--Lord Kelvin, May 3rd, 1883

When you can measure what you are speaking about and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, you knowledge is of a meager and unsatisfactory kind; it may be the beginning of knowledge but you have scarcely, in your thoughts advanced to the stage of science, whatever the matter may be. --Lord Kelvin, May 3rd, 1883 /3/003 OFB Chapter 5 1

OFB Chapter 5 The Gaseous State 5-1 The Chemistry of Gases 5- Pressure and Boyle s Law 5-3 Temperature and Charles s Law 5-4 The Ideal Gas Law 5-5 Chemical Calculations for Gases 5-6 Mixtures of Gases 5-7 Real Gases /3/003 OFB Chapter 5

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OFB Chapter 5 The Gaseous State Early discoveries of gases formed by chemical reactions: heat HgO(s) Hg(l) + O (g) Lavoisier used this to establish the conservation of mass theory heat Marble: CaCO 3 (s) CaO(s) + CO (g) heat NH 4 Cl(s) HCl(g) + NH 3 (g) Nitroglycerin: 4 C 3 H 5 (NO 3 ) 3 (l) 6 N (g) + 1 CO (g) + O (g) + 10 H O(g) CaCO 3 (s) + HCl(aq) CaCl (aq) + H O(g) + CO (g) /3/003 OFB Chapter 5 4

Pressure and Boyle s Law In physics, a force (F) is a simple push exerted by one object on another. Applying a force to a stationary object sets it in motion, unless the object pushes back with an equal force. Applying a force to an object that pushes back creates a pressure (P) on the object. Applying a force to an object that pushes back creates a pressure (P) on the object. The pressure equals the force divided by the area (A) over which the force is applied: /3/003 OFB Chapter 5 5

Pressure and Boyle s Law force (F) mass * acceleration Newton (N) kg m s - acceleration (a) velocity per unit of time [m s - ] mass (m) quantity of matter [kg] area (A) m /3/003 OFB Chapter 5 6

Pressure and Boyle s Law /3/003 OFB Chapter 5 7

Pressure and Boyle s Law P gdh g acceleration of gravity at the surface of the Earth 9.80665 m s - d density of the liquid for Hg at 0ºC 13.5951 g cm -3 13.5951 kg m -3 h height of mercury in the column 76 cm 760 mm 0.76 m P gdh (9.80665 m s - )(13.5951 kg m -3 ) (0.76 m) /3/003 OFB Chapter 5 8

A pressure of 101.35 kpa is need to raise the column of Hg 760 mm or 76 cm Called standard pressure /3/003 OFB Chapter 5 9

Boyle s Law: The Effect of Pressure on Gas Volume The product of the pressure and volume, PV, of a sample of gas is a constant at a constant temperature: /3/003 OFB Chapter 5 10

Boyle s Law: The Effect of Pressure on Gas Volume STP For 1 mole of any gas (i.e., 3.0 g of O ; 8.0 g N ;.0 g H ), STP standard temperature and pressure 0 o C and 1 atm /3/003 OFB Chapter 5 11

Boyle s Law: The Effect of Pressure on Gas Volume Exercise 5-3 The long cylinder of a bicycle pump has a volume of 1131 cm 3 and is filled with air at a pressure of 1.0 atm. The outlet valve is sealed shut, and the pump handle is pushed down until the volume of the air is 517 cm 3. The temperature of the air trapped inside does not change. Compute the pressure inside the pump. /3/003 OFB Chapter 5 1

Temperature and Charles Law Charles Law: The Effect of Temperature on Gas Volume t 73.15 C V V 1) /3/003 OFB Chapter 5 13

Charles Law: The Effect of Temperature on Gas Volume Absolute Temperature V V ( t o 1 + ) 73.15 o C Kelvin temperature scale /3/003 OFB Chapter 5 14

Charles Law: The Effect of Temperature on Gas Volume /3/003 OFB Chapter 5 15

Exercise 5-4 The gas in a gas thermometer that has been placed in a furnace has a volume that is.56 times larger than the volume that it occupies at 100 o C. Determine the temperature in the furnace (in degrees Celsius). /3/003 OFB Chapter 5 16

Boyle s Law Charles Law P 1 V 1 P V (at a fixed temperature) V 1 / V T 1 / T (at a fixed pressure) Avogadro (at a fixed pressure and temperature) /3/003 OFB Chapter 5 17

The Ideal Gas Law V ntp -1 /3/003 OFB Chapter 5 18

The Ideal Gas Law R PV 1 1 R PV n T 1 1 n T /3/003 OFB Chapter 5 19

Exercise 5-5 At one point during its ascent, a weather balloon filled with helium at a volume of 1.0 10 4 L at 1.00 atm and 30 o C reaches an altitude at which the temperature is -10 o C yet the volume is unchanged. Compare the pressure at that point. /3/003 OFB Chapter 5 0

