How Do Gases Behave?

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How Do Gases Behave?
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What is a solid, liquid or gas?

• Help Marvin the Martian understand what a solid,
  liquid and gas are!
• Draw what solids, liquids, gases look like
• Describe physical/chemical properties
• What would happen if we changed pressure?
• What would happen if we changed temperature?

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What is Pressure?

• Pressure Force/Area
• 1 atmosphere (atm)
• 760 Torr
• 760 mmHg
• 1.01 Bar
• 101,327 Pascal
• 101.3 Kpa
• 14.7 lbs/in2
• Measured with
• a barometer

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MANOMETER

• Column of mercury to measure pressure.
• h is how much lower or higher the pressure is
  than outside.
• Pgas Patm - h
• Pgas Patm h

h
h
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What is Temperature?

• Average Kinetic Energy (1/2 mv2) of an atom or
  molecule
• Measured in Fahrenheit, Celsius or Kelvin (SI)
• F (C x 1.8) 32
• K C 273
• 0 Kelvin absolute zero (atom stops moving
  completely)
• Is there a maximum temperature in the universe?

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Kinetic Molecular Theory

• Theory explains why ideal gases behave the way
  they do.
• Assumptions that simplify the theory, but dont
  work in real gases.
• The particles are so small we can ignore their
  volume.
• The particles are in constant motion and their
  collisions cause pressure.
• The particles do not affect each other, neither
  attracting or repelling.
• The average kinetic energy is proportional to the
  Kelvin temperature.
• The molecules move in straight path and all
  collisions are elastic

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What is an Ideal Gas?

• An ideal gas or perfect gas is a hypothetical gas
  consisting of identical particles of
• Negligible volume
• With no intermolecular forces
• Atoms or molecules undergo perfectly elastic
  collisions with the walls of the container
• Ideal gas law calculations are favored at low
  pressures and high temperatures.
• Real gases existing in reality do not exhibit
  these exact properties, although the
  approximation is often good enough to describe
  real gases.

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What is Boyles Law?

• In the mid 1600's, Robert Boyle studied the
  relationship between the pressure P and the
  volume V of a confined gas held at a constant
  temperature.
• Boyle observed that the product of the pressure
  and volume are observed to be nearly constant.
• The product of pressure and volume is exactly a
  constant for an ideal gas.
• P V constant
• This relationship between pressure and volume is
  called Boyle's Law in his honor.

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BOYLES LAW
V
P (at constant T)
10
Slope k
V
1/P (at constant T)
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22.41 L atm
O2
PV
CO2
P (at constant T)
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• 20.5 L of nitrogen at 25ºC and 742 torr are
  compressed to 9.8 atm at constant T. What is the
  new volume?
• P1V1P2V2
• (0.98 atm)(20.5 L) (9.8 atm)(V2)
• 20.09 atmL/9.8 atm V2
• 2.1 L V2
• 30.6 mL of carbon dioxide at 740 torr is
  expanded at constant temperature to 750 mL. What
  is the final pressure in kPa?
• (30.6mL)(740Torr)(750 mL)(P2)
• 22,644 mLTorr/750 mL P2
• 30.2 Torr P2
• (30.2 Torr) (1 atm/760 Torr) (101.3 kPa/1 atm)
• 3059.3 kPa/760 4.03 kPa

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What is Charles Law?

• The relationship between temperature and volume,
  at a constant number of moles and pressure, is
  called Charles and Gay-Lussac's Law in honor of
  the two French scientists who first investigated
  this relationship.
• Charles did the original work, which was verified
  by Gay-Lussac. They observed that if the pressure
  is held constant, the volume V is equal to a
  constant times the temperature T, or
• V / T constant

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CHARLES LAW
He
CH4
H2O
V (L)
H2
T (ºC)
-273.15ºC
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Examples

• What would the final volume be if 247 mL of gas
  at 22ºC is heated to 98ºC , if the pressure is
  held constant?
• 247 ml/295 K X ml/371 K
• 91,637 mL K 295 X K
• 91,637 mL K/295 K X
• 310 mL X
• If the volume of oxygen at 21 C is 785 L, at
  what temperature would oxygen occupy 804 L?
• 785 L/294 K 804 L/X K
• 785 X 236,376
• X 236,376/785
• X 301 K 28 C

