Units Used in Measurement GLY 4241 - Lecture 4 Fall, 2018 Geochemical measurements are expressed in a variety of ways. All scientific measurements are based on the “metric system.”

The “Metric System” Metric system was actually two systems MKS, or Meter-Kilogram-Second system CGS, or Centimeter-Gram-Second system To resolve differences between the system, the 10th 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. The MKS (Meter-kilogram-second) system derived from the system introduced in France in 1791 The CGS (centimeter-gram-second) system adopted by the British Association for the Advance of Science in 1874

Basic Units in the SI System There are seven basic units in the SI system, from which other units are derived, shown in the following table Table 4-1 in lecture notes Many other units can be derived from the seven basic SI units. Some examples of these are shown on the next slide.

Derived Units Table 4-2 in lecture notes 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 are 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 106 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 14.5̊C to 15.5̊C, is equal to 4.184 J. One food calorie, sometimes called a large calorie, is 1000 calories or 4184 joules.

Temperature 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 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 0.01̊C The ice point (point at which water melts at 1 atmosphere) is 0̊C, or 273.15K

Kelvin-Celsius Relationship Thus, the Kelvin and Celsius scales are related by In thermodynamics, all temperatures must be expressed in Kelvin Equation 4-1 in lecture notes

Prefixes Table 4-3 in lecture notes 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.

Extensive and Intensive Units 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)

Modifying Units 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, Cp Specific heat capacity at constant pressure, cp = Cp/m In addition to the use of prefixes, some terms may be used to modify units

Solutes and Solvents Many units 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.

Concentration in Liquid Solution Mass Concentrations Parts per million (ppm) Milligrams per liter (mg/L) Equivalent weights per liter (Eq/L) Molar Concentrations Molarity (M) Molality (m) Mole Fraction (X)

Parts per million ppm = 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

Milligrams per liter mg/L = 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: For dilute solutions near 25̊C 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 Equation 4-2 in lecture notes

Units Related to ppm 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 Also ppb, meaning parts per billion, and ppt, meaning parts per trillion

Equivalents per liter (Eq/L) 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

Uses of Normality Acid-base chemistry - either hydrogen ion (H+) or hydroxide ions (OH-1) in a solution Redox reactions - # of electrons that an oxidizing or reducing agent can accept or donate Precipitation reactions - number of ions which will precipitate 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 (H2SO4) 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.

Possible Confusion A solution of MgCl2 that is 1N with respect to Mg2+ ions is 2N with respect to Cl-1 ions Both IUPAC and NIST discourage the use of normality For both acid/base and redox chemistry, the concept has value IUPAC = International Union of Pure and Applied Chemistry NIST = National Institute of Standards and Technology, formerly the National Bureau of Standards, or NBS

The 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 12C 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 (IUPAC definition)

Use of “Mole” 1 mol of H2 contains about 6.022×1023 H2 molecules, or 12.044×1023 H atoms 1 mol of HgCl has a mass of 236.04 g 1 mol of Hg2Cl2 has a mass of 472.08 g 1 mol of Hg2+ has a mass of 401.18 g and a charge of 192.97 kC 1 mol of Fe0.91S 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 5×1014 Hz has energy of about 199.5 kJ From IUPAC, The international system of units (SI), section 1.4, 2002

Molar (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 temperature as well The advantage of molarity is the ease of measurement of the volume of a liquid, rather than its weight, in many situations

Molality and Mole Fraction 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

Concentration in a Gas Two common methods are used to express concentration in gas One involves a certain number of particles per unit volume The second method is to express the mass per unit volume

Particles Per Unit Volume ppmv, or parts per million by volume, is one example Similar expressions are ppbv, or parts per billion by volume, and pptv, or parts per trillion by volume

Mass Per Unit Volume A typical example is mg/m3 It is possible to convert from one method to the other – at 1 atmosphere pressure: Where T = temperature in Kelvin and M = molecular mass of the substance in question Equation 4-3 in lecture notes

Conversion to Mass Per Unit Volume To convert from ppmv to mg/m3:

Dry vs. Wet Atmosphere 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

Conversion to “Dry Basis” It is possible to convert measurements made in air containing water to a “dry basis” using the following formula where C = concentration of the substance in question and w = fraction of the gas sample which is water vapor

Example Calculation 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: