4.3 Physical Principles and Background

4.3.1 Basic Material from Physics and Chemistry4.3.1.1 Atoms and Molecules

Basic Material from Physics and ChemistryIn this section we will look at basic background material from physics and chemistry needed to understand the nature of the chemical hazards we will be modeling.2AtomsMatter is made up of atoms and molecules. Atoms are the smallest components of the basic chemical elements, which include hydrogen, carbon, iron, uranium, etc.As of November 2011, 118 elements have been identified the first 98 occur naturally on earth, 80 are stable, and the others are radioactive and decay into other elements.Periodic Table of the Elements: http://www.atomic-elements.info/

3AtomsAtoms are made up of a nucleus, surrounded by orbiting electrons.The nucleus is composed of protons and neutrons usually an atom has the same number of protons as neutrons.The number of protons in an atom determines its atomic number, so for example, carbon has 6 protons, hence an atomic number of 6.An atoms atomic weight is determined by its total number of protons and neutrons, which is approximately twice its atomic number.

4Atomic WeightLooking at Table 4.2 on page 111 of our textbook, we see that an elements atomic weight is not an integer for example, carbon has an atomic weight of 12.011.The reason for this is that atoms of the same element may have different numbers of neutrons for example carbon atoms usually have 6 neutrons, but may have 7 or 8 neutrons, leading to an atomic number of 13 or 14.Carbon atoms with more than 6 neutrons are radioactive the different types of carbon are called isotopes of carbon.

5Atomic WeightRadioactive carbon 14 is used for carbon 14 dating to determine the age of fossils or old artifacts.To get an elements atomic weight, scientists have determined how much of each isotope of an element occurs in the universe and have computed a weighted average.

6MoleculesMost substances are made up of a combination of atoms.A molecule is a collection of atoms bound together in particular combinations and structures.For example, water molecules are made up of two oxygen and one hydrogen atom we denote water by H2O.Another example of a molecule is CH4, natural gas (methane), which is used for cooking it is made up of 4 hydrogen atoms and one carbon atom.Ozone molecules (O3) are comprised of three oxygen atoms!

7Molecular WeightThe molecular weight of a molecule is the sum of the atomic weights of the atoms making up the molecule.For example, the molecular weights of the molecules on the last slide are:Water: 2H + 1O = 2(1.008) + 1(15.9994) = 18.0154Methane: 1C + 4H = 1(12.011) + 4(1.008) = 16.043Ozone: 3O = 3(15.9994) = 47.99982

8Molecular WeightWhat would be the molecular weights of these hydrocarbons:Acetylene (C2H2)Trichloroethylene (C2HCI3)Propane (C3H8)Butane (C4Hl0)Ethanol (C2H5OH).Note that many hazardous materials such as these which are used as fuels, solvents, etc., are made up of hydrocarbons!

94.3.1 Basic Material from Physics and Chemistry4.3.1.2 Physical Properties of Matter

States of matterThere are three common states of matter solid, liquid, and gas.We will mostly be concerned with liquids or gases, especially the transition from liquids to gases as spilled hazardous liquids evaporate or react to form gases.These gases can be toxic or flammable and may move from the scene of an accident to a location with an unprepared or unsuspecting population. 11DensityDefinition: The density of a substance is its mass per unit volume.Typical units are: lb/ft^3, gm/cm^3, etc.For example, Water has a density of 62.4 lb/ft^3 or one g/cm^3.Solid rock has a density of about 200 lb/ft^3.Air has a density of 0.004 lb/ft^2 at sea level.

