Chapter.10 Gases

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Chapter.10 Gases

• Soo Jeon

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10.1 Characteristics of Gases

• Gases
• are composed entirely of nonmetal elements.
• expand spontaneously to fill its container(
  volume of gas volume of its container).
• are highly compressible.
• form homogeneous mixtures with each other
  regardless of the identities.
• molecules are far apart.
• different gases behave similarly.

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10.2 Pressure

• Pressure conveys the idea of a force, a push that
  tends to move something else in a given
  direction.
• Pressure Force / Given area
• Force(Newton) Mass Acceleration)
• Pressure 1105 N/1m2 1105N/M
• 1105Pascal 100 kpa 1 bar
• Blaise Pascal(1623-1662) French Scientist,
  discovered pascal(N/m2)

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Standard temperature and pressure

• STP Typical pressure at sea level.
• At STP
• 1) Pressure 1atm 760mmHg 760 torr
• 1.01325105 pa 101.325 kpa.
• 2) 1 mole of gas occupies 22.4 liters.

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Tools for measuring atmospheric pressure

1. Mercury barometer height of mercury column
   changes as the atmospheric pressure changes.
2. Manometer measures the pressure of enclosed
   gases. Difference in the heights of mercury
   levels in the two arms of the manometer relates
   the gas pressure. If the pressure of enclosed gas
   is less than atmospheric pressure, the mercury
   will be higher in the arm exposed to the enclosed
   gas. Pgas Patm P (difference in height of
   arms)

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Problems 1

• Convert
• a) 0.357atm to torr.
• b) 6.610-2 torr to atm.
• c) 147.2kPa to mmHg.

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Solution 1

• (0.357atm)(760torr/1atm) 271 torr
• (6.610-2torr)(1atm/760torr)
• 8.710-5atm
• (147.2kPa)(760mmHg/101.325kPa)
• 1104torr

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10.3 The Gas Laws

• Boyles Law( the pressure-volume Relationship)
  when a volume of gas is compressed, the pressure
  of gas increase. The volume of a fixed quantity
  of gas maintained at constant temperature is
  inversely proportional to the pressure.
• British Chemist Robert Boyle(1627-1691) first
  investigated the relationship between pressure of
  gas and volume.

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• V constant (1/p)
• PV Constant

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Charless Law (temperature volume)

• Charless Law the volume of a fixed amount of
  gas maintained at constant pressure is directly
  proportional to its absolute temperature.
• French Scientist Jacques Charles (1746-1823)
  found that volume of fixed quantity of gas at
  constant pressure increases linearly with
  temperature.

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• In 1848 William Thomson(1824-1907) proposed an
  absolute temperature scale, Kelvin.
• Absolute zero -273.15C.

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Avogadros Law

• In 1808, Gay Lussac(1778-1823) observed the law
  of combining volumes at a given pressure and
  temperature, the volumes of gases that react with
  one another are in the ratios of small whole
  numbers.

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• Avogadro interpreted Lussacs observation and
  concluded.
• Avogadros law The volume of a gas maintained
  at constant temperature and pressure is directly
  proportional to the number of moles of the gas.
• Volume constant X n
• STP 22.4L, 0C, 6.021023 molecules,
• 1atm

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10.4 The Ideal-Gas Equation

• Ideal-gas equation
• PressureVolume of moles R(0.0821L-atm/mol-K
  ) temperature
• Ideal gas is STP.
• The ideal-gas equation does not always accurately
  describe real gas.
• P1/T1P2T2, P/TnR / V,
• P1V1/T1 P2V2/T2

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Problem 2

• An ideal gas is contained in a 5.0L chamber at a
  temperature of 37C. If the gas exerts a pressure
  of 2.0atm on the walls the chamber, what
  expression is equal to the number of moles of the
  gas?

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Solution 2

• n PV/RT
• (2.0atm)(5.0L)/(0.0821L-atm)(310K)
• moles

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Problem 3

• A 0.5 mol sample of oxygen gas is confined at 0C
  in a cylinder with a movable piston. The gas has
  an initial pressure of 1.0atm. The gas is then
  compressed by the piston so that its final volume
  is half the initial volume. The final pressure of
  gas is 2.2atm. What is the final temperature?