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Combined Gas Law

• Combining Charless Law and Boyles Law in a
  single statement
• P1V1/T1 P2V2/T2
• 39.8 mg of caffeine gives 10.1 mL of nitrogen gas
  at 23C and 746 mmHg. What is the volume of
  nitrogen at 0C and 760 mmHg?
• First change temperature to Kelvin
• V1 10.1mL P1 746 mmHg K1 296 K
• V2 ? P2 760 mmHg K2 273
  K
• 10.1 746/296 V2 760/273
• V2 9.14 mL

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Other Gas Laws

• Gay-Lussac Law
• At constant volume, pressure and absolute
  temperature are directly related.
• P/T k (constant)
• Avogadros Law
• At constant temperature and pressure, the volume
  of gas is directly related to the number of
  moles.
• V /n k (n is the number of moles)

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Gas Law Summary
Law Statement Equation Constant
Boyles P inversely proportional to V PV k1 T, n
Charles V directly proportional to T V/T k2 P, n
Gay-Lussac P directly proportional to T P/T k3 V, n
Avogadros V directly proportional to n V/n k4 P, T
What equation would we get if we combined them
all?
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What is the Ideal Gas Law?

• Combining Boyles Law, Charles law Avogadros
  Law we derive the Ideal Gas Law
• P V n R T
• P Pressure (atm)
• V Volume (L)
• n moles (mol)
• R Gas Constant (0.0821 L atm /mol K)
• T Temperature (K)
• Ideal gas law calculations are favored at low
  pressures and high temperatures
• Tells you about a gas NOW.
• The other laws tell you about a gas when it
  changes.

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Let Try It!

• Example
• If we had 1.0 mol of gas at 1.0 atm of pressure
  at 0C (STP), what would be the volume?
• PV nRT
• V nRT/P
• V (1.0 mol)(0.0821 L atm/mol K)(273 K)/(1.0
  atm)
• V 22.41 L
• 1 mole of ANY gas at STP will occupy 22.4 Liters
  of volume

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Gas Density and Molar Mass

• D m/V
• Let M stand for molar mass
• M m/n
• n m/M
• PV nRT
• PV (m/M) RT
• P mRT/VM (m/V)(RT/M)
• P d RT/M
• PM/RT d (density)

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Examples

• What is the density of ammonia at 23ºC and 735
  torr?
• Units must be atm, K
• 735 torr(1 atm/760 torr) 0.967 atm
• 23 273 296 K
• Molar mass of NH3 17.0 g
• d 0.967 17.0 g
• (0.0821 L atm/mol K)(296 K)
• d 0.676 g / L

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Gases and Stoichiometry

• Reactions happen in moles
• At Standard Temperature and Pressure (STP, 0ºC
  and 1 atm) 1 mole of gas occupies 22.42 L.
• If not at STP, use the ideal gas law to calculate
  moles of reactant or volume of product.

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Examples

• Consider the following reaction
• Suppose you heat 0.0100 mol of potassium
  chlorate, KClO3, in a test tube. How many liters
  of oxygen can you produce at 298 K and 1.02 atm?
• Break it into 2 problems, one involving
  stoichiometry and the other using the ideal gas
  law

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0.0100 mol KClO3 X 3 mol O2/2 mol KClO3 0.0150
mol O2 Now that you have the moles of oxygen use
the ideal gas law to calculate the volume V
nRT/P 0.0150 mol x 0.0821 L atm (K mol) x
298 K 1.02 atm V 0.360 L
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• Using the following reaction
• Calculate the mass of sodium hydrogen carbonate
  necessary to produce 2.87 L of carbon dioxide at
  25ºC and 2.00 atm.
• n PV/RT (2.00 atm)(2.87 L)
• (0.0821 Latm/Kmol)(298 K)
• n 0.235 mol CO2
• 0.235 mol CO2 (1 mol NaHCO3) ( 84.0 g)
• (1 mol CO2 )
  (1 mol NaHCO3)
• 19.7 g NaHCO3

