Gas Laws Chapters 10

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Gas LawsChapters 10 11

• Pressurechemical, physical and conversions
• Boyles Law
• Charless Law
• Combined Gas Law

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Chemical Properties Produce Gases

• Chemists harness chemical properties to produce a
  desired gas through chemical reactions. Such as
  the reaction of zinc and hydrochloric acid.

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Physical Properties of Gases

• Gases are
• compressible and they assume the shape and volume
  of any container.
• infinitely soluble in one another.

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Physical Properties of Gases are affected by
temperature and pressure
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Pressure

• The mercury in the inverted tube is pushed upward
  by the force of atmospheric pressure pushing down
  on the surface of the mercury in the dish. The
  height of the mercury in the tube changes with
  changing atmospheric pressure. Under conditions
  of standard atmospheric pressure, the height of
  the mercury in the tube is 760 mm. (1 atm 760
  mm Hg 760 torr 101.3 kPa)

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Collisions cause Pressure

• The pressure of a gas is caused by the collision
  of molecules against the sides of the container.

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Low Pressure vs. High Pressure inside a System

• The number of collisions of gas molecules
  against the wall of the container determines the
  pressure in the container. Notice the difference
  in the number of collisions. Figure (a) would
  have a lower pressure than Figure (b).

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Pressure Practice

• Convert the following
• 145 mm Hg into bars
• 450 psi into kPa
• 900 mm Hg into torrs
• 4580 Pa into kPa

• 5. 25 psi into atm
• 6. 150 atm into Pa
• 109 kPa into atm
• 76.9 mm Hg into bars
• 98.6 torr into kPa
• 3 atm into kPa

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Answers

• 0.19 bars
• 3102.4 kPa
• 900 torr
• 4.58 kPa
• 1.7 at5m
• 15199108.32 Pa

• 0.10 bars
• 13.14 kPa
• 303.98 kPa
• 1.08 atm

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Robert Boyle

• Robert Boyle, an Irish chemist (1627-1691),
  performed the first quantitative experiments on
  gases used a j-shaped tube to study the
  relationship between the pressure of the trapped
  gas and its volume.

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Boyles Law

• Boyles Law states that at constant temperature
  the volume of a fixed amount of gas is inversely
  proportional to its pressure.
• Boyles Law
• P1V1 P2V2

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Boyle Proves Changes in Pressure cause Changes in
Volume

• As the pressure in a closed system (like a
  piston) decreases, the volume of the gas inside
  the system increases. The pressure in the system
  decreases exponentially. Proving an indirect
  relationship.

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Example

• Sulfur dioxide (SO2), a gas, that plays a central
  role in the formation of acid rain, is found in
  the exhaust of automobiles and power plants.
  Consider a 1.53 L sample of gaseous SO2 at a
  pressure of 5.6 x 103 Pa. If the pressure is
  changed to 1.5 x 104 Pa at a constant
  temperature, what will be the new volume of the
  gas?

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Solution

• P1V1 P2V2
• P1 5.6 x 103 Pa P2 1.5 x 104 Pa
• V1 1.53 L V2 ?
• Rearrange the formula to isolate V2.
• P1V1 (5.6X 103 Pa)(1.53 L) O.57 L
• P2 (1.5 X 104 Pa)

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Does Boyles law really work?

• Since Boyles experiments (only three centuries
  of technological advances!) we have found that
  his law only holds precisely at very low
  pressures.
• We describe a gas that strictly follows Boyles
  law an ideal gas.

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Jacques Charles

• In the century following Boyle, a French
  physicist, Jacques Charles (1746-1823), was the
  first person to fill a balloon with hydrogen gas
  and who made the first solo balloon flight.

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Charless Law

• Charless Law states that at constant pressure
  the volume of a fixed amount of gas is directly
  proportional to its absolute temperature.

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Volume vs. Temperature Charles Law

• Notice the linear relationship. This
  relationship between temperature and volume
  describes a direct relationship. This means
  when temperature increases, so does the volume.

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The importance of 0 Kelvin

• At temperatures below 0 K, the extrapolated
  volume of gases would be negative. The fact that
  a gas cant have a negative volume tells us 0 K
  has a special significance.
• Absolute temperature is measured in Kelvins. At
  0 K, all motion of any atom or bond ceases,
  therefore producing no energy. Temperatures of
  approximately 0.000001K have been produced in
  laboratories, but 0 K has never been reached.

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Example

• A sample of a gas at 15C and 1 atm has a volume
  of 2.58 L. What volume will the gas occupy at
  38C and 1 atm?
• (NOTE The pressure did not change. So you do
  not need to worry about it!)

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Solution

• V1 V2 Dont forget to convert C to
  K
• T1 T2
• V1 2.58L V2?
• T1 15C288K T2 38C311K
• Rearrange to solve for V2.
• V1T2 (2.58L)(311K) 2.79 L
• T1 (288K)

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The Combined Gas Law

• The combined gas law was derived from Boyles and
  Charless work. A direct relationship was
  observed. As temperature increased, volume
  increased. As volume increased pressure
  increased. This resulted in a combined formula
  to calculate changes observed in a gas due to
  changes in either temperature, pressure or volume.

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Combined Gas Law Equation

• By combining the equation for Boyles Law and
  Charless Law. We derive the Combined Gas Law
  Equation where

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Example

• A sample of a gas at 15C and 2.0 atm has a
  volume of 2 mL. What volume will the gas occupy
  at 38C and 1 atm?

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Solution

• P1V1 P2 V2 Dont forget to convert
  Temperatures!
• T1 T2
• P1 2 atm P2 1 atm
• V12 mL V2?
• T115C288K T238C311K
• Rearrange to solve for V2!
• V2 P1V1T2 (2 atm)(2 mL)(311K) 4.32 mL
• T1P2 (288K)(1
  atm)

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Summary

• Boyles Law Inverse relationship
• when P?V? and if P?V?
• Charless Law -- Direct relationship
• When V?T? and if
  V?T?