3.2 The Gas Laws Secton 3.2 1 FOCUS Key Concepts What causes gas pressure n a closed contaner? What factors affect gas pressure? How are the temperature, volume, and pressure of a gas related? Vocabulary pressure absolute zero Charles s law Boyle s law The woman n Fgure 10 s takng a deep breath. Ths acton helps reduce her breathng rate and ncrease the volume of ar she nhales. When you nhale, the volume of your chest cavty ncreases and ar moves nto your lungs. When you exhale, the volume of your chest cavty decreases and ar s pushed out of your lungs. After you read ths secton, you wll understand how changng the volume of your chest cavty causes ar to move nto and out of your lungs. Changes n the volume, the temperature, the pressure, and the number of partcles have predctable effects on the behavor of a gas. Pressure At many hockey rnks, a layer of shatterproof glass keeps the puck away from the spectators. The force wth whch the puck hts the glass depends on the speed of the puck. The faster the puck s travelng, the greater the force s. The smaller the area of mpact s, the greater the pressure produced. Pressure s the result of a force dstrbuted over an area. If the edge of the puck hts the glass, t exerts more pressure than f the face of the puck hts the glass at the same speed. The SI unt of pressure s derved from SI unts for force and area. Force s measured n newtons (N) and area n square meters (m 2 ). When a force n newtons s dvded by an area n square meters, the unt of pressure s newtons per square meter (N/m 2 ). The SI unt for pressure, the pascal (Pa), s shorthand for newtons per square meter. One pascal s a small amount of pressure. Scentsts often express larger amounts of pressure n klopascals. One klopascal (kpa) s equal to 1000 pascals. Secton Resources Prnt Readng and Study Workbook Wth Math Support,Secton 3.2 and Math Skll:The Combned Gas Law Math Sklls and Problem Solvng Workbook, Secton 3.2 Transparences, Secton 3.2 Readng Strategy Identfyng Cause and Effect Copy the dagram. As you read, dentfy the varables that affect gas pressure. Gas pressure s affected by a.? b.? c.? Fgure 10 Takng a deep breath ncreases the volume of your chest cavty, whch causes ar to move nto your lungs. States of Matter 75 Technology Interactve Textbook, Secton 3.2 Presentaton Pro CD-ROM, Secton 3.2 Go Onlne, Scence News, Propertes of matter Objectves 3.2.1 Defne pressure and gas pressure. 3.2.2 Identfy factors that affect gas pressure. 3.2.3 Predct changes n gas pressure due to changes n temperature, volume, and number of partcles. 3.2.4 Explan Charles s law, Boyle s law, and the combned gas law. 3.2.5 Apply gas laws to solve problems nvolvng gases. Buld Vocabulary Paraphrase Replace less famlar words n a defnton wth more famlar words or phrases. Readng Strategy a. Temperature b. Volume c. Number of partcles 2 Readng Focus INSTRUCT Pressure Buld Scence Sklls Observng Purpose Show the effect of area on pressure. Materals clay, CD case, textbook Advance Prep Prepare two flattened peces of clay 3 cm thck. Procedure Put the broad sde of the CD case on a pece of clay wth the book on top. After about 30 seconds, carefully remove the book and case. Then, put the case on the other pece of clay, narrow sde down. Balance the book on the case for 30 seconds. (Place your hands on ether sde of the book as a precauton.) Remove the book and case. Ask, How do the depths of the mprnts compare? (The mprnt s deeper when the case s placed on ts edge.) What caused ths dfference? (Because the weght of the book was appled to a smaller area, the pressure was greater.) Expected Outcome When the same force s appled to a smaller area, the depth of the mprnt ncreases. Vsual States of Matter 75
Secton 3.2 (contnued) Factors that Affect Gas Pressure Changng Volume of a Balloon Purpose Students observe the effect of temperature on the volume of a balloon. Materals nflated balloons, refrgerator, warm place Advance Prep One day ahead, nflate a balloon for each class. Place the balloons n a refrgerator overnght. Procedure At the begnnng of class, brng out a balloon and tell students where t has been. Ask, Do you predct that the volume of the balloon wll ncrease, decrease, or stay the same after the balloon has been n a warm place? (Increase) Place the balloon n a warm place untl shortly before the end of class. Make sure the balloon has room to expand, and