12Specific GravityA quantity related to density is specific gravity.Definition: The specific gravity of a substance is the ratio of its density to the density of water.For example, the specific gravity of solid rock with a density of 200 lb/ft^3 would be:Specific gravity of rock = (density of rock)/(density of water)= (200 lb/ft^3)/(62.4 lb/ft^3)= 2.5In metric units, the same rock would have a specific gravity of 2.5 g/cm^3, since the density of water is 1 g/cm^3.For this reason, one may encounter instances of the terms density and specific gravity being used interchangeably.13Density and TemperatureMost substances will expand when heated.Thus, the same amount of material which is heated will require more volume, which means it will have a lower density!Can you think of a substance that doesnt behave this way?http://www.ehow.com/info_8272150_types-materials-shrink-heated.htmlhttp://phys.org/news/2011-11-incredible-material-reveal-scandium-trifluoride.htmlhttp://www.ncnr.nist.gov/AnnualReport/FY1998/rh1.pdf14EvaporationConsider an open container of some chemical liquid, such as water, antifreeze, alcohol, etc.What would you expect to happen over time?Which would you expect to evaporate more quickly?Intuitively, evaporation is the process of a liquid turning into a gas!15EvaporationWe will need to understand the process of evaporation, since it will play a major role in spills of hazardous materials!Here are two principles to keep in mind when considering evaporation:1. The rate of evaporation is proportional to the surface area (all other factors being equal).2. The rate of evaporation increases as the temperature of the liquid increases.16Evaporation and Surface AreaPhysically, evaporation is a process in which molecules close to the surface of a liquid that have sufficient kinetic energy to break through the surface do so and escape individually into the space above the liquid.The molecules that escape become part of the gaseous or vapor component of the chemical. It follows that if the liquid has a larger surface area, then more molecules will be able to escape for example, doubling the surface area will double the rate of evaporation!17

Evaporation and Surface Area18Image Courtesy Charles Hadlock: Mathematical Modeling in the EnvironmentEvaporation and TemperatureThe temperature of a substance such as a liquid is a measure of the average kinetic energy of the substances molecules. Thus, when heat is applied to a liquid, the liquid will gain more energy, causing the liquids molecules to increase their movement, in turn increasing the liquids average energy.It follows that a proportion of the molecules near the liquids surface will have higher energy, leading to an increase in the evaporation rate!19Evaporation and Temperature

20Image Courtesy Charles Hadlock: Mathematical Modeling in the EnvironmentVapor PressureLets consider a simple experiment!Place a beaker of chemical under a larger closed glass cover.Initially, all of the chemical is inside of the beaker.

21Image Courtesy Charles Hadlock: Mathematical Modeling in the EnvironmentVapor PressureThe rest of the space inside the glass cover is filled with some other material such as air that doesnt react with the chemical (i.e. it is inert with respect to the chemical.

22Image Courtesy Charles Hadlock: Mathematical Modeling in the EnvironmentVapor PressureNow, suppose the material in the beaker begins to evaporate.Some of the molecules from the beaker join those in the vapor space inside the cover, outside of the beaker.

23Image Courtesy Charles Hadlock: Mathematical Modeling in the EnvironmentVapor PressureSince none of the original gas molecules have any place to go, there is an increase in the total number of molecules in the same space.This results in an increase in the pressure under the cover.

24Image Courtesy Charles Hadlock: Mathematical Modeling in the EnvironmentVapor PressureThis process will eventually slow down and reach an equilibrium point once there are so many chemical molecules in the vapor space that the chemical is no longer able to evaporate.

25Image Courtesy Charles Hadlock: Mathematical Modeling in the EnvironmentVapor PressureA similar effect happens on hot days when there is high relative humidity there is so much water vapor in the air that sweat produced on a body is unable to evaporate!

26Image Courtesy Charles Hadlock: Mathematical Modeling in the EnvironmentVapor PressureTechnically, what is really happening is that at all times there are molecules with sufficient energy leaving the liquid and entering the vapor space as well as molecules in the gas space colliding with and rejoining the liquid.Initially, more molecules leave the liquid than enter, but as time increases, the rates even out until evaporation no longer is able to take place at this point the system is at equilibrium.

27Image Courtesy Charles Hadlock: Mathematical Modeling in the EnvironmentVapor PressureOnce equilibrium is reached, since there are more total gas molecules in the vapor space than there were initially, the total pressure will be higher.The amount of pressure increase, denoted P, is called the vapor pressure of the chemical at the systems current temperature.

28Image Courtesy Charles Hadlock: Mathematical Modeling in the EnvironmentVapor PressureSince increasing the temperature would increase evaporation, it follows that vapor pressure would also increase.Thus, vapor pressure is an increasing function of temperature!

