ENVIRONMENTAL ENGINEER’S MATHEMATICS HANDBOOK - CHAPTER 5 doc

Table 5.1 shows the relationship between the temperature, specific weight,and density of fresh water.. Specific gravity is defined as the weight or density of a substance compared to the w

PART II

Fundamental Science and Statistics Review

Fundamental Chemistry and Hydraulics

5.1 INTRODUCTION

It is not sufficient for a future working environmental engineer to understand the causes and effects

of environmental problems in qualitative terms only He or she must also be able to express theperceived problem and its potential solution in quantitative terms To do this, environmentalengineers must be able to draw on basic sciences such as chemistry, physics, and hydrology (aswell as others) to predict the fate of pollutants in the environment and to design effective treatmentsystems to reduce impact In this chapter, we discuss fundamental chemistry and basic hydraulicsfor environmental engineers

5.2 FUNDAMENTAL CHEMISTRY

The chemists are a strange class of mortals, impelled by an almost insane impulse to seek their pleasure among smoke and vapor, soot and flame, poisons and poverty; yet among all these evils I seem to live so sweetly that I may die if I would change places with the Persian King.

Johann Joachim Becher

All matter on Earth consists of chemicals This simplified definition may shock those who thinkchemistry is what happens in a test tube or between men and women Chemistry is much more; it

is the science of materials that make up the physical world Chemistry is so complex that no oneperson could expect to master all aspects of such a vast field; thus, it has been found convenient

to divide the subject into specialty areas For example:

• Organic chemists study compounds of carbon Atoms of this element can form stable chains and rings, giving rise to very large numbers of natural and synthetic compounds.

• Inorganic chemists are interested in all elements, particularly in metals, and are often involved in the preparation of new catalysts.

• Biochemists are concerned with the chemistry of the living world.

• Physical chemists study the structures of materials, and rates and energies of chemical reactions.

• Theoretical chemists use mathematics and computational techniques to derive unifying concepts

to explain chemical behavior.

• Analytical chemists develop test procedures to determine the identity, composition, and purity of chemicals and materials New analytical procedures often discover the presence of previously unknown compounds.

96 ENVIRONMENTAL ENGINEER’S MATHEMATICS HANDBOOK

Why should we care about chemistry? Is it not enough to know that we do not want unnecessarychemicals in or on our food or harmful chemicals in our air, water, or soil?

Chemicals are everywhere in our environment The vast majority of these chemicals are natural.Chemists often copy from nature to create new substances superior to and cheaper than naturalmaterials Our human nature makes us work to make nature serve us Without chemistry (and theother sciences), we are at nature’s mercy To control nature, we must learn its laws and then use them.Environmental engineers must also learn to use the laws of chemistry; however, they must knoweven more Environmental engineers must know the ramifications of chemistry out of control.Chemistry properly used can perform miracles, but, out of control, chemicals and their effects can

be devastating In fact, many current environmental regulations dealing with chemical safety andemergency response for chemical spills resulted because of catastrophic events involving chemicals

5.2.1 Density and Specific Gravity

When we say that iron is heavier than aluminum, we mean that iron has greater density thanaluminum In practice, what we are really saying is that a given volume of iron is heavier than thesame volume of aluminum Density (p) is the mass (weight) per unit volumeof a substance at aparticular temperature, although density generally varies with temperature The weight may beexpressed in terms of pounds, ounces, grams, kilograms, etc The volume may be liters, milliliters,gallons, cubic feet, etc Table 5.1 shows the relationship between the temperature, specific weight,and density of fresh water

Suppose we had a tub of lard and a large box of crackers, each with a mass of 600 g Thedensity of the crackers would be much less than the density of the lard because the crackers occupy

a much larger volume than the lard occupies The density of an object can be calculated by usingthe formula:

(5.1)

In water/wastewater operations, perhaps the most common measures of density are pounds percubic foot (lb/ft3) and pounds per gallon (lb/gal)

• 1 ft 3 of water weighs 62.4 lb — density = 62.4 lb/ft 3

Table 5.1 Water Properties (Temperature, Specific Weight and Density)