that the temperature does not exceed 42 C. Ask, What happened to the volume of the gas nsde the balloon? (It ncreased.) Explan that as temperature ncreases, the partcles move faster, on average, whch ncreases the pressure of the gas nsde the balloon. The ncreased pressure causes the balloon to expand. Expected Outcome The balloon s volume wll ncrease as the temperature ncreases. Vsual, Logcal Fgure 11 Brng n a pressure gauge lke the one n the photo. (The gauge measures how much the ar pressure n the tre exceeds atmospherc pressure.) Have a volunteer note the unts of pressure on the gauge. (Pounds per square nch) Explan that n the Unted States, pressure s not always measured n SI unts. Ask, Have you seen any other unts used for pressure? (Students may have seen barometrc pressure reported n nches of mercury.) Why s data from experments measured and reported n SI unts? (Scentsts must use standard unts so that ther data can be shared wth and tested by scentsts n all countres.) Logcal, Vsual Fgure 11 The frefghter s usng a pressure gauge to check the ar pressure n a tre on a fretruck. If the tres on the truck have a 44.5-nch dameter, the pressure on a front tre should be about 125 pounds per square nch (ps). 76 Chapter 3 Customze for Incluson Students Vsually Impared Have students wth vsual mparments observe dfferent ar pressures n a bcycle tre. Brng a bcycle tre and a pump wth a bult-n gauge. Let out all of the ar n the tre. Attach the pump to the nner tube valve. Read the pressure on the gauge and allow students to feel that the tre s completely flat. Pump up the tre to a An object does not need to be as large as a hockey puck to exert pressure when t colldes wth another object. Recall that the helum atoms n a balloon are constantly movng. The pressure produced by a sngle helum atom colldng wth a wall s extremely small. However, there are more than 10 22 helum atoms n a small balloon. When so many partcles collde wth the walls of a contaner at the same tme, they produce a measurable pressure. Collsons between partcles of a gas and the walls of the contaner cause the pressure n a closed contaner of gas. The more frequent the collsons, the greater the pressure of the gas s. The speed of the partcles and ther mass also affect the pressure. How does the frequency of collsons affect the pressure of a gas? Factors That Affect Gas Pressure Thnk agan about the collsons that produce gas pressure. What changes mght affect the pressure of a gas n a contaner? The partcles n the gas could move faster or slower. The gas could be moved nto a larger or smaller contaner. You could add gas or remove gas from the contaner. Factors that affect the pressure of an enclosed gas are ts temperature, ts volume, and the number of ts partcles. Temperature Suppose you are about to go on a long drve. The drver suspects that the ar pressure n the automoble tres mght be low. You check the pressure n each tre, usng a pressure gauge lke the one n Fgure 11. You fnd that the measurements are well wthn the automoble manufacturer s gudelnes. If you checked the tre pressures agan after a few hours on the hghway, would you be surprsed to fnd that the pressure n the tres had ncreased? The constant moton of tres on the hghway causes the tres and the ar n the tres to warm up. As the temperature rses, the average knetc energy of the partcles n the ar ncreases. Wth ncreased knetc energy, the partcles move faster and collde more often wth the nner walls of the tres. The faster-movng partcles also ht the walls wth greater force. The ncrease n the number of collsons along wth the ncrease n the force of the collsons causes an ncrease n the pressure of the ar n the tres. Rasng the temperature of a gas wll ncrease ts pressure f the volume of the gas and the number of partcles are constant. thrd of the maxmum recommended pressure (marked on the tre). Read the pressure on the gauge and allow students to feel the tre agan. Pump up the tre to the maxmum recommended pressure and allow students to repeat the observaton. Dscuss wth students how the quantty of ar n the tre affects the frmness of the tre. 76 Chapter 3
