Chapter 20 I ACIDS AND BASES - Physci.us

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Chapter 20 I ACIDS AND BASESSection 20.1DESCRIBINGACIDS AND BASESSection 20.2HYDROGEN IONSAND ACIDITYThese tart-tasting fruits contain a weak acid called citric acid.FEATURESDISCOVER IT!Effect of Foods on Baking SodaSMALL-SCALE LABIonization Constants of Weak AcidsMINI LABIndicators from Natural SourcesCHEMathUsing LogarithmsCHEMISTRY SERVING.THE ENVIRONMENTRain Like VinegarCHEMISTRY IN CAREERSStone ConservatorLINK TO LIBRARY SCIENCEChemistry Rescues Crumbling BooksLINK TO HEALTHTooth DecayStay current with SCIENCE N W 6Find out more about acids and mtmt 576Chapter 20IDISCOVER IT!EFFECT OE FOODS ONBAKING SODAYou need baking soda (sodium hydrogen carbonate, NaHC03), alarge paper plate, a knife, paper towels, and a variety of fruits andvegetables (e.g., a celery stalk, a banana, a grape, a tomato, a lemon,an apple, an orange, a grapefruit).1. Carefully cut the fruits and vegetables into small pieces and placethem on the plate. Make sure the pieces are well separated fromeach other. Be sure to wipe any juice off the knife after cuttingeach fruit.2. Sprinkle a pinch of baking soda on each sample.What do you observe? Is there any relationship between whatyou observe and which foods you know from experiencehave a sour taste? After reading about acids and bases, provide anexplanation for what you observed.

DESCRIBING ACIDS AND BASESdome ants can give painful stings when threatened ordisturbed. Certain ant species called formicines havepoison glands that produce venom containing formic acid.Formicines protect themselves by spraying this venom ontheir predators. Formic acid can stun or even kill the ants' most common enemies.A formicine attack on a human, however, is much less severe, usually resulting onlysection 20.1objectives* List the properties of acids andbases Name an acid or base whengiven the formulakey terms acid basein blistered skin. What are some of the properties of acids?Properties of Acids and BasesDid you know that acids and bases play a central role in much of the chemistry that affects your daily life? Most manufacturing processes use acids orbases. Your body needs acids and bases to function properly. Vinegar, carbonated drinks, and foods such as citrus fruits contain acids. Theelectrolyte in a car battery is an acid. Bases are present in many commercial products, including antacid tablets and household cleaning agents.Figure 20.1 shows some of the many products that contain acids andbases. As you read this chapter, you will learn about the qualitative andquantitative aspects of acids and bases. You will see how these two classesof compounds ionize or dissociate in water. And you will learn how pH isused to describe the concentrations of acidic and basic solutions.As you just read and perhaps already knew, many common items contain acids. Acids have several distinctive properties with which you areprobably familiar. Acidic compounds give foods a tart or sour taste. Forexample, vinegar contains ethanoic acid, sometimes called acetic acid.Lemons, which taste sour enough to make your mouth pucker, contain citric acid. What type of acid do you think limes contain?Aqueous solutions of acids are electrolytes. Recall from Chapter 17 thatelectrolytes conduct electricity. Some acid solutions are strong electrolytesand others are weak electrolytes. Acids cause certain chemical dyes, calledindicators, to change color. Many metals, such as zinc and magnesium,react with aqueous solutions of acids to produce hydrogen gas. Acids reactwith compounds containing hydroxide ions to form water and a salt.Figure 20.1All of these items contain acidsor bases, or produce acids orbases upon dissolving in water.Tomatoes contain ascorbic acid;tea contains tannic acid. The basecalcium hydroxide is a componentof mortar, which was used tobuild the Great Wall of China.Antacids use a variety of bases toneutralize excess stomach acid.Acids and Bases577