The Ideal Gas Law R universal gas constant? for fixed V, P, and T, the number of n is fixed as well, and independent of the particular gas studied R PV nt (.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 - ) /3/003 OFB Chapter 5 1

Exercise 5-6 What mass of Hydrogen gas is needed to fill a weather balloon to a volume of 10,000 L at 1.00 atm and 30 C? /3/003 OFB Chapter 5

Exercise 5-6 What mass of Hydrogen gas is needed to fill a weather balloon to a volume of 10,000 L at 1.00 atm and 30 C? /3/003 OFB Chapter 5 3

Gas Density and Molar Mass PV nrt PV m M RT /3/003 OFB Chapter 5 4

Gas Density and Molar Mass Exercise 5-7 Calculate the density of gaseous hydrogen at a pressure of 1.3 atm and a temperature of -45 o C. /3/003 OFB Chapter 5 5

Molar Mass PV nrt PV m M RT /3/003 OFB Chapter 5 6

Exercise 5-8 Fluorocarbons are compounds of fluorine and carbon. A 45.60 g sample of a gaseous fluorocarbon contains 7.94 g of carbon and 37.66 g of fluorine and occupies 7.40 L at STP (P 1.00 atm and T 73.15 K). Determine the approximate molar mass of the fluorocarbon and give its molecular formula. /3/003 OFB Chapter 5 7

Exercise 5-8 Fluorocarbons are compounds of fluorine and carbon. A 45.60 g sample of a gaseous fluorocarbon contains 7.94 g of carbon and 37.66 g of fluorine and occupies 7.40 L at STP (P 1.00 atm and T 73.15 K). Determine the approximate molar mass of the fluorocarbon and give its molecular formula. M d M RT P 45.60g 7.40L 0.08 L atm mol 1atm 138 g mol 1 1 K 1 x 73K n n 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 /3/003 OFB Chapter 5 8

Chemical Calculations for Gases Why use Volume for gases in chemical reaction calculations? The volume of a gas is easier to measure than the mass of a gas. Exercise 5-9 Ethylene burns in oxygen: C H 4 (g) + 3 O (g) CO (g) + H O(g) A volume of 3.51 L of C H 4 (g) at a temperature of 5 o C and a pressure of 4.63 atm reacts completely with O (g). The water vapor is collected at a temperature of 130 o C and a pressure of 0.955 atm. Calculate the volume of the water vapor. /3/003 OFB Chapter 5 9

Exercise 5-9 Ethylene burns in oxygen: C H 4 (g) + 3 O (g) CO (g) + H O(g) A volume of 3.51 L of C H 4 (g) at a temperature of 5 o C and a pressure of 4.63 atm reacts completely with O (g). The water vapor is collected at a temperature of 130 o C and a pressure of 0.955 atm. Calculate the volume of the water vapor. 1part n P V T P T V P 1V 1 n T 1 1 Condition and C C C H H C H H H H H O Conditon 98K 0.955 403K PV n T C H 4 for parts H O n V 46.0 L H 0 H O 4.63atm O /3/003 OFB Chapter 5 30 4 O 4 4 4 x 1 is 3.51L C is atm H 4 H P n O C C H H V C C H 4 4 4 T H 4 P n H H O O V T H H O O

Exercise 5-10 Hydrazine (N H 4 ), a rocket fuel, is prepared by the reaction of ammonia with a solution of sodium hypochlorite: NH 3 (g) + NaOCl(aq) N H 4 (aq) + NaCl(aq) + H O(g) What volume of gaseous ammonia at a temperature of 10 o C and a pressure of 3.63 atm is required to produce 15.0 kg of hydrazine according to this equation. /3/003 OFB Chapter 5 31

Exercise 5-10 Hydrazine (N H 4 ), a rocket fuel, is prepared by the reaction of ammonia with a solution of sodium hypochlorite: NH 3 (g) + NaOCl(aq) N H 4 (aq) + NaCl(aq) + H O(g) What volume of gaseous ammonia at a temperature of 10 o C and a pressure of 3.63 atm is required to produce 15.0 kg of hydrazine according to this equation. PV 1mol V V V V NH NH NH NH 3 3 3 nrt N H4 mol NH3 n NH R P NH NH T NH n ( 0.08 x 83K) 3.63atm /3/003 OFB Chapter 5 3 3 3 3 3 m N R T H4 NH3 NH3 M N P H4 NH3 3 15 x 10 g NH4-1 30.04 g mol NH 3 6.4 x 10 L 3 V N nrt P 4 H 4 P R NH NH 3 3 T m M NH 3 RT P