Daphragm contracts. Rb cage s lfted up and out. Inhalng Lungs Rb cage Daphragm Exhalng Volume Imagne that you have a plastc bottle that appears empty. If you twst the cap onto the bottle and then squeeze the bottle, what wll happen? At frst, the plastc wll gve a lttle, reducng the volume of the bottle. But soon you wll feel pressure from nsde the bottle resstng your efforts to further reduce the volume. The pressure you feel s a result of the ncreased pressure of the ar trapped nsde the bottle. As the volume s decreased, partcles of trapped ar collde more often wth the walls of the bottle. Reducng the volume of a gas ncreases ts pressure f the temperature of the gas and the number of partcles are constant. Fgure 12 shows how the relatonshp between volume and pressure explans what happens when you breathe. As you nhale, a muscle called the daphragm (DY uh fram) contracts. The contracton causes your chest cavty to expand. Ths temporary ncrease n volume allows the partcles n ar to spread out, whch lowers the pressure nsde the chest cavty. Because the pressure of the ar outsde your body s now greater than the pressure nsde your chest, ar rushes nto your lungs. When you exhale, your daphragm relaxes and the volume of your chest cavty decreases. The partcles n the ar are squeezed nto a smaller volume and the pressure nsde your lungs ncreases. Because the pressure of the ar nsde your chest s now greater than the pressure of the ar outsde your body, ar s forced out of your lungs. Number of Partcles You can probably predct what wll happen to the pressure when you add more gas to a contaner. Thnk about a tre. Once the tre s nflated, ts volume s farly constant. So addng more ar wll ncrease the pressure nsde the tre. The more partcles there are n the same volume, the greater the number of collsons and the greater the pressure. At some pont the rubber from whch the tre s made wll not be strong enough to wthstand the ncreased pressure and the tre wll burst. Increasng the number of partcles wll ncrease the pressure of a gas f the temperature and the volume are constant. Daphragm relaxes. Rb cage moves down and n. Fgure 12 Movement of a muscle called the daphragm changes the volume of your chest cavty. The volume ncreases when you nhale and decreases when you exhale. Interpretng Dagrams How does the movement of your rb cage affect the volume of your chest cavty? For: Artcles on propertes of matter Vst: PHSchool.com Web Code: cce-1032 Predct Refer to page 66D n ths chapter, whch provdes the gudelnes for predctng. Lst on the board examples of volume, temperature, and number of partcles ncreasng or decreasng. Tell students to predct how each change wll affect gas pressure n a closed contaner. Ask students to use the number of partcle collsons to explan ther predctons. As students provde ther predctons and explanatons, wrte the correct effect on pressure and the correct explanaton on the board. Logcal, Portfolo Scence News provdes students wth current nformaton on propertes of matter. States of Matter 77 F t d Fgu Fantng Couches Durng the Vctoran era, well-to-do households often had fantng couches. The tghtly laced, whalebone corsets women wore restrcted ther ablty to breathe deeply. As a result, they had low levels of oxygen n ther blood, causng them to fant, or swoon. Today, Vctoran fantng couches can be seen n hstorc houses or museums. Antque fantng couches and reproductons are avalable n some furnture and antque stores. wer to Fgure 12 The volume ncreases as the rb cage s lfted up and out. The volume decreases as the rb cage moves down and n. The more frequent the collsons, the greater the pressure of the gas s. States of Matter 77
Secton 3.2 (contnued) Charles s Law Usng Tables and Graphs Have students analyze Fgure 13. Have students look frst at the graph for Charles s law. Pont out the straght lne wth the postve slope. Ask, What relatonshp does ths lne descrbe? (It descrbes a drect relatonshp between volume and temperature: As temperature ncreases, volume also ncreases.) Ask, Why s part of the lne sold and part dashed? (The sold lne represents actual data, whle the dotted lne s the extenson of the collected data toward the zero pont for volume.) Have students refer to the Boyle s Law graph. Ask, What happens to pressure as volume ncreases? (As volume ncreases, pressure decreases.) Vsual, Logcal Lne Graphs Students are lkely to need help understandng why Charles s law does not apply when temperatures are expressed n degrees Celsus. Have students fnd the pont on the graph where the temperature s 0ºC and ask them to estmate the volume at that temperature. Then, tell them that the