Temperature

(°F)

Specific weight (lb/ft 3 )

Density (slugs/ft 3 )

Temperature (°F)

Specific weight (lb/ft 3 )

Density (slugs/ft 3 )

FUNDAMENTAL CHEMISTRY AND HYDRAULICS 97

The density of a dry material (e.g., cereal, lime, soda, or sand) is usually expressed in poundsper cubic foot The densities of plain and reinforced concrete are 144 and 150 lb/ft3, respectively.The density of a liquid (liquid alum, liquid chlorine, or water) can be expressed as pounds percubic foot or as pounds per gallon The density of a gas (chlorine gas, methane, carbon dioxide,

or air) is usually expressed in pounds per cubic foot

As shown in Table 5.1, the density of a substance like water changes slightly as the temperature

of the substance changes This occurs because substances usually increase in volume (size — theyexpand) as they become warmer Because of this expansion with warming, the same weight isspread over a larger volume, so the density is lower when a substance is warm than when it is cold

Specific gravity is defined as the weight (or density) of a substance compared to the weight (ordensity) of an equal volume of water (The specific gravity of water is 1.) This relationship is easilyseen when a cubic foot of water (62.4 lb) is compared to a cubic foot of aluminum (178 lb).Aluminum is 2.7 times as heavy as water Finding the specific gravity of a piece of metal is notdifficult We weigh the metal in air, then weigh it under water Its loss of weight is the weight of

an equal volume of water To find the specific gravity, divide the weight of the metal by its loss ofweight in water

Note that in a calculation of specific gravity, the densities must be expressed in the same units.

As stated earlier, the specific gravity of water is one, which is the standard — the reference towhich all other liquid or solid substances are compared Specifically, any object that has a specificgravity greater than one will sink in water (rocks, steel, iron, grit, floc, sludge) Substances with aspecific gravity of less than one will float (wood, scum, and gasoline) Because the total weightand volume of a ship is less than one, its specific gravity is less than one; therefore, it can float,The most common use of specific gravity in water/wastewater treatment operations is in gallons-to-pounds conversions In many cases, the liquids handled have a specific gravity of 1.00 or verynearly 1.00 (between 0.98 and 1.02), so 1.00 may be used in the calculations without introducingsignificant error However, in calculations involving a liquid with a specific gravity of less than0.98 or greater than 1.02, the conversions from gallons to pounds must consider the exact specificgravity The technique is illustrated in the following example

98 ENVIRONMENTAL ENGINEER’S MATHEMATICS HANDBOOK

Solution:

If the substance’s specific gravity were between 0.98 and 1.02, we would use the factor 8.34lb/gal (the density of water) for a conversion from gallons to pounds However, in this instance thesubstance has a specific gravity outside this range, so the 8.34 factor must be adjusted

Step 1 Multiply 8.34 lb/gal by the specific gravity to obtain the adjusted factor:

Step 2 Convert 1455 gal to pounds using the corrected factor:

(8.34 lb/gal) (0.94) = 7.84 lb/gal (roundedd)

(1455 gal) (7.84 lb/gal) = 11,407 lb (roundeed)

Weight = specific gravity × weight of water

FUNDAMENTAL CHEMISTRY AND HYDRAULICS 99

5.2.2 Water Chemistry Fundamentals

Whenever we add a chemical substance to another chemical substance (adding sugar to tea oradding hypochlorite to water to make it safe to drink), we are performing the work of chemistsbecause we are working with chemical substances; how they react is important to success Envi-ronmental engineers involved with water treatment operations, for example, may be required todetermine the amount of chemicals or chemical compounds to add (dosing) to various unit pro-cesses Table 5.2 lists some of the chemicals and their common applications in water treatmentoperations

Just about everyone knows that water is a chemical compound of two simple and abundant elements:

