Gases

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Chapter 5

• Gases

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Objectives

• Describe the properties of gases
• Describe the Kinetic Molecular Theory, Ideal
  Gases
• Explain air pressure and barometers
• Convert pressure units
• Perform calculations using the ideal gas law

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Why Study Gases?

• We deal with gases on a daily basis
• Filling your car tires
• Barometric Pressure (Weather)
• Breathing air
• Many reactants and products are gases
• We need to know how to work with gases
• In the lab gases are usually measured in volumes
  instead of masses

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Properties of Gases

• Gases expand to fill their container
• Gases can be compressed
• Gases are fluids
• Meaning they flow
• Gases have a low density
• Liq. N2 .807g/mL at -196ºC
• Gas N2 .625 g/L at 0ºC
• Or about 1000 times different!
• Gases effuse and diffuse

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Kinetic Molecular Theory

• Particles of a gas are in constant motion
• Volume of the individual particles is zero
• Particles colliding with the side of the
  container cause pressure
• Particles exert no force on each other
• Means No Intermolecular Forces
• Temperature of a gas is directly related to its
  Kinetic Energy

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Whats Wrong?

• Gas particles do have volume
• However the ratio of the particle volume to
  container volume is almost zero
• Gas particles experience intermolecular forces
• However, the particles are relatively far apart
  and free to move so
• Forces are weak

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Ideal Gas

• Gases that behave according to the kinetic
  molecular theory (KMT)
• No such gas exists
• Good approximation most of the time
• Simplifies our treatment of gases
• Corrections for real gases are fairly small

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Gas Variables

• Pressure (P) in atm, mmHg, torr, kPa
• Volume (V) in mL, L
• Temperature (T) in K
• Moles (n) in mol
• These 4 variables can completely describe a gas

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Pressure

• Measure of force per unit area
• Force/Area
• SI Unit is N/m2 or Pascal (Pa)
• 1 Newton is about 100 grams
• So, 1 Pa is about 100 grams on 1m2
• Or a very small pressure
• Atmospheric pressure is quite substantial
• 101,300 Pa or 101.3 kPa

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Measuring Pressure

• Pressure is most commonly measured with a
  barometer
• Invented by Evangelista Torricelli in
  approximately 1644
• Filled a glass tube with liquid mercury and
  inverted the tube in a dish of mercury
• At sea level the column stood at 76 cm
• When the barometer was taken to higher elevation
  the level dropped

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Torricellis Explanation

• Air pressed down on the dish of mercury
• Mercury was forced up the column
• Mercury rose until the weight of the mercury
  equaled the weight of the air

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Figure 11.404a
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Pressure Measurements

• Normal pressure at sea level in a barometer
• 760. millimeters mercury (mmHg)
• 1.00 atmospheres (atm)
• 101.3 kilopascals (kPa)
• 760. torr (in honor of Torricelli)
• 14.7 pounds per square inch (psi)
• 29.9 inches of mercury (inHg)
• We will use the first three the most

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Example

• Convert 728 mmHg to A) atm B) kPa

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Temperature

• Kelvin temperature is the ONLY scale used in gas
  calculations
• Used because 0 K is absolute zero
• Note it is NOT ºK!
• Converting from Celsius to Kelvin
• Temp. in K Temp in C 273
• 0 ºC 273 K
• 100 ºC 373 K
• Room temp is about 22 ºC or 295 K

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The Ideal Gas Law

• Mathematical equation that relates all variables
  for a gas
• PVnRT
• P,V,n,T have been discussed
• What is R?
• Universal Gas Constant
• Same for ALL gases
• But can change with pressure unit
• Works well at low pressures and high temp.