29Image Courtesy Charles Hadlock: Mathematical Modeling in the EnvironmentVapor PressureNote that if the gas in the vapor space is truly inert with respect to the chemical in the beaker and undergoes no interactions with the chemical (in either liquid or gaseous form), then the vapor pressure P is independent of initial pressure!

30Image Courtesy Charles Hadlock: Mathematical Modeling in the EnvironmentVapor PressureWhile in practice, idealized conditions like this never occur, it turns out that the only factor that significantly impacts vapor pressure is the systems temperature.For this reason, when working with vapor pressure, one must know the temperature of the system in question.

31Image Courtesy Charles Hadlock: Mathematical Modeling in the EnvironmentBoiling ProcessSuppose a beaker that contains a liquid chemical is gradually heated to higher and higher temperatures, in a fashion similar to heating a pot of water on a stove.Keep in mind that ordinary atmospheric pressure of the air is always pushing down on the liquid in the figure this is represented by an imaginary piston.32

Image Courtesy Charles Hadlock: Mathematical Modeling in the EnvironmentBoiling ProcessIf the vapor pressure of the liquid is increased enough so that it is greater than the atmospheric pressure, then vapor bubbles of the chemical can expand rapidly, causing the effect known as boiling.At this point, the chemical can enter the vapor form throughout the liquid, not just at the surface, since vapor bubbles create their own vapor space where they develop!33

Image Courtesy Charles Hadlock: Mathematical Modeling in the EnvironmentBoiling ProcessUnder boiling conditions, much larger quantities of the chemical can move into the vapor state rapidly the primary limiting factor is the heat provided.The reason for this is that it takes a certain amount of heat energy to change a fixed amount of a given chemical from liquid to gaseous form.This is true for both evaporation and boiling.34

Image Courtesy Charles Hadlock: Mathematical Modeling in the EnvironmentBoiling ProcessAs an example, 540 calories of heat energy are needed to convert one gram of water from liquid to gas under normal conditions. This amount of energy is called waters heat of vaporization. 35

Image Courtesy Charles Hadlock: Mathematical Modeling in the EnvironmentBoiling ProcessOnce a liquid reaches its boiling point, all of the heat energy being applied to it is used up to convert more of the liquid to gaseous form.At this point, the liquids temperature essentially stays constant right at the boiling point, rather than continuing to rise higher.36

Image Courtesy Charles Hadlock: Mathematical Modeling in the EnvironmentBoiling ProcessTo illustrate these ideas, consider the process of boiling an egg.In New York, NY (at sea level), if it takes 4 minutes to boil the egg at 100 degrees Celsius, will it take the same amount of time at the same temperature in Denver, CO?37

Image Courtesy Charles Hadlock: Mathematical Modeling in the EnvironmentBoiling ProcessSince Denvers elevation is one mile, the atmospheric pressure is lower, so to heat the water to boiling requires less heat.Thus, the egg will take longer to cook than 4 minutes.38

Image Courtesy Charles Hadlock: Mathematical Modeling in the EnvironmentBoiling ProcessPressure cookers are specially designed pots with a screw-on lid designed to build up the pressure inside the pot to a pressure higher than atmospheric pressure.Then, to reach the boiling point, more heat needs to be applied to get the pots ingredients to boil, which means the food cooks more quickly!39

Image Courtesy Charles Hadlock: Mathematical Modeling in the EnvironmentBoiling PointWe tend to equate boiling point with high temperature, most likely because when cooking, this is usually the case.For many dangerous chemicals, it turns out that the boiling point is already achieved at room temperature because the chemicals have very high vapor pressures. For example, propane gas is stored in small metal cylinders or bottles under high pressure.At room temperature, under normal atmospheric conditions, propane will boil.40

Boiling PointSimilar to a pressure cooker, by holding the propane liquid at a pressure at or slightly above vapor pressure, the liquid doesnt boil.But what if a tanker truck full of propane crashes and breaks open?The propane liquid would pour on the ground, boil just like water on a hot griddle, and form a highly flammable expanding gas cloud that can float off into a surrounding neighborhood.The goal of this chapter is to analyze situations like this!

