. As scientists, it is our job to choose units carefully so as to convey maximum information and not, however inadvertently, deceive the reader. Units, slide 11 here Concentrations in liquid solution are commonly expressed in one of six ways. These may be divided into mass concentrations, or molar concentrations. Mass concentration may be expressed as parts per million (ppm), milligrams per liter (mg/l), or equivalent weights per liter (Eq/L). Molar concentrations may be expressed as molarity (M), molality (m), or mole fraction (X). Each is explained below. Units, slide 12 here Parts per million = Mass of solute in mg / Mass of solution in kg Parts per million really means parts by million by mass. There is another unit, ppm (V) which means parts per million by volume. When expressed as ppm, parts per million by mass is understood. 4
Units, slide 13 here Millgrams per liter = Mass of solute in mg / volume of solution in liters The density of a solution, denoted ρ, expressed as g/ml or kg/l, may be used to relate ppm and mg/l measurements: Concentration( ppm) concentration of solute ( g / L) ( g / ml) Eq. 4-2 For dilute solutions near 25 C the density of the solution is very close to pure water, which has ρ = 1.00 kg/l, so there is little difference between ppm and mg/l. Units, slide 14 here There are several quantities related to parts per million. These include the familiar percent (%), and the less familiar per mille ( ) which means parts per thousand. There are also ppb, meaning parts per billion, and ppt, meaning parts per trillion. Units, slide 15 here N = equivalent weight of solute in g / volume of solution in L N stands for normality. Context should avoid confusion with the Newton, also denoted N. It is commonly used in three cases: Units, slide 16 here Acid-base chemistry: Used to express the concentration of either hydrogen ion (H + ) or hydroxide ions (OH -1 ) in a solution. Each solution can produce one or more equivalents of reactive species when dissolved. For example, hydrochloric acid (HCl) produces one mole of hydrogen ion per mole of hydrochloric acid, whereas sulfuric acid (H 2 SO 4 ) produces two moles of hydrogen ion per mole of sulfuric acid. Redox reactions: The equivalence factor describes the number of electrons that an oxidizing or reducing agent can accept or donate Precipitation reactions: The equivalence factor measures the number of ions which will precipitate in a given reaction. Units, slide 17 here 5
Normality may be a confusing measure of the concentration of solution. For example, a solution of MgCl 2 that is 1N with respect to Mg 2+ ions is 2N with respect to Cl -1 ions. For this reason both the International Union of Pure and Applied Chemistry (IUPAC) and the National Institute of Standards and Technology (NIST, formerly the National Bureau of Standards, or NBS) discourage the use of the term normality. However, for both acid/base and redox chemistry, the concept has value. (IUPAC, The use of the equivalence concept, section 6.3, 2002). Units, slide 18 here Molar concentrations clearly depend on the concept of a mole. The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon-12. When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles. Units, slide 19 here Examples of the use of the mole 1 mol of H 2 contains about 6.022 10 23 H 2 molecules, or 12.044 10 23 H atoms 1 mol of HgCl has a mass of 236.04 g 1 mol of Hg 2 Cl 2 has a mass of 472.08 g 1 mol of Hg + has a mass of 401.18 g and a charge of 192.97 kc 1 mol of Fe 0.91 S has a mass of 82.88 g 1 mol of e -1 has a mass of 548.60 µg and a charge of -96.49 kc 1 mol of photons whose frequency is 5 10 14 Hz has energy of about 199.5 kj (From IUPAC, The international system of units (SI), section 1.4, 2002) Units, slide 20 here Molarity (M) = Moles of solute/ volume of solution in liters Molarity is dependent on the volume of solution. Volume varies as a function of temperature, so molarity depends on these quantities as well. The advantage of molarity is the ease of measurement of the volume of a liquid, rather than its weight, in many situations. Units, slide 21 here Molality (m) = Moles of solute/ mass of solvent in kg Mole fraction (X) = moles of solute/ total moles of solution Both molality and mole fraction are independent of the temperature and pressure. 6
Units, slide 22 here Concentration in a Gas There are two common methods of expressing concentrations in gas. One involves a certain number of particles per unit volume. Units, slide 23 here An example is ppmv, or parts per million by volume. Similar expressions are ppbv, or parts per billion by volume, and pptv, or parts per trillion by volume. Units, slide 24 here Another method is to express the mass per unit volume, such as in mg/m 3. It is possible to convert from one method to the other. For example, at 1 atmosphere pressure, to convert from mg/m 3 to ppmv: ppmv 3 ( 0. 08205 T) mg / m M Eq. 4-3 where T = temperature in K and M = molecular mass of the substance in question. Units, slide 25 here To convert from ppmv to mg/m 3 : mg / m 3 ppmv M ( 0. 08205 T) Eq. 4-4 Units, slide 26 here One problem with gaseous atmospheric measurements is the variable amount of water that air may contain. It is common to give concentrations in dry air, or air which has no water at all. Environmentally, this is entirely unrealistic. Units, slide 27 here 7
It is possible to convert measurements made in air containing water to a dry basis using the following formula. C Dry basis C 1 w Wet basis where C = concentration of the substance in question and w = fraction of the gas sample which is water vapor. Units, slide 28 here Eq. 4-5 Example: a wet basis concentration of 52.3 ppmv in a gas having 3.43 volume percent water vapor would have a dry basis concentration of: C Dry basis 52. 3 ppmv 1 0 0343 54.. 2 References International Union of Pure and Applied Chemistry (IUPAC), Compendium of Analytic Nomenclature, 3 rd edition, 2002, http://old.iupac.org/publications/analytical_compendium/, (last seen August 23, 2016). Kula C. Misra, Introduction to Geochemistry: Principles and Applications, Wiley-Blackwell, 2012. 4241/LN.04_PP_F18.pdf August 17, 2018 8