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Development Team Paper No: 16 Environmental Chemistry Module: 01 Environmental Concentration Units Development Team Prof. R.K. Kohli Principal Investigator & Prof. V.K. Garg & Prof. Ashok Dhawan Co- Principal Investigator Central University of Punjab, Bathinda Prof. K.S. Gupta Paper Coordinator University of Rajasthan, Jaipur Prof. K.S. Gupta Content Writer University of Rajasthan, Jaipur Content Reviewer Dr. V.K. Garg Central University of Punjab, Bathinda Anchor Institute Central University of Punjab 1 Environmental Chemistry Environmental Environmental Concentration Units Sciences Description of Module Subject Name Environmental Sciences Paper Name Environmental Chemistry Module Name/Title Environmental Concentration Units Module Id EVS/EC-XVI/01 Pre-requisites A basic knowledge of concentration units 1. To define exponents, prefixes and symbols based on SI units 2. To define molarity and molality 3. To define number density and mixing ratio 4. To define parts –per notation by volume Objectives 5. To define parts-per notation by mass by mass 6. To define mass by volume unit for trace gases in air 7. To define mass by volume unit for aqueous media 8. To convert one unit into another Keywords Environmental concentrations, parts- per notations, ppm, ppb, ppt, partial pressure 2 Environmental Chemistry Environmental Environmental Concentration Units Sciences Module 1: Environmental Concentration Units Contents 1. Introduction 2. Exponents 3. Environmental Concentration Units 4. Molarity, mol/L 5. Molality, mol/kg 6. Number Density (n) 7. Mixing Ratio 8. Parts-Per Notation by Volume 9. ppmv, ppbv and pptv 10. Parts-Per Notation by Mass by Mass. 11. Mass by Volume Unit for Trace Gases in Air: Microgram per Cubic Meter, µg/m3 12. Conversion from µg m-3 to ppbv 13. Mass by Volume Unit for Aqueous Media: mg per liter or ppm 14. Conversion from One Unit to Another 15. Pressure, Partial Pressure and Units 16. Suggesting Reading Introduction A large number of chemical species are found in the environment. To express their amounts, it is necessary to specify the unit of measurement. In general, SI units (Système international d'unités) are used, although some other units may also be found occasionally. SI unit for length is meter, m, for mass is kilogram, kg, and for time is second, s. These basic units are utilized to obtain derived units for 3 Environmental Chemistry Environmental Environmental Concentration Units Sciences physical parameters. It must be pointed out that environmental chemistry is concerned mainly with air and aquatic chemistry and therefore the discussion on units is concerned mainly with these systems. Exponents The amounts of different substances present in environment differ by several orders of magnitude, say from 0.00000001 to 1,00,00,00,000, i. e., from 1x10-8 to 1x 108. For the sake of brevity, ease in writing and to avoid writing several zeros, the exponents, as given in Table 1, are used. One may come across the use of billion, million etc., hence following equalities may be remembered: tera = trillion; giga = billion; mega = million; kilo = thousand, hecto = hundred and deca = ten. Environmental chemistry deals mainly with trace amounts of contaminants and pollutants in air and aqueous systems, therefore, the entire discussion is based on this... Table 1. Exponents, prefixes and symbols based on SI units. Multiple Prefix Symbol Multiple Prefix Symbol 1012 tera T 10-2 centi c 109 giga G 10-3 milli m 106 mega M 10-6 micro µ 103 kilo k 10-9 nano n 102 hecto h 10-12 pico p 10 deca da 10-15 femto f 10-1 deci d 10-18 atto a 4 Environmental Chemistry Environmental Environmental Concentration Units Sciences Environmental Concentration Units The concentrations of the gaseous substances can be expressed using absolute and relative scales. An example of the former are molarity, molality and number density and of the latter are mixing ratio and mole fraction. Molarity, mol/L The most preferred unit of expressing concentrations of the substances in chemistry is molarity. It is defined as the number of moles of a solute dissolved in one liter of the solution. Its unit is mol/L or mol L-1. It is defined by Eq. 1. molarity = mass of solute in g/(M. W. of solute × volume of solution in L) (1) Problem 1.. A 100 mL solution was prepared by dissolving 0.5845 g NaCl (M. W. = 58.45 g/mol) in water. Calculate molarity of NaCl. Solution. Convert volume100 mL in to 0.1 L and then the molarity of NaCl using Eq. 1. is: molarity of NaCl = 0.5845 g/58.45 g mol-1x 100 mL = 0.5845 g/ 58.45 g mol-1x 0.1L = 0.1 mol L-1. Molality, mol/kg It is defined as the number of moles of a solute dissolved in one kg of the solvent. Its unit is mol/kg as in Eq 2. molality = mass of solute in g/(M. W. x mass of solvent in kg) (2) It does not depend on temperature. 