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Mixtures vs. Pure SubstancesAll of the scientific concepts discussed so far have been for pure substances, i.e. materials consisting of a single chemical.The chemical may be made up of molecules that consist of more than one element, but each molecule is identical.Water, methane, or ozone would be a pure substance.A mixture of water and other chemicals such as acetone or gasoline, or a mixture of gasoline and oil, etc. is not a pure substance.Many hazardous materials are in fact a mixture of chemicals.42Mixtures vs. Pure SubstancesA natural question to ask is: How does a mixtures chemical properties relate to the chemical properties of the mixtures constituents?For example, how are boiling points, vapor pressures, etc. affected?It turns out that mixtures are much more complicated than pure substances instead of a boiling point, a mixture may have a range of temperatures through which they boil.Also, chemicals within a mixture may interact in ways that alter the chemical properties of the individual chemicals in the mixture.43

4.3.2 Characterization of Flammable Vapor Hazards

Hypothetical ExperimentImagine the following experiment (DONT ATTEMPT THIS!):Roll up some newspaper, light one end, and quickly plunge the lit end into the opening of a car gas tank.What do you expect to happen?45

Image Courtesy Charles Hadlock: Mathematical Modeling in the EnvironmentHypothetical ExperimentWhen the lit newspaper torch is plunged into the tank, it should go out!Why does this happen?Gasoline is a highly flammable hydrocarbon, so it ignites easily, thus making it a good fuel.

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Image Courtesy Charles Hadlock: Mathematical Modeling in the EnvironmentHypothetical ExperimentFor a material to burn, there needs to be oxygen present burning is a chemical reaction under which oxygen combines chemically with some fuel to give off a substantial amount of heat.If there is enough oxygen, this burning process will continue until the fuel is depleted.However, if there isnt enough oxygen, as is the case in the gas tanks vapor space, the burning process will stop!

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Image Courtesy Charles Hadlock: Mathematical Modeling in the EnvironmentHypothetical ExperimentA natural question to ask is what about putting the torch near the entrance to the gas tank could there be more oxygen there?The answer is yes, in fact there may be enough to cause an explosion (this is how a car engine works enough oxygen and gasoline vapor are mixed to cause an explosion, driving a piston).This is why the experiment we are discussing is hypothetical!48

Image Courtesy Charles Hadlock: Mathematical Modeling in the EnvironmentFlammable LimitsLets look at this type of situation in a more scientific fashion!Consider the situation we discussed earlier of a beaker containing a chemical, placed under a glass cover.After evaporation has taken place to the point at which equilibrium is reached, there will be a mixture of both chemical and inert gas molecules in the vapor space. 49

Image Courtesy Charles Hadlock: Mathematical Modeling in the EnvironmentFlammable LimitsFor a certain range of percentages of chemical molecules in the vapor space, burning can take place!Outside of this range of percentages, burning will not be able to occur!50

Image Courtesy Charles Hadlock: Mathematical Modeling in the EnvironmentFlammable LimitsDefinition: The maximum percentage of chemical within the vapor space that allows burning is called the upper flammable limit (UFL). The minimum percentage of chemical within the vapor space that allows burning is called the lower flammable limit (LFL).

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Image Courtesy Charles Hadlock: Mathematical Modeling in the EnvironmentFlammable LimitsFor our gasoline experiment, if may be the case that at the gas tank opening, the concentration of oxygen and gasoline may be within the flammable limits.Of these two percentages, the one that is more crucial for safety is a chemical vapor mixtures LFL as long as the vapor mixture is below the LFL, no burning can occur!What about being above the UFL?52

Image Courtesy Charles Hadlock: Mathematical Modeling in the EnvironmentFlammable Limits ExamplesChemicalLower Flammable Limit (LFL), PercentUpper Flammable Limit (UFL), PercentAcetone213Butane1.88.4Gasoline1.47.5Methanol7.336Vinyl Acetate Monomer2.613.453Flash PointIt turns out that just as in the case of vapor pressure, the percentage of chemical vapor in the vapor space depends on temperature!As the temperature of a chemical is raised, its propensity to evaporate increases, increasing the number of molecules in the vapor space.54

