Whe you ca measure what you are speakig about ad express it i umbers, you kow somethig about it; but whe you caot measure it, whe you caot express it i umbers, you kowledge is of a meager ad usatisfactory kid; it may be the begiig of kowledge but you have scarcely, i your thoughts advaced to the stage of sciece, whatever the matter may be. --Lord Kelvi, May 3rd, 1883 1/5/004 OFB Chapter 5 1
OFB Chapter 5 The Gaseous State 5-1 The Chemistry of Gases 5- ressure ad Boyle s Law 5-3 Temperature ad Charles s Law 5-4 The Ideal Gas Law 5-5 Chemical Calculatios for Gases 5-6 Mixtures of Gases 5-7 Real Gases 1/5/004 OFB Chapter 5
OFB Chapter 5 The Gaseous State Early discoveries of gases formed by chemical reactios: heat go(s) g(l) + O (g) Lavoisier used this to establish the coservatio of mass theory heat Marble: CaCO 3 (s) CaO(s) + CO (g) heat N 4 Cl(s) Cl(g) + N 3 (g) Nitroglyceri: 4 C 3 5 (NO 3 ) 3 (l) 6 N (g) + 1 CO (g) + O (g) + 10 O(g) CaCO 3 (s) + Cl(aq) CaCl (aq) + O(g) + CO (g) 1/5/004 OFB Chapter 5 3
ressure ad Boyle s Law force (F) mass * acceleratio Newto (N) kg m s - acceleratio (a) velocity per uit of time [m s - ] mass (m) quatity of matter [kg] area (A) m 1/5/004 OFB Chapter 5 4
ressure ad Boyle s Law 1/5/004 OFB Chapter 5 5
ressure ad Boyle s Law gdh g acceleratio of gravity at the surface of the Earth 9.80665 m s - d desity of the liquid for g at 0ºC 13.5951 g cm -3 13.5951 kg m -3 h height of mercury i the colum 76 cm 760 mm 0.76 m gdh (9.80665 m s - )(13.5951 kg m -3 ) (0.76 m) 1/5/004 OFB Chapter 5 6
A pressure of 101.35 ka is eed to raise the colum of g 760 mm or 76 cm Called stadard pressure 1/5/004 OFB Chapter 5 7
Boyle s Law: The Effect of ressure o Gas olume The product of the pressure ad volume,, of a sample of gas is a costat at a costat temperature: 1/5/004 OFB Chapter 5 8
Boyle s Law: The Effect of ressure o Gas olume ST For 1 mole of ay gas (i.e., 3.0 g of O ; 8.0 g N ;.0 g ), ST stadard temperature ad pressure 0 o C ad 1 atm 1/5/004 OFB Chapter 5 9
Boyle s Law: The Effect of ressure o Gas olume Exercise 5-3 The log cylider of a bicycle pump has a volume of 1131 cm 3 ad is filled with air at a pressure of 1.0 atm. The outlet valve is sealed shut, ad the pump hadle is pushed dow util the volume of the air is 517 cm 3. The temperature of the air trapped iside does ot chage. Compute the pressure iside the pump. 1/5/004 OFB Chapter 5 10
Temperature ad Charles Law Charles Law: The Effect of Temperature o Gas olume t 73.15 C 1) 1/5/004 OFB Chapter 5 11
Charles Law: The Effect of Temperature o Gas olume Absolute Temperature ( t o 1 + ) 73.15 o C Kelvi temperature scale 1/5/004 OFB Chapter 5 1
Charles Law: The Effect of Temperature o Gas olume 1/5/004 OFB Chapter 5 13
Exercise 5-4 The gas i a gas thermometer that has bee placed i a furace has a volume that is.56 times larger tha the volume that it occupies at 100 o C. Determie the temperature i the furace (i degrees Celsius). 1/5/004 OFB Chapter 5 14
Boyle s Law Charles Law 1 1 (at a fixed temperature) 1 / T 1 / T (at a fixed pressure) Avogadro (at a fixed pressure ad temperature) 1/5/004 OFB Chapter 5 15
The Ideal Gas Law T -1 1/5/004 OFB Chapter 5 16
The Ideal Gas Law R 1 1 R T 1 1 T 1/5/004 OFB Chapter 5 17
Exercise 5-5 At oe poit durig its ascet, a weather balloo filled with helium at a volume of 1.0 10 4 L at 1.00 atm ad 30 o C reaches a altitude at which the temperature is -10 o C yet the volume is uchaged. Compare the pressure at that poit. 1 1 T 1 1 T 1/5/004 OFB Chapter 5 18
The Ideal Gas Law R uiversal gas costat? for fixed,, ad T, the umber of is fixed as well, ad idepedet of the particular gas studied R T (.414L)(1atm) (1.00 mol)(73.15 K) R -3 3 (.414 x 10 m )(101.35x10 (1.00 mol)(73.15k) 3 N m - ) 1/5/004 OFB Chapter 5 19
RT ideal gas law R 0.08 L atm mol -1 K -1 R 8.31 J mol 1 K 1 1/5/004 OFB Chapter 5 0