section 20.1Bases are compounds that react with acids to form water and a salt.Milk of magnesia (a suspension of magnesium hydroxide in water) is a baseused to treat the problem of excess stomach acid. Aqueous solutions ofbases taste bitter and feel slippery. Like acids, bases will change the colorof an acid-base indicator and can be strong or weak electrolytes.Names and Formulas of Acids and BasesAn acid is a compound that produces hydrogen ions when dissolved inwater. Therefore, the chemical formulas of acids are of the general formHX, where X is a monatomic or polyatomic anion. When the compoundHCl(g) (hydrogen chloride) dissolves in water to form HCl{aq), it is namedas an acid. How, then, is an acid named? To illustrate the naming of anacid, consider the following three rules as applied to the acid HX dissolvedin water. Notice that the rules focus on the name of the anion, in particularthe suffix of the anion name. Table 20.1 summarizes these rules.Figure 20.2(a) Carbonated soft drinks containcarbonic acid (H2C03), and manyalso contain phosphoric acid(H3PO4). These two acids givea drink its fizz and sharp, tangytaste, (b) Sodium hydroxide(NaOH) is used to prepare woodpulp for the manufacture of paper.1. When the name of the anion (X) ends in -ide, the acid name beginswith the prefix hydro-. The stem of the anion has the suffix - ic and isfollowed by the word acid. Therefore, HCl(ag) (X chloride) is namedhydrochloric acid. H2S{aq) (X sulfide) is named hydrosulfmic acid.2. When the anion name ends in -ite, the acid name is the stem of theanion with the suffix -ous, followed by the word acid. Thus H2S03(a 7)(X sulfite) is named sulfurows acid.3. When the anion name ends in -ate, the acid name is the stem ofthe anion with the suffix -ic, followed by the word acid. ThusHN0 3 (ag) (X nitrate) is named nitric acid.These rules can be used in reverse fashion to write the formulas of acidswhen given their names. For example, what is the formula of chloric acid?According to Rule 3, chloric acid {-ic ending) must be a combination ofhydrogen ion (H ) and chlorate ion (C103 ). The formula of chloric acid isHCIO3. What is the formula of hydrobromic acid? Following Rule 1, hydrobromic acid {hydro- prefix and -ic suffix) must be a combination ofhydrogen ion and bromide ion (Br"). The formula of hydrobromic acid isHBr. What is the formula for phosphorous acid? Using Rule 2, hydrogen ionand phosphite ion (P0 3 3 ) must be the components of phosphorous acid.The formula of phosphorous acid is H 3 P0 3 . {Note: Do not confuse phosphorous with phosphorus, the element name.)Table 20.1Naming AcidsAnionending-ide-ite-ate578Chapter 20ExamplecrchlorWeS032sulf/feNO3nitrateAcid nameExamplehydro-{stem)-ic acidhydrochloric acid(stem) -ous acidsulfuroi/s acid(stem)-/c acidnitr/c acid

section 20.1A base is a compound that produces hydroxide ions when dissolved inwater. Ionic compounds that are bases are named in the same way as anyother ionic compound—the name of the cation followed by the name ofthe anion. For example, NaOH, a base used in making paper pulp, detergents, and soap, is called sodium hydroxide. What would you call Ca(OH)2 ?You write the formulas for bases by balancing the ionic charges, just as youdo for any ionic compound.Sample Problem 20-iName these compounds as acids.a. HCIOb. HCNc. H 3 P0 41. ANALYZE Plan a problem-solving strategy.The rules for naming acids can be applied because the formulas of the acids are given.2. SOL VE Apply the problem-solving strategy.a. Use Rule 2. The anion name (hypochlorite) ends in -ite,so add the suffix -ous to the anion stem, followed by theword acid. The correct name is hypochlorous acid.b. Use Rule 1. The anion name (cyanide) ends in -ide, sothis acid name begins with the prefix hydro- and endswith the suffix -ic, followed by the word acid. The correct name is hydrocyanic acid.c. Use Rule 3. The anion name (phosphate) ends in -ate.So add the suffix -ic to the anion stem (in this case,modified slightly to phosphor), followed by the wordacid. The correct name is phosphoric acid.3. EVALUATE Do the results make sense?Practice Problems1. Name each acid or base.a. HFc. KOHb. HN0 3d. H2S042. Write formulas for each acidor base.a. chromic acidb. iron(II) hydroxidec. hydriodic acidd. lithium hydroxideOwn ASAP!Problem-Solving 20Solve Problem 2 with the helpmLmkof an interactive guided tutorial.The names are consistent with the indicated rules.section review 20.13. Identify each property as applying to an acid, a base, or both.a. bitter tastec. indicator color changeb. electrolyted. sour taste4. Write the formula for each acid or base.a. barium hydroxidec. rubidium hydroxideb. hydrobromic acidd. hydroselenic acid5. Name each acid or base.a. HFc. H 2 C0 3b. HCIO3d. Al(OH)3(hem ASAP! Assessment 20.1 Checkyour understanding of the importantideas and concepts in Section 20.1.Acids and Bases579