H2O Yet scientists continue to argue the merits of rival theories on the structure of water The fact

is that we still know little about water — for example, we do not know how water works.The reality is that water is very complex, with many unique properties that are essential to lifeand determine its environmental chemical behavior The water molecule is different Two hydrogenatoms (the two in the H2 part of the water formula) always come to rest at an angle of approximately105° from each other The hydrogens tend to be positively charged, and the oxygen tends to benegatively charged This arrangement gives the water molecule an electrical polarity; that is, oneend is positively charged and one end negatively charged This 105° relationship makes waterlopsided, peculiar, and eccentric; it breaks all the rules (Figure 5.1)

In the laboratory, pure water contains no impurities, but in nature water contains a lot of materialsbesides water The environmental professional tasked with maintaining the purest or cleanest waterpossible must always consider those extras that ride along in water’s flow Water is often calledthe universal solvent, a fitting description when you consider that given enough time and contact,water will dissolve anything and everything on Earth

Table 5.2 Chemicals and Chemical Compounds Used in Water Treatment

Name Common application Name Common application

Sodium hexametaphosphate Corrosion control Sodium hydroxide pH adjustment

Source: Spellman, F.R., 2003, Handbook of Water and Wastewater Treatment Plant Operations Boca Raton, FL: Lewis Publishers.

Percent heavier

1.0

=1 30 1 0. –

= 30

100 ENVIRONMENTAL ENGINEER’S MATHEMATICS HANDBOOK

A solution is a condition in which one or more substances are uniformly and evenly mixed ordissolved In other words, a solution is a homogenous mixture of two or more substances Solutionscan be solids, liquids, or gases (drinking water, seawater, or air, for example) We focus primarily

on liquid solutions

A solution has two components: a solvent and a solute (see Figure 5.2) The solvent is thecomponent that does the dissolving Typically, the solvent is the substance present in the greaterquantity The solute is the component that is dissolved When water dissolves substances, it createssolutions with many impurities

Generally, a solution is usually transparent, not cloudy, and visible to longer wavelengthultraviolet light Because water is colorless (hopefully), the light necessary for photosynthesis cantravel to considerable depths However, a solution may be colored when the solute remains uni-formly distributed throughout the solution and does not settle with time

When molecules dissolve in water, the atoms making up the molecules come apart (dissociate)

in the water This dissociation in water is called ionization When the atoms in the molecules comeapart, they do so as charged atoms (negatively charged and positively charged) called ions Thepositively charged ions are called cations and the negatively charged ions are called anions

Figure 5.1 A molecule of water (From Spellman, F.R., 2003, Handbook of Water and Wastewater Treatment

Plant Operations Boca Raton, FL: Lewis Publishers.)

Figure 5.2 Solution with two components: solvent and solute (From Spellman, F.R., 2003, Handbook of Water

and Wastewater Treatment Plant Operations Boca Raton, FL: Lewis Publishers.)

FUNDAMENTAL CHEMISTRY AND HYDRAULICS 101

Some of the common ions found in water are:

Solutions serve as a vehicle to (1) allow chemical species to come into close proximity so thatthey can react; (2) provide a uniform matrix for solid materials, such as paints, inks, and othercoatings, so that they can be applied to surfaces; and (3) dissolve oil and grease so that they can

be rinsed away

Water dissolves polar substances better than nonpolar substances Polar substances (mineralacids, bases and salts) are easily dissolved in water Nonpolar substances (oils and fats and manyorganic compounds) do not dissolve easily in water

Specifying the relative amounts of solvent and solute, or specifying the amount of one ponent relative to the whole, usually gives the exact concentrations of solutions Solution concen-trations are sometimes specified as weight percentages

Ca ++

Calcium ion (cation) +

CO3–2 Carbonate ion (anion) NaCl ↔

Sodium chloride

Na + Sodium ion (cation) +

Cl – Chloride ion (anion)

102 ENVIRONMENTAL ENGINEER’S MATHEMATICS HANDBOOK

If 1 mol of C atoms equals 12 g, how much is the mass of 1 mol of H atoms?

Key point: 1 mol of H equals 1 g.