Image Courtesy Charles Hadlock: Mathematical Modeling in the EnvironmentFlash PointThus, if the temperature is kept low enough, the percentage of chemical in the vapor space will stay below the LFL, so there wont be a flammable vapor hazard!For any given flammable chemical, there must be a critical temperature, below which the amount of vapor is below LFL and above which the amount of vapor reaches or exceed LFL.This temperature is called the flash point.55

Image Courtesy Charles Hadlock: Mathematical Modeling in the Environment

Flash Point ExamplesChemicalFlash Point (degrees Fahrenheit)Acetone0Butane-101Gasoline*-45Methanol51Vinyl Acetate Monomer18*Gasolines flash point can vary, depending on its blend.56Flash PointAll other factors being equal, It is preferable to handle a flammable material at a temperature below its flash point.Materials with a higher flash point are safer.The term flammable usually refers to chemicals with a flash point below some threshold, such as 73 degrees Fahrenheit or 100 degrees Fahrenheit (this limit varies and is somewhat arbitrary).Materials that burn, but have a higher flash point are called combustible.57Volatile MaterialsThe term volatile is used to describe how easily a material evaporates.For example, gasoline is more volatile than water.Usually, a material with a lower flash point tends to be more volatile and have a higher vapor pressure at any fixed temperature.58Explosive LimitsIn some sources, upper and lower flammable limits are referred to as upper and lower explosive limits they mean the same thing.Thus, instead of LFL or UFL, one may see LEL or UEL.Just like flammable limits, explosive limits refer to fire, not explosions.59Material Safety Data SheetsFor a given chemical, properties such as LFL, UFL, flash point, density, boiling point, etc. can be found in handbooks or Material Safety Data Sheets (MSDS).Almost any organization that uses, buys, sells, or handles a chemical or potentially hazardous material will have on file an MSDS for the material.For example, here are two MSDSs for acetone:http://www.sciencelab.com/msds.php?msdsId=9927062http://blogs.nwic.edu/rocketteam/files/2011/09/Acetone.pdf 60

4.3.2 Characterization of Toxicity Hazards

Toxic HazardsIn this section we will look at toxic hazards.It turns out, as we will see that these types of hazards can occur at much lower concentration levels than flammable hazards.There are two types of toxic hazards acute toxic hazards and chronic toxic hazards.62Acute Toxic HazardsAn example of an acute toxic hazard is a poisonous gas that causes severe injury or death almost immediately, such asA strongly acidic gas that damages the respiratory tract so much one can no longer breathe effectively, orA gas such as carbon monoxide that attaches to the hemoglobin in blood, making it impossible to transfer oxygen to vital organs.

63Chronic Toxic HazardsAn example of a chronic toxic hazard might be when long term exposure to a gaseous chemical causes gradual organ deterioration or some type of cancer.In such cases, short term exposure may have no noticeable effect.