section 20.2objectives Given the hydrogen-ion orhydroxide-ion concentration,classify a solution as neutral,acidic, or basic Convert hydrogen-ion concentrations into values of pH andhydroxide-ion concentrationsinto values of pOHkey terms hydroxide ion (OH") hydronium ion (H30 ) self-ionization neutral solution ion-product constantfor water (/Cw) acidic solution basic solution alkaline solutions pHFigure 20.3What is the name and formula ofthe particle that results when awater molecule gains a hydrogenion? How is a hydroxide ionformed from a water molecule?A. patient is brought to a hospital unconscious and with afruity odor on his breath. The doctor suspects the patient hasfallen into a diabetic coma. To confirm her diagnosis, sheorders several tests, including one of the acidity of thepatient's blood. The results from this test will be expressed in units ofpH, not molarconcentration. How is the pH scale used to indicate the acidity of a solution, andwhy is this scale used?Hydrogen Ions from WaterAs you already know, water molecules are highly polar and are in continuous motion, even at room temperature. Occasionally, the collisionsbetween water molecules are energetic enough to transfer a hydrogen ionfrom one water molecule to another. See Figure 20.3. A water molecule thatloses a hydrogen ion becomes a negatively charged hydroxide ion (OH ).A water molecule that gains a hydrogen ion becomes a positively chargedhydronium ion (H 3 0 ).9H:0: H:Q:j(H) H:0:HH H20 H30 HydroxideionThe reaction in which two water molecules produce ions is called theself-ionization of water. This reaction can also be written as a simpledissociation.H20(Z)* H (oq)Hydrogen ion-OH'ioq)Hydroxide ionIn water or aqueous solution, hydrogen ions (H ) are always joined towater molecules as hydronium ions (H 3 0 ). The hydronium ions are themselves solvated to form species such as H 9 0 4 . Hydrogen ions in aqueoussolution have several names. Some chemists call them protons. Others prefer to call them hydrogen ions, hydronium ions, or solvated protons. In thistextbook, either H or H 3 0 is used to represent hydrogen ions in aqueoussolution.The self-ionization of water occurs to a very small extent. In pure waterat 25 C, the concentration of hydrogen ions ([H ]) and the concentrationof hydroxide ions ([OH - ]) are each only 1.0 x 10"7M. This means that theconcentrations of H and O H - are equal in pure water. Any aqueous solution in which [H ] and [OH - ] are equal is described as a neutral solution.580Chapter 20