By the same principle:

• 1 mol of Cl – = 35.5 g

In other words, we can calculate the mass of a mole if we know the formula of the “item.”

Molarity (M) is defined as the number of moles of solute per liter of solution The volumeof

a solution is easier to measure in the lab than its mass.

(5.4)

Molality (m) is defined as the number of moles of solute per kilogramof solvent

(5.5)

Key point: Molality is not as frequently used as molarity, except in theoretical calculations.

Especially for acids and bases, the normality (N) rather than the molarityof a solution is often

reported — the number of equivalents of solute per liter of solution (1 equivalent of a substance

reacts with 1 equivalent of another substance)

(5.6)

In acid/base terms, an equivalent (or gram equivalent weight) is the amount that will react with

1 mol of H+ or OH– For example,

1 mol of HCl will generate 1 mol of H +

Therefore, 1 mol HCl = 1 equivalent

1 mol of Mg(OH)2 will generate 2 mol of OH –

Therefore, 1 mol of Mg(OH)2 = 2 equivalents

By the same principle:

-Chemists titrate acid/base solutions to determine their normality An endpoint indicator is used toidentify the point at which the titrated solution is neutralized.

Key point: If 100 mL of 1 N HCl neutralizes 100 mL of NaOH, then the NaOH solution must also

Liquid–Solid Solubility

Solids always have limited solubilities in liquids because of the difference in magnitude of their

intermolecular forces Therefore, the closer the temperature comes to the melting point of aparticular solid, the better the match is between a solid and a liquid

Key point: At a given temperature, lower melting solids are more soluble than higher melting

solids Structure is also important; for example, nonpolar solids are more soluble in nonpolar solvents.

Liquid–Gas Solubility

As with solids, the more similar the intermolecular forces, the higher the solubility Therefore, thecloser the match is between the temperature of the solvent and the boiling point of the gas, the

higher the solubility is When water is the solvent, an additional hydration factor promotes solubility

of charged species Other factors that can significantly affect solubility are temperature and pressure

In general, raising the temperature typically increases the solubility of solids in liquids

Key point: Dissolving a solid in a liquid is usually an endothermic process (i.e., heat is absorbed),

so raising the temperature “fuels” this process In contrast, dissolving a gas in a liquid is usually

an exothermic process (it emits heat) Therefore lowering the temperature generally increases the

solubility of gases in liquids

Interesting point: “Thermal” pollution is a problem because of the decreased solubility of O2 in water at higher temperatures.

Pressure has an appreciable effect only on the solubility of gases in liquids For example,carbonated beverages like soda water are typically bottled at significantly higher atmospheres.When the beverage is opened, the decrease in the pressure above the liquid causes the gas to bubbleout of solution When shaving cream is used, dissolved gas comes out of solution, bringing theliquid with it as foam

Some properties of a solution depend on the concentrations of the solute species rather than theiridentity:

• Lowering vapor pressure

True colligative properties are directly proportional to the concentration of the solute but entirelyindependent of its identity

Lowering Vapor Pressure

With all other conditions identical, the vapor pressure of water above the pure liquid is higher than

that above sugar water The vapor pressure above a 0.2-m sugar solution is the same as that above

a 0.2-m urea solution The lowering of vapor pressure above a 0.4-m sugar solution is twice as great as that above a 0.2-m sugar solution Solutes lower vapor pressure because they lower the concentration of solvent molecules To remain in equilibrium, the solvent vapor concentration must

decrease (thus the vapor pressure decreases)

Raising the Boiling Point

A solution containing a nonvolatile solute boils at a higher temperature than the pure solvent Theincrease in boiling point is directly proportional to the increase in solute concentration in dilutesolutions This phenomenon is explained by the lowering of vapor pressure already described

Decreasing the Freezing Point

At low solute concentrations, solutions generally freeze or melt at lower temperatures than the puresolvent

Key point: The presence of dissolved “foreign bodies” tends to interfere with freezing, so solutions

can only be frozen at temperatures below that of the pure solvent.

Key point: We add antifreeze to the water in a radiator to lower its freezing point and increase its

boiling point.