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Solution 3

• 1atm XL/ 273K
• 2.2atm .5XL/temperature
• X/273 1.1X/temperature
• 300.3K 27C

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10.5 Further Applications of the Ideal-gas
equation

• Gas densities and molar mass(M)
• nM/V PM/RT
• moles/Liter grams/mole grams/liter
• density(g/L)
• M dRT / P
• Density PM/RT
• 1) higher the molar mass and pressure, the
  more dense the gas
• 2) higher temperature, less dense gas

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Problem 4

• Molar mass is 28.6g/mol, temperature is 95K, and
  the pressure is 1.6atm. Calculate the density

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Solution 4

• D PM/RT (28.6g/mol)(1.6atm)/(0.0821L-atm/mol-k
  )(95K) 5.9 g/L

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Problem 5

• Find the molar mass of an unknown gas. First, a
  large flask is evacuated and found to weigh
  134.567g. Its then filled with the gas to a
  pressure of 735torr at 31 and reweighed. Its
  mass is now 137.456g. Finally, the flask is
  filled with water at 31C and found to weigh
  1067.9g.(the density of the water at this
  temperature is 0.977g/ml.) calculate the molar
  mass of unknown gas.

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Solution 5

• The mass of the gas 137.456g 134.567g
  2.889g
• The mass of water 1067.9g 134.567g 933.3g
• Volume of flask m/d (933.3g)/(0.997g/ml)
  936 ml
• So, the density of the gas 2.889g/0.936L
  3.09g/L
• Molar mass of the gas dRT/ P
• (3.09g/L)(0.0821L-atm/mol-K)(304K)/(735/760)atm
  
• 79.7 g/mol

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Problem 6

• Volumes of Gases in Chemical Reactions
• Ammonia reacts with oxygen gas at 850C and
  5.00atm in the presence of a suitable catalyst.
  The following reaction occurs
• 4NH3(g) 5O2 ? 4NO(g) 6H20(g)
• How many liters of NH3 at 850C and 5.00atm are
  required to react with 1.00mol of 02 in this
  reaction?

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Solution 6

• 850C 1123K, 5atm, 1 mol of O2
• V nRT/P
• (1mol of O2)(0.0821L-atm/mol-)(1123K)/ (5atm)
  18.4 L
• 18.4L of O2 (4 mol NH3)/(5 mol O2)
• 14.8L of NH3

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10.6 Gas Mixtures and Partial Pressures

• John Dalton(1766-1844), English chemist, tells us
  that the total pressure of mixture of gases is
  just the sum of all the partial pressures of the
  individual gases in the mixture.
• Daltons Law Ptotal Pa Pb ..
• Ptotal of toal moles(RT/V)

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Problem 7

• A gaseous mixture made from 6.00g O2 and 9.00g
  CH4 is placed 15L . What is partial pressure of
  each gas and total pressure?

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Solution 7

• nO2 (6.00g O2)(1molO2/32.0g O2)0.188mol O2
• nCH4 (9.00gCH4)(1molCH4/16g CH4) 0.563mol
• PO2 no2 RT/ V (0.188mol)(0.0821)(273K)/(15L)
• 0.281atm
• PCH4 (0.563mol)(0.0821)(273K)/(15L)
• 0.841atm
• Pt 0.281atm 0.841atm 1.122atm

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Partial pressures and mole fraction

• P1/Pt (nRt/V)/(ntRT/V) n1/nt
• P1 (n1 / n total)Pt X Pt
• Thus, the partial pressure of a gas in a mixture
  is its mole fraction times the total pressure.

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Problem 8

• The atmosphere is composed of 1.5mol percent CO2,
  18.0mol percent O2, and 80.5 mol percent Ar. a)
  calculate the partial pressure of O2 in the
  mixture if the total pressure is 745torr. b) if
  this atmosphere is to be held in a 120L space at
  295K, how many moles of O2 are needed?

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Solution 8

• a) PO2 (0.180(745torr) 134torr
• b) PO2 (134torr)(1atm/760torr)0.176atm
• V 120L, T 295K
• nO2 PO2(V/RT) (0.176atm)(120L)/(0.0821L-atm/
  K-mol)(295K) 0.872mol

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Collecting gases over water

• The volume of gas collected is measured until the
  inside water levels and outside the bottle are
  same.
• The total pressure inside is the sum of the
  pressure of gas collected and pressure of water
  vapor in equilibrium with liquid water.
• Ptotal Pgas Pwater

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Problem 9

• Ammonium nitrate, NH4NO2, decomposes upon heating
  to form N2 gas.
• NH4NO2? N2 2H2O
• When a sample of NH4NO2 is decomposed in a test
  tube, 511ml of N2 gas is collected over water at
  26C and 745torr total pressure. How many grams
  of NH4NO2 were decomposed?