section 20.2In any aqueous solution, [H ] and [OH - ] are interdependent. In otherwords, when [H ] increases, [OH - ] decreases. When [H ] decreases, [OH ]increases. Le Chatelier's principle, which you learned about in Chapter 19,applies here. If additional ions (either hydrogen ions or hydroxide ions) areadded to a solution, the equilibrium shifts. The concentration of the othertype of ion decreases. More water molecules are formed in the process.U (aq) OH"H20(Z)For aqueous solutions, the product of the hydrogen-ion concentrationand the hydroxide-ion concentration equals 1.0 x 10 14.[H ] X [OH - ] 1.0 x 10"14The product of the concentrations of the hydrogen ions and hydroxide ionsin water is called the ion-product constant for water (Xw).*fw [H ] x [OH - ] 1.0 x 10- 14Not all solutions are neutral. When some substances dissolve in water,they release hydrogen ions. For example, when hydrogen chloride dissolves in water, it forms hydrochloric acid. How does hydrochloric aciddiffer from hydrogen chloride?HCl(g) -2&* H (aq) Cl (aq)Figure 20.4(a) One of these two chemicalreagents is an acid and the otheris a base. Which of these reagentswould increase the hydrogen-ionconcentration when added to anaqueous solution ? Which wouldincrease the hydroxide-ionconcentration ? (b) Unrefinedhydrochloric acid, commonlyknown as muriatic acid, is usedto clean stone buildings andswimming pools, (c) Sodiumhydroxide, or lye, is commonlyIn such a solution, the hydrogen-ion concentration is greater than thehydroxide-ion concentration. The hydroxide ions are present from the selfionization of water. An acidic solution is one in which [H ] is greater than[OH - ]. Therefore, the [H ] of an acidic solution is greater than 1.0 X 10 7M.When sodium hydroxide dissolves in water, it forms hydroxide ions insolution.NaOH(s) - - Na {aq) OK (aq)In such a solution, the hydrogen-ion concentration is less than thehydroxide-ion concentration. The hydrogen ions are present from theself-ionization of water. A basic solution is one in which [H ] is less than[OH - ]. Therefore, the [H ] of a basic solution is less than 1.0 X 10"7M.Basic solutions are also known as alkaline solutions. Look at Figure 20.4.What are the names of the acids and bases shown?[ ACID 1 [C0NCused as a drain cleaner.Ijnmiuw fejKtH0i y ITOBOXIR(a)(b)(c)Acids and Bases581

section 20.2fSample Problem 20-2If the [H ] in a solution is 1.0 x 10 5M, is the solution acidic,basic, or neutral? What is the [OH - ] of this solution?1. ANAL YZE List the knowns and theKnowns: [H ] l.o x 10" 5 M Ion-product constant for water:Kw [H ] X [OH - ] 1 X 10 - 1 4unknowns.Unknowns: solution acidic, basic, or neutral? [OH - ] ?M2. CALCULATE Solve for the unknowns.[H ] 1.0 X 10"5M. Because this is greater than 1.0 X 10"7M,the solution is acidic. By definition, Kw [H ] X [OH - ].Therefore, [OH"] -§?-.I H JSubstituting the known numerical values, [OH - ] is computedas follows.[OH"]Practice Problems6. If the hydroxide-ion concentration of an aqueous solution is1.0 X 10"3M, what is the [H ]in the solution? Is the solutionacidic, basic, or neutral?7. Classify each solution as acidic,basic, or neutral.a. [H ] 6.0 x 10 -10 Mb. [OH - ] 3.0 x 10 - 2 Mc. [H ] 2.0 x 10" 7 Md. [OH - ] 1.0 X 10" 7 M1.0 x 1Q14 1.0 X 10" a M1.0 X 10'5MEVALUA TE Do the results make sense?If [H ] is greater than 1.0 x 10 7M, then [OH - ] must be lessthan 1.0 X 10 -7 M. At 1 X 10"9M, [OH - ] is less than 1 X 10"7M.Notice that when the concentration of the acid is 1.0 X 10 x andthe concentration of the base is 1.0 X 10 y , x y 14. In thisspecial case, you can easily find the value of [H ] when youknow [OH - ], or vice versa. To do so, subtract the exponent of theknown, either [H ] or [OH ], from 14. For example, if[H ] 1.0 X 10"9M,then [OH - ] 1.0 X 10 -(14-9) M 1.0 X 10 5M. EThe pH ConceptExpressing hydrogen-ion concentration in molarity is cumbersome.A more widely used system for expressing [H ] is the pH scale, proposed in1909 by the Danish scientist Soren Sorensen (1868-1939). On the pH scale,which ranges from 0 to 14, neutral solutions have a pH of 7. A pH of 0 isstrongly acidic. What is a solution with a pH of 14? Calculating the pH of asolution is straightforward. The pH of a solution is the negative logarithmof the hydrogen-ion concentration. The pH m a y b e represented mathematically using the following equation.pH - l o g [H ]582Chapter 20