64Threshold Limit ValuesLevels of exposure that may be hazardous are determined by a combination of both concentration and time.An example of such an exposure level is the threshold limit value (TLV).TLVs represent levels of acceptible exposures under normal working conditions.TLVs may also be given as daily time weighted averages or limits for short term (15 minute) exposures.TLVs are issued by the American Conference of Government Industrial Hygienists (ACGIH).65Threshold Limit ValuesWhat is a drawback to TLVs?They are not much use for determining acute risk levels associated with one-time or sporadic events, such as a hazardous spill.If the TLVs are permitted on a daily basis, would a one-time higher level of exposure be tolerable?If so, how much higher than the normal TLV would be considered safe?66IDLH ValuesAnother measure used that is more relevant to an emergency situation or one-time accident are the immediately dangerous to life or health (IDLH) values.IDLH values are published by the National Institute for Occupational Safety and Health (NIOSH).These levels have been developed to indicate when occupational workers should wear respirators to protect against airborne toxins. While not specifically designed for emergency situations, IDLH values can be used for practice or rough emergency planning calculations.For our purposes (mathematical modeling of hazardous situations), IDLH values and information from MSDSs will be sufficient!67Parts per Million (PPM)Unlike LFLs and UFLs, which are specified in percentages, toxic levels are usually specified in parts per million (ppm).As an example, a 5% concentration in terms of ppm would correspond to 50,000 molecules of a chemical for every one million molecules in the vapor space, since 50,000/1,000,000 = 0.05 = 5%.68Parts per Million (PPM)One reason that ppm are used is that toxic concentrations that appear in the IDLH are measured in tens, hundreds, or even lower ppm!Note that unlike ppm for water contamination in which ppm are based on weight or mass percentages, chemical ppm are measured in terms of molecular or volume percentages.69Fundamental Chemistry PrinciplesSuppose we know that a toxic concentration level in the air for the chemical ethylene glycol (C2H6O2, commonly known as antifreeze) is 110 mg/m^3.What is this concentration in ppm?To answer this we need a few fundamental principles from chemistry!70Fundamental Chemistry Principles(a) (Avogadros principle 1811): Under fixed conditions of pressure and temperature, a given volume of gas will contain the same number of molecules of any gaseous substance whether the molecules are small, light molecules or larger, heavier ones.Molecules are sufficiently far apart in a gas that their individual size has no impact on how much volume the gas takes up at a given pressure and temperature!71Fundamental Chemistry Principles(b) If M is the molecular weight of a gaseous substance, then M grams of that substance should take up the same space and contain the same number of molecules as N grams of a substance whose molecular weight is N.Thus, since nitrogen gas (N2) has a molecular weight of about 28 and hydrogen gas (H2) has a molecular weight of about 2, it follows that 28 grams of nitrogen gas should occupy the same space and have the same number of molecules as 2 grams of hydrogen gas!72Fundamental Chemistry Principles(c) The actual number of molecules contained in M grams of a substance with molecular weight M is about 6.022 x 1023 molecules.The number 6.022 x 1023 is known as Avogadros number.This quantity is called one mole of the substance.By part (b) of these principles, we know this number is the same no matter what substance we have.Thus, one mole is M grams of a material with molecular weight M, and the number of molecules in this amount of material is Avogadros number.73Fundamental Chemistry Principles(d) One mole of a gas under standard temperature and pressure conditions occupies a volume of 22.4 liters.This fact has been determined by chemists, both experimentally and theoretically!74Fundamental Chemistry Principles(e) If we have x grams of a gas and if its molecular weight is M, then we would have x/M moles of the gas and the number of molecules would be (x/M) x 6.022 x 1023. As an example, since nitrogen gas has a molecular weight of about 28, 56 grams of nitrogen gas = 56/28 = 2 moles of nitrogen gas = 2 x 6.022 X 1023 molecules of nitrogen gas.75Back to the C2H6O2 Example!Suppose an emergency level of concentration for ethylene glycol (C2H6O2) is published as 110 mg/m^3.What does this correspond to in ppm?To answer this, we need to know the molecular weight of ethylene glycol.M = 2(12.011) + 6(1.008) + 2(15.9994) = 62.0688

76Back to the C2H6O2 Example!Thus, we have(110 mg glycol)/(m^3 air)= (110 mg glycol)/(m^3 air)*(1 m^3)/(100 cm)^3*(1000 cm^3)/(1 liter)*(22.4 liter air)/(1 mole air)*(1 mole air)/(6.022 x1023 molecules air)*(10^6 molecules)/(1 million molecules)* 77Back to the C2H6O2 Example!*(1 g)/(1000 mg)*(1 mole glycol)/(62.0688 g glycol)*(6.022 x1023 molecules glycol)/(1 mole glycol)= (39.6979 molecules of glycol)(million molecules of air)= 39.6979 ppmNote that the red calculations converted the denominator to million molecules of air and the blue calculations converted the numerator to molecules of glycol.78Resourceshttp://www.atomic-elements.info/http://www.ehow.com/info_8272150_types-materials-shrink-heated.htmlhttp://phys.org/news/2011-11-incredible-material-reveal-scandium-trifluoride.htmlhttp://www.ncnr.nist.gov/AnnualReport/FY1998/rh1.pdfhttp://www.sciencelab.com/msds.php?msdsId=9927062http://blogs.nwic.edu/rocketteam/files/2011/09/Acetone.pdfCharles Hadlock Mathematical Modeling in the Environment, Section 4.379