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Daltons Law

• The total pressure in a container is the sum of
  the pressure each gas would exert if it were
  alone in the container.
• The total pressure is the sum of the partial
  pressures.
• PTotal P1 P2 P3 P4 P5 ...
• For each P nRT/V

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Dalton's Law

• PTotal n1RT n2RT n3RT ... V
  V V
• In the same container R, T and V are the same.
• PTotal (n1 n2 n3...)RT V
• PTotal (nTotal)RT V

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The Mole Fraction

• Ratio of moles of the substance to the total
  moles.
• symbol is Greek letter chi c
• Because pressure of a gas is proportional to
  moles, for fixed volume and temperature then,
• c1 n1 P1 nTotal PTotal

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Calculating the Partial Pressure and Mole
Fraction of a Gas Mixture

• A 1.00 L sample of dry air at 25C and 786 mmHg
  contains 0.925 g N2, plus other gases including
  oxygen, argon and carbon dioxide.
• What is the partial pressure (in mmHg) of N2 in
  the air sample?
• What is the mole fraction and mole percent of N2
  in the mixture?

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• Convert grams into moles
• 0.925 g N2 x (1 mol N2/28.0g N2)
• 0.0330 mol N2
• Substitute into ideal gas law
• PN2 nN2RT/V
• 0.0330mol x 0.0821 Latm/Kmol x 298
• 1.00 L
• 0.807 atm 613 mmHg

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• The mole fraction of N2 in the air is
• PN2/P 613 mmHg/786 mmHg
• 0.780
• Mole percent equals mole fraction x 100
• 0.780 x 100 78
• Air contains 78.0 mole percent of N2

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Vapor Pressure

• Water evaporates!
• When that water evaporates, the vapor has a
  pressure.
• Gases are often collected over water so the vapor
  pressure of water must be subtracted from the
  total pressure.
• Vapor pressure varies by temperature and must be
  given in the problem or in a table.

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• Hydrogen gas is produced by the reaction of
  hydrochloric acid, HCl, on zinc metal
• 2HCl (aq) Zn (s) gt ZnCl2 (aq) H2 (g)
• The gas is collected over water. If 156 mL of
  gas is collected at 19C and 769 mmHg total
  pressure, what is the mass of hydrogen collected?

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• First find the Partial Pressure. The vapor
  pressure of water at 19C is 16.5 mmHg
• P PH2 PH2O
• PH2 P - PH2O
• PH2 769 16.5 752 mmHg
• Use the ideal gas law to find the moles of
  hydrogen collected.
• P 752 mmHg x (1 atm/760 mmHg) 0.989 atm
• V 156 mL x (1 L/1000 mL) 0.156 L
• T 19 273 292 K
• R 0.0821 Latm/Kmol
• n ?

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• Solve for moles
• n PV/RT
• 0.989 x 0.156/0.0821 x 292
• 0.00644 mol H2
• Convert moles to grams
• 0.00644 mol H2 x (2.02g/1 mol H2)
• 0.0130 g H2

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Whats Diffusion and Effusion?

• Only a few physical properties of gases depends
  on the identity of the gas.
• Diffusion - The rate at which two gases mix.
• Effusion - The rate at which a gas escapes
  through a pinhole into a vacuum.

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What is Grahams Law?

• We know that Kinetic energy 1/2 mv2
• If two bodies of unequal mass have the same
  kinetic energy, which moves faster?
• The lighter one!
• Thus, for two gases at the same temperature, the
  one with lower molecular mass will diffuse/effuse
  faster.
• The rate of effusion/diffusion of a gas is
  inversely proportional to the square root of its
  mass.

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• Calculate the ratio of effusion rates of
  molecules of carbon dioxide and sulfur dioxide
  from the same container and at the same
  temperature and pressure
• Rate of effusion of CO2 vMm SO2
• Rate of effusion of SO2 vMm CO2
• v64.1/44.0 1.21
• In other words, carbon dioxide effuses 1.21 times
  faster than sulfur dioxide.