section 20.2In a neutral solution, [H ] 1 X 10 7M. The pH of a neutral solution is 7.0.pH - l o g (1 X 10 7) - ( l o g l loglO" 7 ) -(0.0 (-7.0)) 7.0To summarize, the pH of pure water or a neutral aqueous solution is7.0. A solution in which [H ] is greater than 1 x 10" 7 Mhas a pH less than7.0 and is acidic. A solution with a pH greater than 7 is basic and has a [H ]of less than 1 X 10 7 M. See Figure 20.5 for a visual representation of thisinformation.Fiqur? Z0.5Greater than1 x 10"7MH30 In acidic solutions, [H ] is greaterthan [0H ]. In basic solutions,[0H ] is greater than [H ]. Neutral solutions are those in which[H ] is equal to [0H ].OH"IH30 70H-.1 x 1(T /WooH30 0H-Less than1 x 1(T7MAcidic SolutionNeutral SolutionBasic Solution Acidic solution:pH 7.0[H ] greater than 1 X 10 7M Neutral solution:pH 7.0[H ] equals 1 X 10 7M Basic solution:pH 7.0[H ] less than 1 x 10 7MThe pH values of several common aqueous solutions are listed inTable 20.2 on the following page. The table also summarizes the relationship among [H ], [OH ], and pH. You may notice that pH can sometimesbe read from the value of [H ]. If [H ] is written in scientific notation andhas a coefficient of 1, then the pH of the solution equals the exponent, withthe sign changed from minus to plus. For example, a solution with [H ] 1 X 10 2M has a pH of 2.0. What is the pH of a solution with [H ] 1 X 1Q-4M?Acids and Bases583

section 20.2Table ZO.ZRelationship among [ H ] , [ O H - ] , and pHA"oCOCC/3CDoNeutraloC«.QCOaso\'[H ] (mol/L)[OH"] (mol/L)1 x10 1 x 10 11 x 1(T21 x10" 31 x lir41 x 10 51 x 1(T61 x 1(T71 x 10 -81 x1(T 91 x 10"101 x1(T 111 x 10-121 x1(T 131 x10" 1 41 x 1(T141 x 1(T131 x 10"121 x10" 1 11 x10 101 x 10"91 x 10"8Aqueous systempH0.0 -— 1MHCI1 . 0 * — 0.1MHCI— Gastric juiceLemon juice2.0 Z —3.04.0 —Tomato juice5.0 * — Black coffee6.0 —7.0 *—71 x 1CT1 x 10"61 x 10"51 x 10"41 x 10-31 x 1(T21 x1(T 11x10 8.09.0 MilkPure water" -Blood" Sodium hydrogen carbonate,sea water10.0— Milk of magnesia11.0*—Household ammonia1 2 . 0 * —Washing soda1 3 . 0 * —0.1/WNaOH1 4 . 0 * — 1/WNaOHIn a definition similar to that of pH, the pOH of a solution equals thenegative logarithm of the hydroxide-ion concentration.pOH -log [OH-]A neutral solution has a pOH of 7. A solution with a pOH less than 7 is basic.A solution with a pOH greater than 7 is acidic. A simple relationship betweenpH and pOH makes it easy to find either one when the other is known.pH 4- pOH 14pH 14 - pOHpOH 14 - pHFor pH calculations, you should express the hydrogen-ion concentration in scientific notation. For example, a hydrogen-ion concentration of0.0010M, rewritten as 1.0 x 10 3M in scientific notation, has two significant figures. The pH of this solution is 3.00, with the two numbers to theright of the decimal point representing the two significant figures inthe concentration. A solution with a pH of 3.00 is acidic, as shown inFigure 20.6. How many significant figures are indicated in a pH of 7.61?PH7Figure Z0.6The pH scale shows the relationship between pH and thehydrogen-ion concentration.Notice that acids have lower pHsthan bases.JChapter 20910J11J121314IILIncreasing acidity 2 Increasing basicity10 10"or 15848l L10"2 10"3 10"4 10-5 10 6 10"7 10[H ]10"9 10-1010-11 10- 12 10- 13 10"

