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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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overview
Overview
  • Pressure
    • Barometer & Atmospheric Pressure
  • Standard Conditions
  • Gas Laws
    • Boyle’s Law
    • Charles’ Law
    • Avogadro’s Law
    • Ideal Gas Law
slide3
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
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
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)
slide6
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
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
  • Avogadro’s Law
    • V µ n constant P, T
    • volume increases as moles of gas (n) increases
slide8
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)
slide9
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
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
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
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

slide13
P1 = n1 therefore P1 = n1 PTPT nT nTn1 = X1 mole fractionnTP1 = X1 PT
kinetic molecular theory
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
slide15
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

slide16
Effusion/Diffusion
    • small molecules will effuse/diffuse faster than large molecules
    • effusiondiffusion
slide17
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
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
slide19
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

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