1 Units Used in Measurement GLY Lecture 4 Fall, 2016

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 10 th 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. 2

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 3

Derived Units 4

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/ 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 K 5

Kelvin-Celsius Relationship Thus, the Kelvin and Celsius scales are related by In thermodynamics, all temperatures must be expressed in Kelvin 6

Prefixes 7

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) 8

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, C p  Specific heat capacity at constant pressure, c p = C p /m 9

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. 10

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) 11

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 12

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 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 13

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 14

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 15

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 16

Possible Confusion A solution of MgCl 2 that is 1N with respect to Mg 2+ 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 17

The Mole The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in kilogram of 12 C 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) 18

Use of “Mole” 1 mol of H 2 contains about 6.022×10 23 H 2 molecules, or ×10 23 H atoms 1 mol of HgCl has a mass of g 1 mol of Hg 2 Cl 2 has a mass of g 1 mol of Hg 2 + has a mass of g and a charge of kC 1 mol of Fe 0.91 S has a mass of g 1 mol of e -1 has a mass of µg and a charge of kC 1 mol of photons whose frequency is 5×10 14 Hz has energy of about kJ 19

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 20

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 21

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 22

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 23

Mass Per Unit Volume A typical example if mg/m 3 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 24

Conversion to Mass Per Unit Volume To convert from ppmv to mg/m 3 : 25

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 26

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 27

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: 28