straght lne must pass through (0, 0) for the respondng varable to be drectly proportonal to the manpulated varable. Logcal, Portfolo Drect students to the Math Sklls n the Sklls and Reference Handbook at the end of the student text for addtonal help. Volume (ml) 10 8 6 4 2 273.15 Charles s Law 0 300 250 200 150 100 50 0 50 100 Temperature ( C) Fgure 13 These graphs compare the effects of temperature and volume on the pressure of a gas. Charles s law descrbes the drect relatonshp between the temperature and the volume. Boyle s law descrbes the nverse relatonshp between the volume and the pressure. Controllng Varables For each graph, name the manpulated varable and the respondng varable. Charles s Law Durng hs lfetme, the French physcst Jacques Charles (1746 1823) was known for hs nventons, ncludng the hydrogen balloon. Today, Charles s best known for hs nvestgatons of the behavor of gases. Charles collected data on the relatonshp between the temperature and volume of gases. When he graphed the data, the graph was a straght lne, as shown n Fgure 13. The graph shows that the volume of a gas ncreases at the same rate as the temperature of the gas. Charles extended the lne on hs graph beyond the measured data to see what the temperature would have to be to produce a volume of 0 L. The temperature at the pont where the lne crossed the x-axs was 273.15 C. Ths temperature s equal to 0 K on the Kelvn temperature scale. A temperature of 0 K s called absolute zero. No scentst has produced a temperature of absolute zero n a laboratory, but some have come extremely close. As a gas cools to temperatures near 0 K, the gas changes to a lqud, a sold, or sometmes a Bose-Ensten condensate. Charles s law states that the volume of a gas s drectly proportonal to ts temperature n kelvns f the pressure and the number of partcles of the gas are constant. Charles s law can be wrtten as a mathematcal expresson n whch T 1 and V 1 represent the temperature and volume of a gas before a change occurs. T 2 and V 2 represent the temperature and volume after a change occurs. Pressure (kpa) 250 200 150 100 50 0 0 0.5 1.0 1.5 2.0 2.5 Volume (L) V 1 T 1 Boyle s Law V 2 T 2 The temperatures must be expressed n kelvns. If temperatures n degrees Celsus are used n the expresson, the volume wll not be drectly proportonal to the temperature. 78 Chapter 3 F t d Fgu Absolute Zero Based on the decrease n the volume of a gas as t cooled, scentsts hypotheszed that f an deal gas were cooled to absolute zero (0 K on the Kelvn temperature scale or 273.15 on the Celsus scale), ts volume would be zero. However, as actual gases are cooled, they reach temperatures at whch they change to lquds or solds. Theoretcally, all moton of partcles n matter should cease at absolute zero. But accordng to quantum mechancs, a substance wll contan some energy of moton, regardless of ts temperature. For that reason, substances cannot be cooled to absolute zero. However, Bose-Ensten condensates produced n laboratores exst at temperatures very close to absolute zero. 78 Chapter 3
Boyle s Law Robert Boyle, who was born n Ireland n 1627, was the frst to descrbe the relatonshp between the pressure and volume of a gas. The graph n Fgure 13 shows what happens when the volume of a cylnder contanng a set amount of gas s decreased. What happens when the volume of the cylnder s reduced from 2.0 lters to 1.0 lter? The pressure of the gas n the cylnder doubles from 50 klopascals to 100 klopascals. P 1 V 1 P 2 V 2 Boyle s law states that the volume of a gas s nversely proportonal to ts pressure f the temperature and the number of partcles are constant. Boyle s law can be expressed mathematcally. P 1 and V 1 represent the pressure and volume of a gas before a change occurs. P 2 and V 2 represent the pressure and volume of a gas after a change occurs. How s Boyle s law expressed mathematcally? Boyle s Law r ffe f Te ra re re re Objectve After completng ths actvty, students wll be able to predct the effect of temperature on the pressure of a gas. Ths lab helps dspel the msconcepton that a gas does not have mass. Explan that ar pressure s the result of partcles n ar colldng wth the can. The force of the collsons (and pressure) depends on the mass and speed of the partcles. Sklls Focus Inferrng r ffe f T ra re Materals pan, metrc ruler, empty beverage can, maskng tape, hot plate, clock, tongs Procedure 1. Fll a pan wth cold water to a depth of 3 cm. 2. Use maskng tape to cover half the openng of the can. CAUTION Do not cover the entre openng wth tape. 3. Place the can on the hot plate and turn the hot plate to a hgh settng. Heat the can for 5 mnutes and then turn off the hot plate. 