rUSING LOGARITHMSLogarithms are used throughout mathematics and science. Examples include the decibel scale for loudness,the Richter scale for earthquakes, and the pH scale foracidity. Because the pH scale is a logarithmic scale, itallows a tremendous range of values (from 1 to 10 14)to be expressed as a number between 1 and 14.To find the logarithm of a number that is less than1 or greater than 10, write the number in scientificnotation and use the formulas below. See Example 1.log (ax b) log a log b, and log (10*) xThe common logarithm of a number is the exponent to which ten must be raised to produce the givennumber: log x y if x 10y. Thus log 0.01 - 2because 0.01 10 2, and log 10 000 4 because10 000 104. The common logarithm is also known asthe base-10 logarithm. Logarithms can have otherbases, but this textbook only uses common logarithms.Logarithms of numbers between 1 and 10 can beevaluated directly using Table B.1 in Appendix B ofthis textbook. For example, log 7.21 0.8579, asshown 8525.8585.8645A logarithm is rounded so that its number of decimal places equals the number of significant figures inthe original number.The antilog of a number x is the number y whoselogarithm is x Because log y x means y 10* theantilog of x is the same as 10x. Antilogs of numbersbetween 0 and 1 can be found directly from Table B.1.To find the antilog of any number, write it as a sum ofits decimal part (between 0 and 1) and its integer part(less than or equal to the given number). Then use theformula 10 o 6 10 fl x 10fc. See Example 2.Many calculators can be used to find logarithmsand antilogs. In general, use IQG for a logarithm, or@ for an antilog. The exact keystrokes depend on yourcalculator. Do not confuse the IQG key with the LN key. The I -N I key gives another kind of logarithm,called the natural logarithm, whose base is the constant e 2.718.Example!Find the antilog of -8.375.Evaluate log 0.0000721.5Write -8.375 as a sum. Note that the decimal part is0.625, not-0.375 or 0.375.log 0.0000721 log (7.21 x 10 )5 log 7.21 log (10 )-8.375 (-8.375 9) (-9) 0.625 (-9) 0.8579 (-5) -4.1421The original number had 3 significant figures, so theresult should be rounded to 3 decimal places.In Table B.1, the number nearest to 0.625 is 0.6253,and its antilog is 4.22. So,antilog (-8.375) 10"8-375 io a625 - 9) log 0.000072110o.625x10-9-4.142 4.22x 10" 9Practice ProblemsPrepare for upcoming problems in this chapter by using Table B.1 in Appendi x B to evaluate the followingexpressions. Then checl your work using;i calculator.E. antilog 0.969G log 17 800H log 0.0067J. antilog 6.281K. antilog (--3.192)F. antilog (-5 0.782)1. log 0.0000738L. antilog (--5.936)A. log 1.68B. log (3.57 x 104)D. antilog - 8C. log (2.18 x 1 0 - 8 )Acids and Bases585