Osmotic Pressure

Water moves spontaneously from an area of high vapor pressure to an area of low vapor pressure

If allowed to continue, in the end all of the water would move to the solution A similar processoccurs when pure water is separated from a concentrated solution by a semipermeable membrane(one that only allows the passage of water molecules) The osmotic pressure is the pressure justadequate to prevent osmosis In dilute solutions, the osmotic pressure is directly proportional tothe solute concentration and is independent of its identity The properties of electrolyte solutions

follow the same trends as nonelectrolyte solutions, but are also dependent on the nature of the electrolyte as well as its concentration.

NaCl Na2SO4 CaCl2 MgSO4

A solution is a homogenous mixture of two or more substances (seawater, for example) A

suspen-sion is a brief comingling of solvent and undissolved particles (sand and water, for example) A colloidal suspension is a comingling of particles not visible to the naked eye but larger than

individual molecules

Key point: Colloidal particles do not settle out by gravity alone.

Colloidal suspensions can consist of:

water

• Hydrophobic suspensions, which gain stability from their repulsive electrical charges

Colloids are usually classified according to the original states of their constituent parts (see Table5.3) The stability of colloids can be primarily attributed to hydration and surface charge, whichhelp to prevent contact and subsequent coagulation

Key point: In many cases, water-based emulsions have been used to replace organic solvents (in

paints and inks, for example), even though the compounds are not readily soluble in water.

In wastewater treatment, the elimination of colloidal species and emulsions is achieved by

various means, including:

Natural water can contain a number of substances — what we call impurities or constituents When

a particular constituent can affect the good health of the water user, it is called a contaminant or

pollutant These contaminants are the elements that the environmental practitioner works to prevent

from entering or to remove from the water supply

Solids

Other than gases, all water’s contaminants contribute to the solids content Natural waters carry alot of dissolved solids as well as solids that are not dissolved The undissolved solids are nonpolarsubstances and relatively large particles of materials — for example, silt, which will not dissolve.Classified by their size and state, by their chemical characteristics, and by their size distribution,solids can be dispersed in water in suspended and dissolved forms

Table 5.3 Types of Colloids Name Dispersing medium Dispersed phase

Source: Adapted from Types of Colloids Accessed @ http://

www.ch.bris.ac.uk/webprojects2002/pdavies/types.html, December 18, 2002.

Size classifications for solids in water include:

Key point: Although not technically accurate from a chemical point of view because some finely

suspended material can actually pass through the filter, suspended solids are defined as those that can be filtered out in the suspended solids laboratory test Material that passes through the filter

is defined as dissolved solids Colloidal solids are extremely fine suspended solids (particles) of less than 1 µm in diameter; they are so small they will not settle even if allowed to sit quietly for days or weeks, although they may make water cloudy.

Turbidity

One of the first characteristics people notice about water is its clarity Turbidity is a condition in watercaused by the presence of suspended matter, resulting in the scattering and absorption of light rays Inplain English, turbidity is a measure of the light-transmitting properties of water Natural water that isvery clear (low turbidity) allows one to see images at considerable depths High-turbidity water appearscloudy Even water with low turbidity, however, can still contain dissolved solids because they do notcause light to be scattered or absorbed; thus, the water looks clear High turbidity causes problems forthe waterworks operator because the components that cause high turbidity can cause taste and odorproblems and will reduce the effectiveness of disinfection

Color

Water can be colored, but often the color of water can be deceiving For example, color is considered

an aesthetic quality of water, one with no direct health impact Many of the colors associated withwater are not “true” colors but the result of colloidal suspension (apparent color) This apparentcolor can be attributed to dissolved tannin extracted from decaying plant material True color isthe result of dissolved chemicals, usually organics that cannot be seen

Dissolved Oxygen (DO)