4. Use tongs to remove the can from the hot plate and place t upsde down n the pan of water as shown. The openng should be below the surface of the water. Observe the can as t cools. F t d Fgu Expermental Evdence Robert Boyle was a foundng member of The Royal Socety, the oldest contnuous scentfc socety n the world. The socety s motto s Nullus n Verba, Latn for Nothng n Words. The motto means that scence should be based on expermental evdence, not debates. Boyle s adherence to a scentfc method was one of hs most mportant contrbutons to scence. He was among the frst scentsts Analyze and Conclude 1. Inferrng How dd the temperature of the ar nsde the can change when you heated the can? How dd t change when you put the can n the water? 2. Drawng Conclusons What happened to the pressure of the ar nsde the can when you put the can n the cold water? 3. Inferrng Dd the ar pressure outsde the can change durng the experment? 4. Formulatng Hypotheses What caused the change you observed n Step 4? States of Matter 79 to publsh detaled expermental results, even results of unsuccessful experments. In 1661, Boyle s The Sceptcal Chymst was publshed. It dsputed Arstotle s theores about elements. Hs 1662 publcaton of The Sprng and Weght of the Ar ncluded experments that led to Boyle s law. For these and earler experments, Boyle developed an mproved vacuum pump, whch requred only one person to operate. Prep Tme 10 mnutes Materals pan, metrc ruler, empty beverage can, maskng tape, hot plate, clock, tongs Advance Prep Ask students to contrbute clean, empty beverage cans. Use dssectng pans, cake pans, or plastc dshpans. Class Tme 20 mnutes Safety Cauton students not to touch the hot plate or the can once the hot plate has been turned on. Expected Outcome The can wll crack or collapse wthn one mnute after beng placed n cold water. Analyze and Conclude 1. The temperature ncreased when the can was heated and decreased when t was placed n cold water. 2. The pressure decreased. 3. The ar pressure outsde the can dd not change. 4. As the gas nsde the can cooled, ts pressure decreased untl t could no longer offset the outsde ar pressure. wer to Fgure 13 For Charles s law, the manpulated varable s temperature and the respondng varable s volume. For Boyle s law, the manpulated varable s volume and the respondng varable s pressure. P 1 V 1 P 2 V 2 States of Matter 79
Secton 3.2 (contnued) Formulas and Equatons A gas has a pressure of 200 kpa n a 0.5-L contaner. Use Boyle s law to determne the pressure of the gas n a 2.0 contaner. (50 kpa) Logcal Drect students to the Math Sklls n the Sklls and Reference Handbook at the end of the student text for addtonal help. The Combned Gas Law ra Have students show how the combned gas law can be used to derve Boyle s and Charles s laws. If temperature s constant, the temperature cancels out to reveal Boyle s law P 1 V 1 P 2 V 2. Smlarly, f volume remans constant, Charles s law of P 1 /T 1 P 2 /V 2 s derved. Logcal Solutons 1. V 2 (P 1 V 1 /P 2 ) (50 kpa)(5.0 L)/125 kpa 2.0 L 2. T 2 (P 2 T 1 /P 1 ) (825 kpa)(273 K)/388 kpa 580 K 3.T 2 (V 2 T 1 /V 1 ) (0.285 L)(283 K)/0.250 L 323 K or 50 C Logcal For Extra Help Remnd students that before they solve a specfc problem, they should determne whch varable s not changng and remove that varable from the combned gas law. Then, they need to dentfy whch of the varables s the unknown V 2, T 2, or P 2 and rearrange the equaton to solve for that varable. If students are havng trouble rearrangng the equaton, provde students wth the sx possble forms of the equaton. Logcal Addtonal Problems 1. A gas s stored at constant volume at a pressure of 137 kpa at 274 K. If the temperature rses to 296 K, what s the pressure? (148 kpa) 2. At constant temperature, the volume of a gas at 1000 kpa s changed from 100 L to 10 L. What s the new pressure? (10,000 kpa) Logcal 1. A gas has a volume of 5.0 L at a pressure of 50 kpa. What happens to the volume when the pressure s ncreased to 125 kpa? The temperature does not change. 2. Gas stored n a tank at 273 K has a pressure of 388 kpa. The safe lmt for the pressure s 825 kpa. At what temperature wll the gas reach ths pressure? 