Gas Notes (Chapter 10) Part 1

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Gas Notes (Chapter 10)Part 1
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• Gases are made up of atoms and molecules just
  like all other compounds, but because they are in
  the form of a gas we can learn a great deal more
  about these molecules and compounds. It might
  seem a bit confusing because we cant see most
  gases, but we know they exist.

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I. Lets look at some of the Nature of Gases

• 1. Expansion gases do NOT have a definite
  shape or volume.
• 2. Fluidity gas particles glide past one
  another, called fluid just like a liquid.
• 3. Compressibility can be compressed because
  gases take up mostly empty space.
• 4. Diffusion gases spread out and mix without
  stirring and without a current. Gases mix
  completely unless they react with each other.

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II. Kinetic Molecular Theory of Gases

• Particles of matter (any type) are in constant
  motion! Because we know this we have a few
  assumptions that we make about gases, called the
  Molecular Theory of Gases

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• 1. Particles of a gas are in constant,
  straight-line motion, until they collide.
• 2. Gases consist of a large number of tiny
  particles these particles are very far apart,
  therefore gas is mostly empty space.
• 3. Collisions between particles of a gas and the
  container wall are elastic. Which means there is
  no loss of energy.

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• 4. There are no forces of attraction or
  repulsion between particles of gases.
• http//www.bcpl.net/kdrews/kmt/kmtpart4.htmlPart
  204
• 5. The average kinetic energy of gas particles
  depends on the temperate of the gas. KE1/2 mv2
  (mmass in kg and vvelocity is m/sec)
• http//www.bcpl.net/kdrews/kmt/kmtpart5.htmlPart
  205

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III. Ideal VS Real Gases

• Ideal gases always obey the kinetic theory.
  (Closest to ideal would be the noble gases.)
• Real gases vary from the kinetic theory at
  various temperatures and pressures.

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IV. Volume, Pressure, Temperature, Number of
Moles (Descriptions of Gases)

• 1. Volume refers to the space matter (gas)
  occupies. Measured in liters (L).
• 1L 1000mL

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• 2. Pressure the number of times particles
  collide with each other and the walls of the
  container (force exerted on a given area).
  Measured in atmospheres (atm).
• http//chemmac1.usc.edu/bruno/java/pressure.html
• 1atm 760 millimeters Hg ( Barometers use Hg)
• 1atm 760 torr (Named after Torricelli for the
  invention of the barometer)
• 1atm 101.3 kPa - kilopascals

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• Practice Convert 4.40 atm to mmHg.
• Convert 212.4kPa to mmHg.

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• 3. Temperature as temperate increases gas
  particles move faster, as temperature decreases
  gas particles move slower.
• Measured in Kelvin (K).
• K 273 ?C

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• Practice Convert 32.0C to K.
• Convert 400. K to C.

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• 4. Number of Moles tells you how much of a
  certain gas you have
• 1 mole number of grams of the compound or
  element (molar mass)

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STP standard temperature and pressure which
is 0?C and 1.00 atm.

• V. Gas Laws - How do all of pressure,
  temperature, volume, and amount of a gas relate
  to each other? Rules for solving gas law
  problems 1st write down what is given and what
  is unknown, 2nd identify the gas law you want to
  use, and 3rd rearrange the formula to solve for
  the unknown and then solve the problem. (If
  temperature is involved, it MUST be converted to
  Kelvin! K 273 ?C)

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A. Boyles Law - Pressure and Volume (when
temperature remains constant)

• V1 initial or old volume
• V1P1 V2P2 V2 final or new volume
• P1 initial or old pressure
• P2 final or new pressure
• Inverse Relationship (As pressure increases,
  volume decreases and as pressure decreases,
  volume increases.)

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Pressure and Volume (Boyles Law) Gas
Demonstrations

• Bell Jar Shaving Cream
• As pressure decreases the volume of the gas
  increases.
• Bell Jar Balloon
• Bell Jar Peeps
• Cartesian Diver

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• 1a. A gas occupies 3.00L at 1.00atm of pressure.
  What volume does it occupy at 5.00atm?
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• 2a. What is the new pressure when 80.0mL of gas
  at 500.mmHg is moved to a 100.mL container?
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•  3a. A gas at 800.torr of pressure has a volume
  of 5.00L. What volume does this gas occupy at
  1.00X103torr of pressure?
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B. Charles Law -Volume and Temperature (when
pressure is constant) Figure 10-11 page 316

• V1 V2 T1 initial or old temperature
• T1 T2 T2 final or new temperature
• Direct Relationship (As temperature increases,
  volume increases and as temperature decreases,
  volume decreases.)