Mixtures of Gases Dalton s Law of Partial Pressures The total pressure of a mixture of gases equals the sum of the partial pressures of the individual gases. /3/003 OFB Chapter 5 33

Mole Fractions and Partial Pressures P P A tot P P P tot A The mole faction of a component in a mixture is define as the number of moles of the components that are in the mixture divided by the total number of moles present. V A V Mole Fraction of X A A A tot tot n n A tot divide equations V V X n n n n A P RT tot RT RT RT or n P P A tot A A /3/003 OFB Chapter 5 34 + n n n B X A n A +... + A tot or P A n N n n A tot P tot

Exercise 5-11 A solid hydrocarbon is burned in air in a closed container, producing a mixture of gases having a total pressure of 3.34 atm. Analysis of the mixture shows it to contain 0.340 g of water vapor, 0.79 g of carbon dioxide, 0.88 g of oxygen, 3.790 g of nitrogen, and no other gases. Calculate the mole fraction and partial pressure of carbon dioxide in this mixture. /3/003 OFB Chapter 5 35

The Kinetic Theory of Gases 1. A pure gas consists of a large number of identical molecules separated by distances that are large compared with their size.. The molecules of a gas are constantly moving in random directions with a distribution of speeds. 3. The molecules of a gas exert no forces on one another except during collisions, so that between collisions they move in straight lines with constant velocities. 4. The collisions of the molecules with each other and with the walls of the container are elastic; no energy is lost during a collision. /3/003 OFB Chapter 5 36

Temperature and Molecular Motion Pressure (impulse per collision) x (rate of collisions with the walls) impulse pre collision momentum (m u) rate of collisions number of molecules per unit volume (N/V) rate of collisions speed of molecules (u) P (m u) [(N/V) u] /3/003 OFB Chapter 5 37

The Kinetic Theory of Gases PV PV nn 1 Nomu 3 M mn u PV Nmu mean-square speed N 3RT M 1 Nmu nrt 3 if N Avogadro's number o 1 Nmu 3 nrt RT /3/003 OFB Chapter 5 38 o o

Distribution of Molecular Speeds u 3RT M /3/003 OFB Chapter 5 39

Exercise 5-1 At a certain speed, the rootmean-square-speed of the molecules of hydrogen in a sample of gas is 1055 ms -1. Compute the root-mean square speed of molecules of oxygen at the same temperature. /3/003 OFB Chapter 5 40

Exercise 5-1 At a certain speed, the root-mean-square-speed of the molecules of hydrogen in a sample of gas is 1055 ms -1. Compute the root-mean square speed of molecules of oxygen at the same temperature. /3/003 OFB Chapter 5 41

Exercise 5-1 At a certain speed, the root-mean-square-speed of the molecules of hydrogen in a sample of gas is 1055 ms -1. Compute the root-mean square speed of molecules of oxygen at the same temperature. Strategy 1. Find T for the H gas with a u rms 1055 ms -1 T. Find u rms of O at the same temperature ( ) H u rms 3R M H u u O rms O rms 3RT M O 3R u H M 3R O M H u O rms u H M M O H (1005) 3 () /3/003 OFB Chapter 5 4 O u rms 64.8ms 1

Speed Distribution Curves Maxwell-Boltzmann speed distribution Temperature is a measure of the average kinetic energy of molecules when their speeds have Maxwell Boltzmann distribution. I.e., the /3/003 OFB Chapter 5 43 molecules come to thermal equilibrium.

Gaseous Diffusion Rate of effusion of A u A rms Rate of effusion of B u B rms Rate of Rate of 3RT M 3RT M M M Eff Eff A B enrichment factor /3/003 B OFB Chapter 5 44 A A B u u A rms B rms

Exercise 5-13 A gas mixture contains equal numbers of molecules of N and SF 6. A small portion of it is passed through a gaseous diffusion apparatus. Calculate how many molecules of N are present in the product of gas for every 100 molecules of SF 6. /3/003 OFB Chapter 5 45

Exercise 5-13 A gas mixture contains equal numbers of molecules of N and SF 6. A small portion of it is passed through a gaseous diffusion apparatus. Calculate how many molecules of N are present in the product of gas for every 100 molecules of SF 6. enrichment factor M M B A 3 + (6 x 19) x 14.8 100 moleculessf x.8 8 molecules of /3/003 OFB Chapter 5 46 6 N

Skip Section 5-8 Real Gases /3/003 OFB Chapter 5 47

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Chapter 5 The Gaseous State Examples / Exercises 5-1 thru 5-13 Problems 34, 38, 48, 6, 70, 81 /3/003 OFB Chapter 5 49