Gases, including oxygen, carbon dioxide, hydrogen sulfide, and nitrogen, can be dissolved in water.Gases dissolved in water are important For example, carbon dioxide plays an important role in

pH and alkalinity Carbon dioxide is released into the water by microorganisms and consumed byaquatic plants Dissolved oxygen (DO) in water is most important to waterworks operators as anindicator of water quality We stated earlier that solutions could become saturated with solute Watercan become saturated with oxygen The amount of oxygen that can be dissolved at saturationdepends upon the temperature of the water However, in the case of oxygen, the effect is just theopposite of other solutes The higher the temperature is, the lower the saturation level; the lowerthe temperature is, the higher the saturation level

Metals

Metals are common constituents or impurities often carried by water At normal levels, most metalsare not harmful; however, a few metals can cause taste and odor problems in drinking water Some

metals may be toxic to humans, animals, and microorganisms Most metals enter water as part ofcompounds that ionize to release the metal as positive ions Table 5.4 lists some metals commonlyfound in water and their potential health hazards.

Acids

An acid is a substance that produces hydrogen ions (H+) when dissolved in water Hydrogen ionsare hydrogen atoms that have been stripped of their electrons A single hydrogen ion is nothingmore than the nucleus of a hydrogen atom Lemon juice, vinegar, and sour milk are acidic orcontain acid The common acids used in treating water are hydrochloric acid (HCl); sulfuric acid(H2SO4); nitric acid (HNO3); and carbonic acid (H2CO3) Note that in each of these acids, hydrogen(H) is one of the elements The relative strengths of acids in water, listed in descending order ofstrength, are classified in Table 5.5

Table 5.4 Common Metals Found in Water Metal Health hazard

Barium Circulatory system effects and increased blood pressure Cadmium Concentration in the liver, kidneys, pancreas, and thyroid Copper Nervous system damage and kidney effects; toxic to humans Lead Nervous system damage and kidney effects; toxic to humans Mercury Central nervous system disorders

Nickel Central nervous system disorders Selenium Central nervous system disorders Silver Turns skin gray

Zinc Causes taste problems, but not a health hazard

Source: Spellman, F.R., 2003, Handbook of Water and Wastewater ment Plant Operations Boca Raton, FL: Lewis Publishers.

A base is a substance that produces hydroxide ions (OH–) when dissolved in water Lye or commonsoap (bitter things) contains bases Bases used in waterworks operations are calcium hydroxide(Ca(OH)2), sodium hydroxide (NaOH), and potassium hydroxide (KOH) Note that the hydroxylgroup (OH) is found in all bases Certain bases also contain metallic substances, such as sodium(Na), calcium (Ca), magnesium (Mg), and potassium (K) These bases contain the elements thatproduce alkalinity in water

Salts

When acids and bases chemically interact, they neutralize each other The compound other than

water that forms from the neutralization of acids and bases is called a salt Salts constitute, by far,

the largest groups of inorganic compounds A common salt used in waterworks operations, coppersulfate, is used to kill algae in water

pH

pH is a measure of the hydrogen ion (H+) concentration Solutions range from very acidic (having

a high concentration of H+ ions) to very basic (having a high concentration of OH– ions) The pHscale ranges from 0 to 14 with 7 as the neutral value (see Figure 5.3)

Table 5.5 Relative Strengths of Acids in Water Acid Chemical symbol

Raton, FL: Lewis Publishers.

Figure 5.3 pH of selected liquids (From Spellman, F.R., 2003, Handbook of Water and Wastewater Treatment

Plant Operations Boca Raton, FL: Lewis Publishers.)

1 M Hcl gastricjuices tomatoes

pure water

water

household ammonia

The pH of water is important to the chemical reactions that take place within water, and pHvalues that are too high or low can inhibit the growth of microorganisms High pH values areconsidered basic and low pH values are considered acidic Stated another way, low pH valuesindicate a high level of H+ concentration, while high pH values indicate a low H+ concentration.Because of this inverse logarithmic relationship, H+ concentrations have a 10-fold difference The

pH is the logarithm of the reciprocal of the molar concentration of the hydrogen ion In mathematicalform, it is:

(5.7)