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Temperature and Volume (Charles Law) Gas
Demonstrations

• Balloon on Hot Flask
• As temperature of the gas increases the volume
  the gas occupies increases.
• Balloon in Hot Water
• Balloon in Cold Water
• Root Beer Float

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• 1b. A gas has a volume of 500.mL at 298K. What
  volume does it have at 373K?
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• 2b. A gas had a volume of 250.mL and a
  temperature of 125?C. What is the final
  temperature (in K) if the volume is changed to
  100.mL?
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• 3b. This initial volume of a gas is 250.mL at
  30.0?C. What is the temperature of the gas with
  a new volume of 667mL?

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C. Gay-Lussacs Law - Pressure and Temperature
(when volume is constant)

• P1 P2
• T1 T2
• Direct Relationship (As temperature increases,
  pressure increases and as temperature decreases,
  pressure decreases.)

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Temperature and Pressure (Gay-Lussacs Law) Gas
Demonstrations

• Inverted Fountain
• As the temperature of the gas increases the
  pressure of the gas increases. (Inverting the
  flask into the water showed that the pressure
  increased because water was pulled into the
  flask.)

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• 1c. The gas in an aerosol can is at 3atm of
  pressure at 298K. What would the gas pressure in
  the can be at 325K?
• 2c. At 120.?C the pressure of a sample of
  nitrogen gas is 769torr. What will the pressure
  be at 205?C?
• 3c. A gas at 32.0?C has a pressure of 0.0400atm.
  If the temperature increases to 44.0?C what is
  the new pressure of the gas?

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D. Combined Gas Law - Pressure, Temperature, and
Volume (None of the variables are constant)

• V1P1 V2P2
• T1 T2

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• 1d. A helium filled balloon has a volume of
  50.0mL at 298K and 1.08atm. What volume will it
  have at 0.855atm and 203K?
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•  2d. Given 700.mL of oxygen at 7.00?C and
  7.90atm of pressure, what volume does is occupy
  at 27.0?C and 4.90atm of pressure?
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• 3d. A gas has a volume of 1.140L at 37.0?C and
  620.mmHg. Calculate its volume at 0?C and
  760.mmHg.

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• Gas Worksheet 1 is due next class!

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E. Daltons Law of Partial Pressures
The pressure of each gas in a mixture is called
the partial pressure of that gas. Daltons Law of
Partial Pressure states that the total pressure
of a mixture of gases is equal to the sum of the
partial pressures of the component gases.
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• PT P1 P2 P3 . PT total pressure
• P the partial pressures of the individual
  gases

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• 1e. A mixture of gases has the following partial
  pressure for the component gases at 20.0?C in a
  volume of 2.00L oxygen 180.torr, nitrogen
  320.torr, and hydrogen 246torr. Calculate the
  pressure of the mixture.
• 2e. What is the final pressure of a 1.50L
  mixture of gases produced from 1.50L of neon at
  0.3947atm, 800.mL of nitrogen at 150.mmHg and
  1.2oL of oxygen at 25.3kPa? Assume constant
  temperature. (Hint use Boyles law.)

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Daltons Law applied to Gases Collected by Water
Displacement Figure 10-15 page 324

• Patm or PT Pgas PH2O
• Patm or PT barometric pressure or total
  pressure
• Pgas pressure of the gas collected
• PH2O vapor pressure of water at specific
  temperature (Found on page 899 of you textbook.)

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• 3e. Oxygen gas from the decomposition reaction
  of potassium chlorate was collected by water
  displacement at a pressure of 731torr and a
  temperature of 20.0?C. What was the partial
  pressure of the oxygen gas collected?
• 4e. Solid magnesium and hydrochloric acid react
  producing hydrogen gas that was collected over
  water at a pressure of 759mmHg and measured
  19.0mL. The temperature of the solution at which
  the gas was collected was 25.0?C. What would be
  the pressure of the dry hydrogen gas? What would
  be the volume of the dry hydrogen gas at STP?

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F. Ideal Gas Law (PV nRT) to use this law,
all units must be as follows

• P pressure in atm
• V volume in liters
• n number of moles
• T temperature in Kelvin
• R (0.0821L) (1atm)
• (1mol) (1K)
• R is the ideal gas constant (page 342 in book
  describes where this constant came from.)

