Chapter 10:

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# Chapter 10: - PowerPoint PPT Presentation

Chapter 10:. Gases. Overview. Pressure Barometer & Atmospheric Pressure Standard Conditions Gas Laws Boyle’s Law Charles’ Law Avogadro’s Law Ideal Gas Law. Gas Laws under Two Conditions Gas Densities Darlton’s Law of Partial Pressure Kinetic Molecular Theory

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Presentation Transcript
Overview
• Pressure
• Barometer & Atmospheric Pressure
• Standard Conditions
• Gas Laws
• Boyle’s Law
• Charles’ Law
• Ideal Gas Law
Gas Laws under Two Conditions
• Gas Densities
• Darlton’s Law of Partial Pressure
• Kinetic Molecular Theory
• Molecular Effusion/Diffusion
• Graham’s Law
• Deviation from Ideality
Characteristics
• Solids
• have own shape and volume
• particles close together with strong interaction
• Liquids
• have own volume but assume shape of container
• particles farther apart but have moderate interaction
• Gases
• assume shape and volume of container
• particles far apart with little/no interaction
• highly compressible
Pressure
• P = F/A
• Force in Newtons
• Area in m2
• Barometer
• P in N/m2 = Pascal unit
• 1 x 105 N/m2 = 1 x 105 Pa or 100 kPa
• Standard Pressure
• 1 atm = 760 mm Hg = 1.01325 x 105 Pa = 101.325 kPa (or torr)
force of the atmosphere

force of the column

h

when atmospheric force equals the force of the column the atmospheric pressure is measured as “h”

Gas Laws
• Boyle’s Law
• P µ 1/V constant T, n
• volume increases as pressure decreases
• Charles’ Law
• V µ T constant P, n
• volume increases as temperature increases
• V µ n constant P, T
• volume increases as moles of gas (n) increases
Ideal Gas Law
• combines all gas laws PV = nRT
• R = 0.0821 L-atm mol-K
• any volumes must be in liters
• any temperatures must be in kelvin
• any pressures must be in atmospheres
• STP or SC -- standard temperature/pressure
• P = 1 atm (same as 760 mm Hg)
• T = 273 K (same as 0° C)
Problem 10.3: A flashbulb contains 2.4 x 10 -4 mol of O2 gas at 1.9 atm and 19°C . What is the volulme?
• PV = nRT or V = nRT P
• V = 2.4x10 -4 mol x 0.0821 L-atm x 292 K mol-K 1.9 atm

V = 3.0 x 10 -3 L or 3.0 mL or 3.0 cm3

Gas Laws Under Two Conditions
• P1V1 = P2V2 T1 T2
• Problem 10.4: Pressure in a tank is kept at 2.20 atm. When the temp. is -15°C the volume is 28,500 ft3. What is the volume is the temp. is 31°C
• P1 = P2 = 2.20 atm T1 = 258 K T2 = 304 K V1 = 28,500 ft3
• V2 = P1 V1 T2 P2 T1
• V2 = 28,500 ft3 x 304 K = 258 K

33,600 ft3

Gas Densities
• n = P from PV = nRT V RT
• n = moles x g/mol = g = d = PMMV L L RT
• d = PMM RT

(atm)g mol L atm ( K)mol K

Dalton’s Law of Partial Pressures
• total pressure of a mixture = sum of each partial pressure
• PT = P1 + P2 + P3 . . . .
• each partial pressure = the pressure each gas would have if it were alone
• P1 = n1RT P2 = n2RT P3 = n3RT V1 V2 V3
• PT = n1RT+ n2RT + n3RT = (n1 + n2 + n3) RT V1 V2 V3 V

volumes are the same

P1 = n1 therefore P1 = n1 PTPT nT nTn1 = X1 mole fractionnTP1 = X1 PT
Kinetic Molecular Theory
• Gases consist of particles in constant, random motion
• Volume of gas particles is negligible
• Attractive and repulsive forces are negligible
• Average kinetic energy is proportional to temperature
• Collisions are elastic
molecular speed
• u = root mean square speed or speed of molecule with average kinetic energy
• R is the gas constant (8.314 J/mol-K), T is temp. in K & MM is molar mass
• What is the rms speed of an He atom at 25°C?
• u = (3 x 8.314 kg-m2/s2-mol-K x 298 K)1/2 ( 4.00 x 10 -3 kg/mol )
• u =

1.36 x 103 m/s

Effusion/Diffusion
• small molecules will effuse/diffuse faster than large molecules
• effusiondiffusion
Graham’s Law
• where r is rate of speed & MM is the molar mass
• Problem 10.14: Calculate the ratio of the effusion rates of N2 and O2.

rN2 = 1.07 rO2

Deviation from Ideality
• Occurs at very high pressure or very low temperature
• Correction due to volume
• ideal law assumes molecules have no volume
• for molecules which are far apart, this is a good assumption
• must correct for the volume of the molecules themselves
Correction due to attraction of molecules
• ideal law assumes the molecules have no attraction to each other
• for molecules which are far apart, this is a good assumption
• must correct for actual attraction of molecules

correction for molecular volume

correction for molecular attraction