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Solution 9

• Pressure of water vapor 25torr
• 745torr 25torr 720torr
• Number of moles N2 PV/RT
• (720torr(1atm/760torr)(0.511L)
• /(0.0821)(299K) 0.0197 mol N2
• 0.0197molN2(1molNH4NO2/1Mol N2) (64.04g
  NH4NO2/1molNH4NO2) 1.26g NH4NO2

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10.7 kinetic-Molecular Theory

• Kinetic molecular theory developed over 100
  years, culminating in 1857 when Rudolf
  Clausius(1822-1888) published a complete thm
• 1)The volume of an ideal gas particle is
  insignificant when compared with the volume of
  its container.

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• 2) Attractive and repulsive forces between gases
  molecules are negligible.
• 3) Energy can be transferred during collision,
  but the average kinetic energy does not change.
• 4) The average kinetic energy of molecules is
  proportional to the absolute temperature.

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Continued..

• Root mean square(rms) speed, u,
• the speed of a molecule possessing K.E
• Average kinetic energy of gas mole(J)
• m mass of mole(kg) u speed of mole(m/sec)
• ?K.E increases with increasing temperature
  implies that rms speed increases as temperature
  inreases.

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Total Kinetic Energy of gas sample

• Total KE (3/2)nRt
• R 0.0821L-atm/K-moles
• t temperature (K)
• n number of moles

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Application to the gas law

1. At a constant temperature, if the volume is
   increased , the molecules must move a longer
   distance between collision. So, the pressure
   decreases.
2. An increase in temperature means in the average
   kinetic energy of the molecules, and thus
   increase in rms(speed).

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Problem 10

• How is the rms speed of N2 molecules in a gas
  sample changed by
• a) increase in temperature
• b) increase in volume of sample
• c) mixing with a sample of Ar at same temperature

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Solution 10

• A) increase
• B) no change
• C) no change

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10.8 molecular Effusion and Diffusion

• Grahams law of Effusion In 1846, Thomas Graham
  discovered that the effusion rate of gas is
  inversely proportional to the square root of its
  molar mass.
• Average speed of gas
• Lighter molecules move faster than heavier
  molecules.
• M is molar mass

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Problem 11

• An unknown gas composed of homonuclear diatomic
  molecules effuses at a rate that is only
  0.355times that of O2 at the same temperature
  what is the gas?

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Solution 11

• r1 0.355 r2
• r1/r2 0.355 square root of(32g/mol)/M1
• (32g/mol)/M(0.355)20.126
• M1 (32g/mol)/(0.126) 254g/mol
• Only di iodine has this atomic weight.

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Diffusion and mean free path

• Diffusion spread of one substance throughout a
  space or a second substance.
• Diffusion of gas is slower than molecular
  speed, because of molecular collision.
• Mean free path the average distance traveled by
  a molecule between collisions.
• the mean free path for air molecules at sea
  level is about 60nm.

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10.9 Real Gases deviation from ideal behavior

• Real molecules do have finite volumes and they do
  attract one another.
• The difference that remains at high temperature
  stems mainly from the effect of the finite volume
  of the molecuels.

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The Van der Waals Equation

• Johannes van der Waals(1837-1923) proposed the
  useful equation to predict the behavior of real
  gases.
• Ideal gas P nRT/V
• According to Van der Waals

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• Both a and b are given. A has units of
  L2-atm/mol2.
• Van der Waals equation

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Problem 12

• If 1.00mol of an ideal gas were confined to
  22.41L at 0?,it would exert a pressure of
  1.00atm. Use Van der Waals equation to estimate
  the pressure exerted by 1.00mol of Cl2 in 22.4L
  at 0?.

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Solution 12

• n 1mol, R 0.0821, T273K, V22.4L
• a 6.49L2atm/mol, b 0.0562L2atm/mol
• P (1mol)(0.0821)(273.2)/22.4-(1)(0.0562)
• -(12)(6.49)/(22.4)2
• 1.003 atm 0.013atm 0.990atm

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Work cite

• www.google.com
• http//www.molecularsoft.com/help/Gas_Laws-Real_Ga
  s.htm
• www.yahoo.com