section 20.2Sample Problem 20-3What is the pH of a solution with a hydrogen-ion concentration of1.0 X 10"10M?1. ANAL YZE List the knowns and the unknown.Knowns:Unknown: U[H ] l.o x io MpH -log[H ]pH2. CALCULATE Solve for the unknown.pH - l o g [H ]Practice Problems -logd.O X 10 -10 )8. Find the pH of each solution.a. [H ] 1.0 X 10 4 Mb. [H ] 0.0010Mc. [H ] 1.0 X 10 9M9. What are the pH values ofthe following three solutions,based on their hydrogen-ionconcentrations?a. [FT] 1.0 X 10 12 Mb. [FT] 0.010MC. [H ] 1.0 X 10 4 M - ( l o g 1.0 l o g 10"10) - ( 0 . 0 0 (-10.00)) -(-10.00) 10.003. EVALUATE Does the result make sense?[H ] is three orders of magnitude (1000 times) less than1 X 10 7 M (pH 7). Each order-of-magnitude decrease in [H ]equals an increase of 1 pH unit, so the unknown solutionshould have a pH of 7 3 10. This problem can also besolved by inspection. The coefficient of [H ] is 1.0; therefore,the pH is the value of the exponent (-10) with the signchanged from minus to plus. However, the answer based onexperimental data must be reported as 10.00 to show the twosignificant figures of the original value of [H ].Chpm ASAP!.Problem-Solving 9Solve Problem 9 with the helpof an interactive guided tutorial. TJJSample Problem 20-4The pH of an unknown solution is 6.00. What is its hydrogen-ionconcentration?1. ANAL YZE List the knowns and the unknown.Knowns:Unknown: pH 6.00 pH -log[H ] [H ] ?M2. CALCULATE Solve for the unknown.First, rearrange the equation for the definition of pH to solve forthe unknown.- l o g [FT] P HNext, substitute the value of pH.- l o g [FT] 6.00586Chapter 201

section 20.2Sample Problem 20-4 cont.Change the signs on both sides of the equation.log [H ] -6.00Finally, determine the number that has a log of -6.00. Theantilog of -6.00 is 1.0 x 10 - 6 . Therefore,[H ] 1.0 X 10 6M.3. EVALUATE Does the result make sense?This problem can be solved by inspection. Any integral value ofpH, such as 3.00, 5.00, and so forth, can easily be converted to[H ]. The sign of the pH value is changed from plus to minusand is used as the exponent in the numerical expression of[H ]. A decimal point and zeros are attached to the coefficient(1) to obtain the proper number of significant figures. Forexample, for pH 4.00, [H ] 1.0 X 10 4M; for pH 11.00,[H ] 1.0 X 10 n M.Practice Problems10. Calculate [H ] for each solution.a. pH 5.00c. pH 6.00b. pH 7.00d. pH 3.0011. What are the hydrogen-ionconcentrations for solutionswith the following pH values?a. 4.00b. 11.00c. 8.00XCalculating pH ValuesMost pH values are not whole numbers. For example, Table 20.2 on page 584shows that milk of magnesia has a pH of 10.5. Using the definition of pH,this means that [H ] must equal 1 x 10 10'5M. Thus [H ] must be less than1 X 10" 10 M(pH 10.0), but greater than 1 X 1 0 u M ( p H 11.0).If [H ] is written in scientific notation but its coefficient is not 1, then youneed a table of common logarithms or a hand calculator with a log functionkey to calculate pH. A four-place table of common logarithms is provided inAppendix B. Sample Problem 20-5 shows how to make such a pH calculation.Sample Problem 20-5What is the pH of a solution if [OH - ] 4.0 X 10 11 M?1. ANAL YZE List the knowns and the unknown.Knowns:Unknown: [OH - ] 4.0 X 1 0 " n M pH ? Kw [OH - ] X [H ] 1 X 10 - 1 4 pH - l o g [H ]2. CALCULATE Solve for the unknown.To calculate pH, first calculate [H ] by using the definition of KwKw [OFT] X [H ][H ] w[OH - ]1.0 X 10"w4.0 X 10"UM 0.25 X 10 3 M 2.5 X 10 4 MAcids and Bases587