Natural water varies in pH depending on its source Pure water has a neutral pH, with an equalnumber of H+ and OH– Adding an acid to water causes additional “+” ions to be released so thatthe H+ ion concentration goes up and the pH value goes down:

HCl → H+ + Cl–

Changing the hydrogen ion activity in solution can shift the chemical equilibrium of water.Thus, pH adjustment is used to optimize coagulation, softening, and disinfection reactions, and forcorrosion control To control water coagulation and corrosion, the waterworks operator must testfor hydrogen ion concentration of the water to get pH In coagulation tests, as more alum (acid)

is added, the pH value is lowered If more lime (alkali — base) is added, the pH value is raised.This relationship is important; if good floc is formed, the pH should then be determined andmaintained at that pH value until a change occurs in the new water

= −3 log 1 3

pH=3 0 11– =2 89

Alkalinity is defined as the capacity of water to accept protons (positively charged particles); it canalso be defined as a measure of water’s ability to neutralize an acid Alkalinity is a measure ofwater’s capacity to absorb hydrogen ions without significant pH change (to neutralize acids).Bicarbonates, carbonates, and hydrogen cause alkalinity compounds in a raw or treated watersupply Bicarbonates are the major components because of carbon dioxide action on “basic”materials of soil; borates, silicates, and phosphates may be minor components Alkalinity of rawwater may also contain salts formed from organic acids — humic acid, for example Alkalinity inwater acts as a buffer that tends to stabilize and prevent fluctuations in pH Significant alkalinity

in water is usually beneficial because it tends to prevent quick changes in pH, which interfere withthe effectiveness of common water treatment processes Low alkalinity also contributes to thecorrosive tendencies of water When alkalinity is below 80 mg/L, it is considered low

Hardness

Hardness may be considered a physical or chemical parameter of water It represents the totalconcentration of calcium and magnesium ions, reported as calcium carbonate Hardness causessoaps and detergents to be less effective and contributes to scale formation in pipes and boilers,but is not considered a health hazard However, lime precipitation or ion exchange often softenswater that contains hardness Low hardness contributes to the corrosive tendencies of water.Hardness and alkalinity often occur together because some compounds can contribute alkalinity aswell as hardness ions Hardness is generally classified as shown in Table 5.6

The molecular weight of Na2CO3 is 106.

Molarity is number of moles per volume in liters.

Number of moles is actual weight/molecular weight.

The net positive valence of Na2CO3 is 1 × 2 = 2.

The equivalent weight of Na2CO3 is 106/2 = 53.

Table 5.6 Water Hardness Classification mg/L CaCo 3

Boca Raton, FL: Lewis Publishers.

×

Actual weightmolecular weight Volume in lliters

5.2.2.8 Simple Solutions and Dilutions

A simple dilution is one in which a unit volume of a liquid material of interest is combined with

an appropriate volume of a solvent liquid to achieve the desired concentration The dilution factor

is the total number of unit volumes in which a material will be dissolved The diluted materialmust then be thoroughly mixed to achieve the true dilution For example, a 1:5 dilution (verbalize

as “1 to 5” dilution) entails combining 1 unit volume of diluent (the material to be diluted) + 4unit volumes of the solvent medium (thus, 1 + 4 = 5 = dilution factor) The fact that the number

of moles or equivalents of solute does not change during dilution enables us to calculate the newconcentration

Simple Dilution Method

We demonstrate the simple dilution or dilution factor method in the following Suppose we haveorange juice concentration that is usually diluted with four additional cans of cold water (the dilutionsolvent), thus giving a dilution factor of 5 — the orange concentrate represents one unit volume

to which four more cans (same unit volumes) of water have been added Thus, the orange concentrate

is now distributed through five unit volumes This would be called a 1:5 dilution, and the orangejuice is now 1/5 as concentrated at it was originally Therefore, in a simple dilution, add one lessunit volume of solvent than the desired dilution factor value

Serial Dilution

A serial dilution is simply a series of simple dilutions that amplify the dilution factor quickly,

beginning with a small initial quantity of material (bacterial culture, a chemical, orange juice, and

so forth) The source of dilution material for each step comes from the diluted material of the

previous step In a serial dilution, the total dilution factor at any point is the product of the individual

dilution factor in each step up to that point

(5.8)