5 Environmental Chemistry Environmental Environmental Concentration Units Sciences Problem 2. For preparing 0.01 molal solution of NaCl, how many grams of NaCl should be dissolved in 500 g of water? Solution. After converting 500 g of water in to 0.5 kg, use Eq. 2 as follows: 0.01 mol kg-1= mass of NaCl in g /(58.45 g mol-1 x 0.5 kg) mass of NaCl = 0.01 mol kg-1x 58.45 g mol -1x 0.5 kg = 0.29225 g Number Density (n) The number density, n, is defined as the number of molecules per unit volume as in Eq. 1. nx = total number of molecules of X / total volume of air (3) where nx is the number density of gaseous substance X. The unit of number density is molecules /cm3 or molecules cm-3. Number density is widely used in measuring reaction rates and optical properties of atmosphere. While reporting number density, it is necessary to report environmental conditions such as temperature and pressure because the value of volume depends on these parameters and so the number density will also depend on these parameters. -6 6 Problem 3. Then number of CO2 molecules in 4 x 10 L air is 2x10 . Calculate the number density of CO2. Solution. The number density, nCO2, can be calculated as follows: 6 Environmental Chemistry Environmental Environmental Concentration Units Sciences nCO2 = total number of molecules of CO2/Total volume of air. 6 -6 nCO2 = 2x10 / 4 x 10 11 3 nCO2 = 5 x10 molecules/ cm Mixing Ratio Mixing ratio, Cx, is equal to the number of moles per mole of air as in Eq. 2. Cx = total number of moles of X/ total number of moles of air (4) The mixing ratio is a dimensionless quantity because the amounts of X and air are in the same unit of mole, which cancels out. The environmental science, in general, deals with trace amounts of pollutants in gas phase and with trace impurities in aqueous systems. It is, therefore, preferred to express the concentrations of trace substances in the form of parts-per notation, which can be expressed as volume by volume (V/V) or mass by mass (m/m). ppm, ppb and ppt are calculated in volume-per-volume ratio and so the correct representation is ppmv, ppbv and pptv. In an environment if the amount CO be 1 ppmv, it means 1mL of CO is present in 1 million mL of air. Parts-Per Notation by Volume The concentrations of gaseous substances in air determined as volume by volume ratio should be expressed as parts per million by volume (ppmv), parts per billion by volume (ppbv) and parts per trillion by volume (pptv). Unfortunately, most often ‘v’ is dropped and the values are written as ppm, ppb and ppt. 7 Environmental Chemistry Environmental Environmental Concentration Units Sciences ppmv, ppbv and pptv One ppm means one unit volume of the trace substance to be present in one million volume. For example if in air reported CO be 2 ppmv, it means 2mL CO is present in one million mL of air, or 2mL CO is present in one m3 of air. ppbv and pptv have similar meaning. According to parts-per notation the values of ppmv, ppbv and pptv can be expressed as in Eqs.5-7. 푛푢푚푏푒푟 표푓 푝푎푟푡푠 표푓 푎 표푛푠푡푡푢푒푛푡 푝푝푚푣 = ×106 (5) 푡표푡푎푙 푛푢푚푏푒푟 표푓 푝푎푟푡푠 표푓 푎푙푙 푡ℎ푒 푐표푛푠푡푡푢푒푛푡푠 푛푢푚푏푒푟 표푓 푝푎푟푡푠 표푓 푎 푐표푛푠푡푡푢푒푛푡 푝푝푏푣 = ×109 (6) 푡표푡푎푙 푛푢푚푏푒푟 표푓 푝푎푟푡푠 표푓 푎푙푙푡ℎ푒 푐표푛푠푡푡푢푒푛푡푠 푛푢푚푏푒푟 표푓 푝푎푟푡푠 표푓 푎 푐표푛푠푡푡푢푒푛푡 푝푝푡푣 = ×1012 (7) 푡표푡푎푙 푛푢푚푏푒푟 표푓 푝푎푟푡푠 표푓 푎푙푙 푡ℎ푒 푐표푛푠푡푡푢푒푛푡푠 The quantities in numerator and denominator must be in the same unit and hence values of ppmv, ppbv and pptv are dimensionless. The amounts of the components are expressed in several units, which all are proportional to number of moles, for example: number of moles of a gaseous constituent are proportional to its volume, number of molecules of a gaseous constituent are proportional to number of its moles and number of moles of a gaseous constituent are proportional to its partial pressure Based on these considerations, the formulas in Eq. 5 become: 8 Environmental Chemistry Environmental Environmental Concentration Units Sciences 푛푢푚푏푒푟 표푓 푚표푙푒푠 표푓 푎 푐표푛푠푡푡푢푒푛푡 푝푝푚푣 = ×106 (8) 푡표푡푎푙 푛푢푚푏푒푟 표푓 푚표푙푒푠 표푓 푎푙푙 푡ℎ푒 푐표푛푠푡푡푢푒푛푡푠 푣표푙푢푚푒 표푓 푎 푐표푛푠푡푡푢푒푛푡 푝푝푚푣 = ×106 (9) 푡표푡푎푙 푣표푙푢푚푒 표푓 푝푎푟푡푠 표푓 푎푙푙 푡ℎ푒 푐표푛푠푡푡푢푒푛푡푠 푛푢푚푏푒푟 표푓 푚표푙푒푐푢푙푒푠 표푓 푎 푐표푛푠푡푡푢푒푛푡 푝푝푚푣 = ×106 (10) 푡표푡푎푙 푛푢푚푏푒푟 표푓 푚표푙푒푐푢푙푒푠 표푓 푎푙푙 푡ℎ푒 푐표푛푠푡푡푢푒푛푡푠 푝푎푟푡푎푙 푝푟푒푠푠푢푟푒 표푓 푎 푐표푛푠푡푡푢푒푛푡 푝푝푚푣 = ×106 (11) 푡표푡푎푙 푝푟푒푠푠푢푟푒 표푓 푝푎푟푡푠 표푓 푎푙푙 푡ℎ푒 푐표푛푠푡푡푢푒푛푡푠 Likewise, the equations for ppbv and pptv can be written based on Eqs.
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