3. At 10ºC, the gas n a cylnder has a volume of 0.250 L. The gas s allowed to expand to 0.285 L. What must the fnal temperature be for the pressure to reman constant? (Hnt: Convert from degrees Celsus to kelvns usng the expresson ºC 273 K.) 80 Chapter 3 F t d Fgu Weather Balloons Large weather balloons are made of natural or synthetc rubber. They are flled wth ether helum or hydrogen. As the balloon expands, the thckness of the rubber decreases from about 0.051 mm to 0.0025 mm at the alttude when the balloon bursts. A balloon that s about 2 m n dameter at launch wll be about 6 m n dameter after t expands. Balloons are launched twce a day at stes around the world. The Combned Gas Law The relatonshps descrbed by Boyle s law and Charles s law can be descrbed by a sngle law. The combned gas law descrbes the relatonshp among the temperature, volume, and pressure of a gas when the number of partcles s constant. P 1 V 1 T 1 P 2 V 2 T 2 The combned gas law s used to solve many problems nvolvng gases. The Combned Gas Law A cylnder that contans ar at a pressure of 100 kpa has a volume of 0.75 L. The pressure s ncreased to 300 kpa. The temperature does not change. Fnd the new volume of ar. What nformaton are you gven? P 1 100 kpa P 2 300 kpa V 1 0.75 L What unknown are you tryng to calculate? V 2 What expresson can you use? P 1 V 1 P 2 V 2 T 1 T 2 Cancel out the varable that does not change and rearrange the expresson to solve for V 2. P P 1 V 1 P 2 V 2 V 2 1 V 1 P 2 Replace each varable wth ts known value. 0.75 L V 2 100 kpa 300 kpa Is your answer reasonable? Volume should decrease as pressure ncreases. The pressure trpled from 100 kpa to 300 kpa. The answer, 0.25 L, s one thrd the orgnal volume, 0.75 L. Attached to the weather balloon s a radosonde, an nstrument that measures pressure, temperature, and relatve humdty. Because the radosonde can be recondtoned and used agan, a parachute and malng bag are also attached to the weather balloon. (The photograph n Fgure 14 was taken at the Natonal Weather Staton n Maryland.) 80 Chapter 3
It s harder for scentsts to do a controlled experment when they are studyng events that occur n natural settngs. Scentsts need laws lke the combned gas law to deal wth stuatons n whch multple varables are changng. Balloons lke the one n Fgure 14 are used by scentsts to gather data about Earth s atmosphere. The balloon s flled wth hydrogen or helum. It carres a package of weather nstruments up nto the atmosphere. The nstruments measure temperature, pressure, and water content at dfferent levels n the atmosphere. What wll happen to the volume of the weather balloon as t rses through the atmosphere? Both pressure and temperature decrease as the alttude ncreases n Earth s atmosphere. A decrease n external pressure should cause the balloon to expand to a larger volume. A decrease n temperature should cause the balloon to contract to a smaller volume. Whether the balloon actually expands or contracts depends on the sze of the changes n pressure and temperature. Fgure 14 These scentsts are releasng a weather balloon nto the atmosphere. The balloon s desgned to burst when t reaches an alttude of about 27,400 meters. Drawng Conclusons What happens to the pressure nsde a weather balloon as t rses? Secton 3.2 Assessment Use Vsuals Fgure 14 The balloon wll burst when t reaches an alttude of about 27,400 m. Ask, What varables change as the balloon rses? How do they change? (Temperature and pressure both decrease.) How does each change affect the volume of the balloon? (Decreasng atmospherc pressure causes the balloon to expand. Decreasng temperature causes the balloon to shrnk.) Vsual, Logcal ASSESS 3 Evaluate Understandng Have students look at the mathematcal presentatons of Charles s law on p. 78 and Boyle s law on p. 79 and descrbe the relatonshps n ther own words. Reteach Wrte Charles s law and Boyle s law on the board. Have students quz each other about the behavor of the respondng varable when another varable ncreases or decreases. Revewng Concepts 1. How s the gas pressure produced n a closed contaner of gas? 2. What three factors affect gas pressure? 3. How does ncreasng the temperature affect the pressure of a contaned gas? 4. What happens to the pressure of a gas f ts volume s reduced? 