To demonstrate the final dilution factor calculation, a typical lab experiment involves a step 1:100 serial dilution of a bacterial culture The initial step combines 1 unit volume culture (10µL) with 99 unit volumes of broth (990 µL) to equal a 1:100 dilution In the next step, 1 unitvolume of the 1:100 dilution is combined with 99 unit volumes of broth, now yielding a totaldilution of 1:100 × 100 = 1:10,000 dilution Repeated again (the third step), the total dilution would

three-be 1:100 × 10,000 = 1:1,000,000 total dilution The concentration of bacteria is now 1 milliontimes less than in the original sample

When we are diluting solutions, the product of the concentration and volume of the initial solutionmust be equal to the product of the concentration and volume of the diluted solution when thesame system of units is used in both solutions Expressed as a relationship, this would be:

(5.9)

where

C i = concentration of initial solution

V i = volume of initial solution

Final Dilution Factor (DF) = (DF )(DF )(DF1 2 3)) etc

C Vi i = C Vf f

C f = concentration of final solution

V f = volume of final solution

Sometimes using molarity may be more efficient for calculating concentrations A 1.0-M solution

is equivalent to 1 formula weight (FW) (gram/mole) of chemical dissolved in 1.0 L of solvent(usually water) Formula weight is always given on the label of a chemical bottle (use molecularweight if it is not given)

Example 5.12

Problem:

Given the following data, determine how many grams of reagent to use Chemical FW = 195

g/mol; to make 0.15 M solution.

Solution:

Example 5.13

Problem:

A chemical has a FW 190 g/mol and we need 25 mL (0.025 L) of 0.15 M (M = mol/L) solution.

How many grams of the chemical must be dissolved in 25 mL of water to make this solution?

Ci×Vi = Cf×Vf

1.3 × 60 = 0.5 × X

X=1.3 × 60=0.5 156 ml

156 60− = 96 ml of water

(195 g/mol)(0.15 mol/L) = 29.25 g/L

of milliliters per 100 milliliters For example, if we want to make 70% ethanol, we mix 70 mL of100% ethanol with 30 mL water (or the equivalent for whatever volume we need).

To convert from percent solution to molarity, multiply the percent solution value by 10 to getgrams per liter, then divide by the formula weight

Number grams/desired volume (L) = desired moolarity (mol/L) × FW (g/mol)

Number grams = desired volume (L) × desiredmolarity (mol/L) × FW (g/mol)Number grams = (0.025 L)(0.15 mol/L) (190 g//mol) = 0.7125 g/25 mL

of “shells.”

In general, only the “outer shell” or “valence” electrons (the ones farthest from the nucleus)

are affected during chemical change The valence number or valence of an element indicates the

number of electrons involved in forming a compound — that is, the number of electrons it tends

to gain or lose when combining with other elements

Key point: Positive valence indicates giving up electrons Negative valence indicates accepting

atoms instead of only one, so that it is considered to act as a bond between them If an atom gains

or loses one or more valence electrons, it becomes an ion (charged particle).

• Cations are positively charged particles.

• Anions are negatively charged particles.

Physical and Chemical Changes

In physical and chemical changes, recall that a chemical change is the change physical substancesundergo when they become new or different substances To identify a chemical change, look forobservable signs, including color change; light production; smoke; bubbling or fizzing; and presence

of heat

A physical change occurs when objects undergo a change that does not change their chemicalnature This type of change involves a change in physical properties Physical properties can beobserved without changing the type of matter Examples of physical properties include texture;size; shape; color; odor; mass; volume; density; and weight

Heat and Chemical/Physical Reactions

An endothermic reaction is a chemical reaction that absorbs energy, where the energy content of the products is more than that of the reactants; heat is taken in by the system An exothermic

reaction is a chemical reaction that gives out energy, where the energy content of the products is

less than that of the reactants; heat is given out from the system