Exercise 5-6 What mass of ydroge gas is eeded to fill a weather balloo to a volume of 10,000 L at 1.00 atm ad 30 C? Strategy 1.) use RT.) 3.) 1/5/004 OFB Chapter 5 1
Exercise 5-6 What mass of ydroge gas is eeded to fill a weather balloo to a volume of 10,000 L at 1.00 atm ad 30 C? 1/5/004 OFB Chapter 5
Gas Desity ad Molar Mass RT m M RT 1/5/004 OFB Chapter 5 3
Gas Desity ad Molar Mass Exercise 5-7 Calculate the desity of gaseous hydroge at a pressure of 1.3 atm ad a temperature of -45 o C. d RT M 1/5/004 OFB Chapter 5 4
Gas Desity ad Molar Mass RT m M RT Rearrage m RT M m RT M d RT M d RT d RT M 1/5/004 OFB Chapter 5 5
Exercise 5-8 Fluorocarbos are compouds of fluorie ad carbo. A 45.60 g sample of a gaseous fluorocarbo cotais 7.94 g of carbo ad 37.66 g of fluorie ad occupies 7.40 L at ST ( 1.00 atm ad T 73.15 K). Determie the approximate molar mass of the fluorocarbo ad give its molecular formula. 1/5/004 OFB Chapter 5 6
Exercise 5-8 Fluorocarbos are compouds of fluorie ad carbo. A 45.60 g sample of a gaseous fluorocarbo cotais 7.94 g of carbo ad 37.66 g of fluorie ad occupies 7.40 L at ST ( 1.00 atm ad T 73.15 K). Determie the approximate molar mass of the fluorocarbo ad give its molecular formula. M d M RT 45.60g 7.40L 0.08 L atm mol 1atm 138 g mol 1 1 K 1 x 73K C F 1molC 7.94g C x 1g C 1molF 37.66g F x 19 g F 0.661molC 0.661 mol 1part C 1.98mol F 0.661 mol 3 parts F 1/5/004 OFB Chapter 5 7
Chemical Calculatios for Gases Why use olume for gases i chemical reactio calculatios? The volume of a gas is easier to measure tha the mass of a gas. Exercise 5-9 Ethylee burs i oxyge: C 4 (g) + 3 O (g) CO (g) + O(g) A volume of 3.51 L of C 4 (g) at a temperature of 5 o C ad a pressure of 4.63 atm reacts completely with O (g). The water vapor is collected at a temperature of 130 o C ad a pressure of 0.955 atm. Calculate the volume of the water vapor. 1/5/004 OFB Chapter 5 8
1/5/004 OFB Chapter 5 9 Exercise 5-9 Ethylee burs i oxyge: C 4 (g) + 3 O (g) CO (g) + O(g) A volume of 3.51 L of C 4 (g) at a temperature of 5 o C ad a pressure of 4.63 atm reacts completely with O (g). The water vapor is collected at a temperature of 130 o C ad a pressure of 0.955 atm. Calculate the volume of the water vapor. 1 1 1 1 T T x 403K T atm 0.955 98K T 3.51L 4.63atm O parts for C 1part O is Codito ad C 1 is Coditio O O O C C C 0 C 4 4 4 4 4 4 O O O O C C C C T T 4 4 4 4
Exercise 5-9 Ethylee burs i oxyge: C 4 (g) + 3 O (g) CO (g) + O(g) A volume of 3.51 L of C 4 (g) at a temperature of 5 o C ad a pressure of 4.63 atm reacts completely with O (g). The water vapor is collected at a temperature of 130 o C ad a pressure of 0.955 atm. Calculate the volume of the water vapor. 1 1 T 1 1 T O O O C C C4 C4 C4 T 4 C4 O O 46.0 L 1/5/004 OFB Chapter 5 30 T C C 4 4 C4 O 4 C4 T C4 T C4 C4 C4 T O O O O O T O T T O O O O O
Mixtures of Gases Dalto s Law of artial ressures The total pressure of a mixture of gases equals the sum of the partial pressures of the idividual gases. 1/5/004 OFB Chapter 5 31
Mole Fractios ad artial ressures A tot tot A The mole fractio of a compoet i a mixture is defie as the umber of moles of the compoets that are i the mixture divided by the total umber of moles preset. A Mole Fractio of X A A A tot tot A tot divide equatios X A RT tot RT RT RT or A tot A A 1/5/004 OFB Chapter 5 3 + B X A A +... + A tot or A N A tot tot
Exercise 5-11 A solid hydrocarbo is bured i air i a closed cotaier, producig a mixture of gases havig a total pressure of 3.34 atm. Aalysis of the mixture shows it to cotai 0.340 g of water vapor, 0.79 g of carbo dioxide, 0.88 g of oxyge, 3.790 g of itroge, ad o other gases. Calculate the mole fractio ad partial pressure of carbo dioxide i this mixture. 1/5/004 OFB Chapter 5 33
Sectio 5-7 Kietic Theory of Gases Sectio 5-8 Real Gases 1/5/004 OFB Chapter 5 34
Chapter 5 The Gaseous State Examples / Exercises 5-1 thru 5-13 roblems 34, 38, 48, 6, 70, 81 1/5/004 OFB Chapter 5 35