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• 1f. How many moles of CH4 gas are there in 85.0L
  at STP?
• 2f. What volume will be occupies by 1.50grams of
  nitrogen monoxide gas at 348K and pressure of
  300.mmHg?
• 3f. A volume of 11.2L of a gas at STP has how
  many moles?

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G. Solving for Density and /or Molar Mass of a
gas using the Ideal Gas Law

• 1. Density (units are g/L) Use the Ideal Gas Law
  to find moles (n), convert n to grams OR use the
  Ideal Gas Law to find the volume. Divide n (in
  grams) by the volume.

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• 1g. What is the density of a sample of ammonia
  gas, NH3, if the pressure is 0.928 atm and the
  temperature is 63.0?C?
• 2g. What is the density of argon gas at a
  pressure of 551 torr and a temperature of 25.0?C?

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• 2. Molar Mass (units are g/mol) If density is
  given, use the density of the gas to determine
  the molar mass (use 1 L at the volume and solve
  for n). If a mass is given, use the Ideal Gas
  Law to solve for n and then find the molar mass.

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• 3g. The density of a gas was found to be 2.00g/L
  at 1.50atm and 27.0?C. What is the molar mass of
  the gas?
• 4g. What is the molar mass of a gas if 0.427g of
  the gas occupies a volume of 125mL at 20.0?C and
  0.980atm?

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H. Molar Volume of Gases

• Recall that 1 mole of a compound contains 6.022 X
  1023 molecules of that compound it doesnt
  matter what the compound is. One mole of any
  gas, at STP, will occupy the same volume as one
  mole of any other gas at the same temperature and
  pressure, despite any mass differences. The
  volume occupied by one mole of a gas at STP is
  known as the standard molar volume of a gas. It
  has been found to be 22.4liters. We can use this
  as a new conversion factor 1mol of gas/22.4L of
  same gas. (Avogadros Law states that equal
  volumes of gases at the same temperature and
  pressure contain equal numbers of molecules.

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• 1h. What volume, in L, is occupied by 32.0 grams
  of oxygen gas at STP?

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I. Stoichiometry of Gases

• Just like mole ratios can be written from an
  equation so can a volume ratio-same concept!
• 2CO(g) O2 (g) ? 2CO2 (g)

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• 1i. Using the above equation, what volume of
  oxygen gas is needed to react completely with
  0.626L of carbon monoxide to form carbon dioxide?
  
• 2i. How many grams of solid calcium carbonate
  must be decomposed to produce 5.00L of carbon
  dioxide gas at STP?
• 3i. How many liters of hydrogen gas at 35.0?C
  and 0.980atm are needed to produce 8.75L of
  gaseous water according to the following
  equation?
• WO3(s) 3H2(g) ? W(s) 3H2O(g)

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J. Grahams Law IV. Effusion and Diffusion

• Grahams Law states that the rates of
  diffusion/effusion of gases at the same
  temperature and pressure are inversely
  proportional to the square roots of their molar
  masses. Effusion is the process whereby the
  molecules of a gas confined in a container
  randomly pass through a tiny opening in the
  container. (onions on page 352)

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• Rate of diffusion/effusion of A v(MB/MA)
  Rate of diffusion/effusion of B
• MA or B molar mass of that compound
• Gas A is the lighter, faster gas
• Rate of diffusion/effusion is the same as the
  velocity (or speed) of the gas.
• After the rates of diffusion/effusion for two
  gases are determined, the gas with the lower
  molar mass will be the one diffusing/effusing
  fastest.

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• 1j. Compare the rates of effusion for hydrogen
  and oxygen at the same temperature and
• pressure. (Which one effuses faster and how much
  faster is it effusing?)
• 2j. A sample of hydrogen effuses through a porous
  container about 9 times faster than an unknown
  gas. Estimate the molar mass of the unknown gas.

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Grahams Law and Time

• Grahams Law and Time the time it takes a gas
  to effuse is directly proportional to its molar
  mass.
• tA MA t time
• tB MB

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• 3j. A sample of an unknown gas flows through the
  wall of a pours cup in 39.9 minutes. An equal
  volume of helium (under same temperature and
  pressure) flows through in 9.75 minutes. What is
  the molar mass of the unknown gas?

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