section 20.2Sample Problem 20-5 (cont.)With the value of [H ] determined, use the definition of pH tosolve for the pH.pH - l o g [ H ]Practice Problems12. Calculate the pH of eachsolution.a. [H ] 5.0 X 10 - 6 Mb. [H ] 8.3 X 10"10MG. [H ] 2.7 X 10" 7 M13. Calculate the pH of eachsolution.a. [OFT] 4.3 x 10" 5 Mb. [OFT] 2.0 X 10" 5 Mc. [OFT] 4.5 x 10 n M - l o g (2.5 X 10 4) -(Iog2.5 l o g l 0 - 4 )A log table or calculator indicates that log 2.5 0.40, andlog 10 - 4 - 4 . Insert these values to find the pH.p H -(0.40) - ( - 4 ) -0.40 4 3.60, EVALUATE Does the result make sense?A solution in which [OH ] is less than 1 X 10" 7 M would beacidic because [H ] would be greater than 1 X 10"7M. [OH - ] isless than 10 1 0 Mbut greater than 10" n M. Therefore, the solution is somewhere between pOH 10 and pOH 11. Because pOH pH 1 4 , the pH should be less than 4 and greater than 3.CMm.ASAPiProblem-Solving 13Solve Problem 13 with the helpot an interactive guided tutorial.IEYou can calculate the hydrogen-ion concentration of a solution if youknow the pH. For example, if the solution has a pH of 3.00, then [H ] 1.0 x 10 -3 M. When the pH is not a whole number, you will need log tablesor a calculator with a yx function key to calculate the hydrogen-ionconcentration. For example, if the pH is 3.70, the hydrogen-ion concentration must be greater than 1.0 X 10 4M (pH 4.0) and less than 1.0 X 10 - 3 M(pH 3.0). To get an accurate value, use log tables or a calculator. ample Problem 20-6What is [H ] of a solution if the pH 3.70?1 - ANAL YZE List the knowns and the unknown.Knowns: pH 3.70 pH -log[H ]Unknown: [H ] ?M2. CALCULATE Solve for the unknown.First rearrange the equation pH - l o g [H ].log[H ] -pH -3.70A log table cannot be used directly to find a number that has anegative log. To avoid this problem, add and then subtract thewhole number that is closest to and larger than the negative log.In this case, the negative log is 3.70, and the whole number is 4.588Chapter 20

Sample Problem 20-6 (cont.)log[H ] (-3.70 4) - 4 0.30 - 4 [H ] i0( -3 -« io0-30 X io- 4From the log table, the number with a log of 0.30 is 2.0; theantilog of 0.30 is thus 2.0. The number with a log of - 4 is IO-4.Therefore, [H ] 2.0 X 10 4M. A calculator with ay x functionkey can be used because [H ] 10"pH; that is, [H ] is of thePractice Problemsform yx. Thus change the sign of the given pH, in this case to14. What is the molarity of [H ] in-3.70. Enter y 10, x -3.70, and press the yx key in theeach solution?order required by the calculator. The readout gives 1.995 X4 4a. pH 7.30C. pH 7.05IO" . Rounded to two significant figures, [H ] 2.0 X 10 M.b. pH 1.80d. pH 6.70EVALUATE Does the result make sense?15. Calculate the value of [OH-] 4A solution of pH 3.70 should have a [H ] between 1 x 10" Min each solution in Practice3 (pH 4) and 1 X 10" M (pH 3), as found. Because [H ] isProblem 14.greater than 1 x 10"7M, the solution is acidic.I"Measuring pHPeople need to be able to measure the pH of the solutions they use. Frommaintaining the correct acid-base balance in a swimming pool, to creatingsoil conditions ideal for plant growth, to making medical diagnoses, pHmeasurement has valuable applications. For preliminary pH measurements and for small-volume samples, indicators such as the ones shown inFigure 20.7 are often used. For precise and continuous measurements, apH meter is preferred.7Methyl red54PhenolphthaleinFigure Z0.7Acid-base indicators respond to pH changes over a specific range. Methyl red (left)changes from red to yellow at phi 5-7. Phenolphthalein (center) changes from colorlessto pink at pH 7-9. Bromthymol blue (right) changes from yellow to blue at pH 5-7.Acids and Bases 589

section 20.2Acid-Base Indicators An indicator (In) is an acid or a base that undergoesdissociation in a known pH range. An indicator is a valuable tool formeasuring pH because its acid form and base form have different colors insolution. The following generalized equation represents the dissociat

Chapter 20 I ACIDS AND BASES Section 20.1 DESCRIBING ACIDS AND BASES Section 20.2 HYDROGEN IONS AND ACIDITY FEATURES These tart-tasting fruits contain a weak acid called citric acid. DISCOVER IT! Effect of Foods on Baking Soda SMALL-SCALE LAB Ionization Constants of Weak Acids MINI LAB

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