5. How does ncreasng the number of partcles of a contaned gas affect ts pressure? Crtcal Thnkng 6. Predctng What happens to the pressure n a tre f ar s slowly leakng out of the tre? Explan your answer. 7. Comparng and Contrastng What do Boyle s law and Charles s law have n common? How are they dfferent? 8. Applyng Concepts Some lqud products are sold n aerosol cans. Gas s stored n a can under pressure and s used to propel the lqud out of the can. Explan why an aerosol can should never be thrown nto a freplace or ncnerator. 9. Two lters of hydrogen gas are stored at a pressure of 100 kpa. If the temperature does not change, what wll the volume of the gas be when the pressure s decreased to 25 kpa? 10. You know that a gas n a sealed contaner has a pressure of 111 kpa at 23ºC. What wll the pressure be f the temperature rses to 475ºC? Solutons 9. V 2 (P 1 V 1 /P 2 ) (100 kpa)(2.0 L)/25 kpa 8.0 L 10. P 2 (P 1 T 2 /T 1 ) (111 kpa)(748 K)/296 K 280 kpa If your class subscrbes to the Interactve Textbook, use t to revew key concepts n Secton 3.2. States of Matter 81 Answer to... Fgure 14 The pressure ncreases. Secton 3.2 Assessment 1. Collsons between partcles of a gas and the walls of the contaner cause the pressure n a closed contaner of gas. 2. Temperature, volume, and number of partcles 3. Rasng the temperature wll ncrease the pressure f volume and number of partcles are constant. 4. If the volume s reduced, the pressure of a gas ncreases f temperature and number of partcles are constant. 5. Increasng the number of partcles wll ncrease the pressure f temperature and volume are constant. 6. Because the number of partcles of ar s reduced from the leak, the pressure wll slowly decrease. 7. Both laws descrbe a relatonshp between two varables that affect a gas when other varables are constant. Charles s law shows how the volume of a gas s drectly proportonal to ts temperature n kelvns. Boyle s law shows how the volume of a gas s nversely proportonal to ts pressure. 8. At a hgh temperature, the pressure n the gas mght ncrease to the pont where the can would explode. States of Matter 81
Rdng on Ar ro On August 27, 1783, Jacques Charles released hs frst hydrogen-flled balloon, whch was about 4 m n dameter. He prepared the hydrogen by pourng sulfurc acd over scrap ron. Charles also made mprovements to hot-ar balloons, ncludng a valve lne that allowed operators to release gas from the balloon and a wcker basket (a nacelle), whch was attached to the balloon by ropes. The frst publcaton of Charles s work was by Joseph Gay-Lussac, who referred to Charles s work n an 1802 paper. Gay-Lussac also dd balloonng. Hs alttude record of 7016 m (4.3 mles) stood for almost 50 years. Observng Purpose Students wll observe that heatng ar causes t to expand and become less dense. Materals plastc bag (dry cleaner or thn garbage bag), strng, har dryers Class Tme 20 mnutes Procedure Organze students nto groups of two or three. Have students te a strng around the closed end of the plastc bag and place evenly spaced paper clps around the open end as weghts. Tell students to hold the open end of the plastc bag over the har dryer (set on hgh) and let the bag fll wth hot ar. The plastc bag begns to rse as t flls wth hot ar. When the students feel the bag begn to rse, have them release the bag. Ask, What causes the bag to rse? (The heated ar nsde the bag s less dense than the ar outsde the bag.) Use what happened to the plastc bag to explan how a hot-ar balloon works. (A hot-ar balloon rses because ar n the balloon s heated.) Expected Outcome When the ar nsde the bag s heated, the bag begns to rse. Vsual, Group Rdng on Ar Warm ar s less dense than cold ar. So f enough warm ar s confned to a lghtweght contaner, the contaner can rse through the surroundng colder ar. Ths s the prncple that allows a hot-ar balloon to get off and stay off the ground. When ar s heated, the partcles n the ar gan energy and move faster on average. The partcles also move farther apart, so a gven volume of hot ar contans fewer partcles and has less mass than the same volume of cold ar. Ths dfference n densty produces an upward force. In a hot-ar balloon, the force s very small, equvalent to lftng about one tenth of a gram for each lter of ar. A large volume of ar s needed to support the mass of the balloon and any passengers. That s why hot-ar balloons need to be large. To heat the ar, the plot burns propane gas, whch s stored under pressure n tanks. The bottom of the balloon s envelope (the skrt) s treated so that t s not flammable. Takng Off and Landng Launchng and plotng a hot-ar balloon s an actvty that takes skll and patence. 