Gases and gas laws

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Gases and gas laws

• Chapter 12

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Key concepts

1. Understand basic characteristics of gases.
2. Know the definition of pressure and measurement
   units commonly used with pressure
3. Know what a barometer measures.
4. Know the relationships described by Boyles Law,
   Charles Law, and Avogadros Law.
5. Know the ideal gas equation and its derivation.
6. Understand gas density and using molar masses in
   the ideal gas equation.
7. Understand Daltons law of partial pressures and
   its applications.
8. Know the basic principles of the kinetic theory
   of gases and how this explains gas behavior
   described by the ideal gas laws.
9. Know the terms effusion and diffusion know
   Grahams law of effusion.
10. Understand gas interactions that cause deviations
    from ideal gas law behavior.

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Common characteristics of gases (uniquely
different from liquids or solids)

• All gas mixtures are homogeneous mixtures.
• Gases expand to fill the container they occupy
• the volume of EACH GAS in a mixture of gases in a
  container volume of the container.
• The actual space occupied by the gas molecules is
  small relative to the total volume.

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Pressure

• Force applied per unit area
• P F/A
• The same force may result in much different
  pressures

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Pressure units

• pounds per square inch (psi)
• inches of mercury (in Hg)
• mm Hg
• Pascals (SI units)
• torr (from Torricelli, inventor of the barometer)
  
• 1 torr 1 mm Hg
• standard atmospheric pressure
• 760 torr 1 atmosphere (atm) typical pressure
  at sea level.
• conversions
• 1 atm 760 torr 1.01325 ? 105 Pa 14.7 psi

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The barometer

• Mercury barometer
• atmospheric pressure ? force applied on Hg ?
  the change in height of mercury column.

http//www.usatoday.com/weather/wbaromtr.htm
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Basic Gas Laws

• Relationships between gas pressure, temperature,
  volume, and amount (moles).
• Now, lets have some fun.

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Boyles Law

• Boyles law relates to changes in pressure and
  volume.
• At constant temperature, the change in pressure
  is ________ proportional to the change in volume.

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Charles Law

• Charles Law relates changes in volume and
  temperature
• At constant pressure, the change in volume is
  _______ proportional to the change in temperature

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Avogadros Law

• Identical volumes of a gas at the same
  temperature and pressure have the same number of
  gas particles.

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Summary

• P ? 1/V (constant n and T) (Boyle)
• V ? T (constant n and P) (Charles)
• V ? n (constant T and P) (Avogadro)
• Combined, we get.

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PVnRT the ideal gas equation

• Gases that can have their temperature, volume,
  and pressure characteristics completely described
  by this equation are called ideal gases.
• R the gas constant. Its units vary depending
  on the units of P, V, and T.
• If
• P is in atm,
• V is in L,
• T is in K,
• STP standard temperature and pressure. Defined
  as 1 atm and 0 ?C (273.15 K).
• What is the molar volume of a gas at STP?

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Using ideal gas equation to represent gas laws.

• Boyles Law.
• PV nRT
• P and V will change, but n, R and T are constant.

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• Charles Law
• PV nRT
• V and T will change, but n, R, and P are constant.

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• P, V, and T all change, but n is constant
• PV nRT

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More applications of the ideal gas equation.

• Obtaining the density of a gas
• from PV nRT
• d PM/RT (where M is the molar mass)

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volumes of gases in chemical reactions.

• air bags.
• 2 NaN3(s) ? 2 Na (s) 3 N2 (g)
• air bag volume 36 L pressure 1.15 atm
  temperature 26.0 ?C. How much NaN3, in g, needed?

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• 2 KClO3 (s)? 2 KCl (s) 3 O2 (g)
• volume of O2 produced when 1.50 g KClO3
  decomposes?

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Gas mixtures and partial pressures

• Daltons Law of partial pressures
• from PV nRT.
• Ptotal P1 P2 P3 .
• collecting gases over waterthe gas is not alone.

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Kinetic molecular theory of gases.

• An explanation of what happens at the molecular
  level that causes the observations in the ideal
  gas laws.
• Gases consist of large numbers of molecules in
  continuous random motion.
• The volume of all the molecules of gas is
  negligible compared to the total volume (i.e.,
  each gas molecule is basically an infintessimally
  small dot).
• Attractive and repulsive forces between molecules
  are negligible.

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• Energy transitions between molecules are
  perfectly elastic. The average kinetic energy of
  the molecules will not change over time as long
  as the temperature stays constant.
• The absolute temperature is proportional to the
  average kinetic energy of the gas. At any given
  temperature all gases in the mixture have the
  same average kinetic energy.
• KE ½ mu2. u the root mean square (rms) speed
  of the gas. (root mean square is an averaging
  technique, though it is not the same as the
  average)

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The kinetic theory explains the gas law

• Important observations
• volume increases at constant temperature (Boyles
  law). Molecules must travel further to reach the
  wall of a larger container. Thus, collisions
  against the container wall are less frequent, the
  pressure therefore drops.
• Temperature increases at constant volume
  (Charles Law). when temperature (and kinetic
  energy) increase, the speed of the molecules
  increases. Faster molecules collide with the
  container walls more often, so pressure
  increases.

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Effusion and diffusion

• effusion
• diffusion
• Lighter molecules move faster than heavier
  molecules

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Grahams Law of effusion

• the rate of effusion is twice as fast for r1 if
  M1 is 4 times lighter than M2.

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Diffusion vs. effusion

• Diffusion is complicated by the presence of other
  molecules. The mean free path is a determining
  factor.
• Mean free path

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Real gases

• Assumptions in kinetic theory of gases not always
  valid.
• Molecules are not infinitely small
• Attractive and repulsive forces are not
  negligible.
• Collisions are not always elastic.

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Deviations from ideality

• for one mole of an ideal gas (n1). PV/RT always
  1.
• For ANY amount of ideal gas, PV/nRT 1
• However, for real gases, PV/nRT doesnt always
  1.
• Ideal gas equation is better in some regions than
  in others.

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Deviations more likely to occur at

• low temperature Molecules moving slower,
  intermolecular forces become a greater factor
  (especially near liquid/gas interface).
• Higher pressure Molecule size becomes an
  greater factor interfering with travel of
  molecules.
• Corrections to ideal gas equation are made to
  take this into account.
• Van der Waals equation is one example