82 Chapter 3 1 The crew uses fans to fll the envelope wth cold ar. 2 Gas burners are swtched on to heat the ar and nflate the balloon, whch begns to rse. As the balloon nears the chosen alttude, the plot turns the burner off so that the balloon wll stop rsng. The plot mantans the alttude of the balloon by turnng the burner on and off and by openng a valve at the top of the balloon to let hot ar escape. The horzontal movement of the balloon s much harder to control. The wnd speed and wnd drecton vary at dfferent alttudes. The plot uses the burner and the valve to change the alttude of the balloon and take advantage of favorable wnds. A hot-ar balloon cannot land at the same spot from whch t took off. The ground crew must drve to the landng ste to collect the balloon and the passengers. 3 Once up, the plot mantans alttude by occasonally turnng on the burner for a few seconds. Burner Valve 4 To lose alttude, the plot opens a valve at the top of the envelope to let out some hot ar. 82 Chapter 3
Upward force Fast-movng hot ar partcles Slowermovng cold ar partcles Envelope made from tough nylon Flame-resstant skrt Jet of flame from burner Flexble, lghtweght, wcker basket Gong Further The Montgolfer hot-ar balloon that frst carred human passengers had an envelope made of cotton and paper coated wth alum to reduce flammablty. The fuel used was straw. The balloon flew from the center of Pars to the outskrts (a dstance of about 9 klometers) n 25 mnutes on November 21, 1783. (Hot-ar balloons were soon eclpsed by helum balloons or hydrogen balloons.) Modern passenger hot-ar balloons were developed n the Unted States n the 1960s. Ther envelopes are made of nylon and they use propane fuel. Hot-ar balloons generally stay aloft for about an hour. (For long dstance flghts, balloonsts generally use combnaton helum and hot-ar balloons called Rozer balloons after Plâtre de Rozer, a passenger on the frst manned flght.) Verbal 5 The plot selects a sutable place to land before openng the valve all the way. Partcle Pressure Partcles n hot ar move faster and are farther apart than those n cold ar, so hot ar s less dense than cold ar. Wth lower densty, heated ar rses over colder ar. 6 The balloon slowly falls to the ground and collapses. 7 The crew gathers up the envelope. Balloon Valve The valve helps to control the balloon s alttude. When the valve s opened, some hot ar s released from the top of the balloon. The hot ar s replaced by cold ar flowng nto the base of the balloon. Ths exchange of cold ar for hot ar ncreases the mass of the balloon, causng t to descend untl the plot closes the valve. Gong Further Wrte a paragraph comparng early hot-ar balloons wth modern balloons. Include the followng nformaton: the knd of materals used, the length of dstances traveled, and the types of fuel used. Take a Dscovery Channel Vdeo Feld Trp by watchng Up, Up, and Away. Vdeo Feld Trp States of Matter 83 Vdeo Feld Trp Up, Up, and Away After students have vewed the Vdeo Feld Trp, ask them the followng questons: What gases have commonly been used n balloons that carry passengers? (Hot ar, helum, and hydrogen) Why do the partcles of a gas nsde a balloon fll the entre balloon? (A gas has no partcular sze or shape and expands to fll the volume avalable.) What causes a hot-ar balloon to lft off and rse from a surface? (Hot ar nsde the balloon s less dense than the cooler, denser ar outsde the balloon. The dfference n densty results n an upward force.) In 1931, Auguste Pccard, a Swss physcst and educator, bult a balloon that could rse a dstance of 16 mles. Why dd Pccard desgn the balloon so that t could become arborne when t was only partally flled? (Pccard knew the gas nsde the balloon would contnue to expand as the balloon floated up to greater heghts because the outsde ar pressure decreased as the balloon rose.) In Pccard s balloon, the pressure n the cabn was controlled as t s n planes that travel at great heghts above Earth s surface. Ar pressure n the cabn s kept hgher than atmospherc pressure. Why must the ar pressure nsde the cabn be controlled? (Atmospherc pressure decreases wth alttude untl t no longer can sustan respraton.) States of Matter 83