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Universal Gas Constant

• The units of R can change as the pressure units
  change
• R has two values
• R 8.314 (LkPa)/(molK)
• R 0.08206 (Latm)/(molK)
• Use the first if you are in kPa
• Use the second if you are in atm
• If you are in mmHg convert

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Units in the Ideal Gas Law

• PVnRT
• P can be in atm or kPa
• V must be in Liters (L)
• n must be in moles (mol)
• T must be in Kelvins (K)

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Changing the Law

• The ideal gas law can be manipulated to solve for
  an unknown variable
• Often used in stoichiometry problems
• You will always know R.
• It is never a variable
• Just use algebra to isolate the variable you
  desire

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Solve for T
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Solve for P
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Example

• A sample of gas at 25ºC and 3.40 L contains 3.33
  moles. What is the pressure (in kPa)?

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Example

• 5.69 grams of Oxygen gas at 250.ºC has a
  pressure of 722mmHg. What is the volume?

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Changing Gas Conditions

• The conditions of a gas can change
• If two variables change the other two do not
• They are constant
• If three variables change the other one does not
• Rearrange the ideal gas law to solve
• Place variables that change on the same side of
  the equation

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Changing Pressure and Volume

• PVnRT

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Pressure and Volume

• 2.0 L of a gas at 3.0 atm is compressed to 1.0 L
  what is the new pressure?

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Pressure and Volume

• Pressure and Volume are inversely related
• As one increases the other decreases
• Sketch a graph of pressure vs. volume
• Pressure on the Y axis
• Volume on the X axis

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Changing Volume and Temp

• PVnRT

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Volume and Temp.

• Volume and Temp. are directly related
• As one increases so does the other
• Sketch a graph of volume vs. temp.
• Volume on the Y axis
• Temp. on the X axis

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Volume and Temperature

• 1.0 L of a gas at 10.ºC is heated to 30ºC. What
  is the new volume?

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Changing Others

• PVnRT

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Changing Three Variables

• Pressure, Volume, Temperature
• Pressure, Volume, Moles

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STP

• Standard Temperature and Pressure
• Short way to state a temp and pressure
• Temperature is 0ºC or 273K
• Pressure is 1.00atm or 760. mmHg

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Homework

• P. 234 s 31-33,38,42

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Gas Stoichiometry

• We can perform stoichiometry with gases
• Must use the ideal gas law
• Use the ideal gas law to find moles
• Use at beginning or the end
• Perform normal stoichiometry
• Balanced equation
• Mole ratios
• Molar masses

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Example

• 4.55 grams of sodium carbonate is added to excess
  hydrochloric acid. What volume of carbon dioxide
  can be produced at STP?

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Example

• 0.39 grams of MgO is produced when magnesium is
  burned in air at 800.ºC and 729mmHg. What volume
  of oxygen gas is required for the complete
  combustion?

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Daltons Law of Partial Pressure

• Each gas in a container contributes its own
  pressure to the total
• Ptot PA PB PC . . .
• Each gas is independent of the others
• Assumption of the ideal gas law
• Gases exert no force on each other

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Gas Collection Over Water

• Bubbling of a gas into a container filled with
  water
• Convenient way of collecting gases
• Gas rises to the top of the container
• Less dense
• Allows us to measure the volume

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Image from http//www3.moe.edu.sg/edumall/tl/digi
tal_resources/chemistry/images/img_CH_00004.jpg
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Water Vapor Pressure

• The gas you are trying to collect is not the only
  gas above the water
• Water vapor is also present
• Liq. water is always evaporating
• Water vapor contributes to total pressure
• Need to subtract waters vapor pressure to get the
  real pressure of the gas
• Ptot PA PH2O

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Image from http//www3.moe.edu.sg/edumall/tl/digi
tal_resources/chemistry/images/img_CH_00004.jpg
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Water Vapor Pressure

• Vapor Pressure increases with temperature
• Evaporation increases with temp

Temp ºC Vapor Pressure mmHg Temp ºC Vapor Pressure mmHg
0 4.6 25 23.6
15 12.8 50 92.5
20 17.5 70 233.7
22 19.8 100 760.0
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Example

• 43.00mL of Hydrogen gas is collected over water.
  The room pressure is 751mmHg and the temp. is
  22ºC. How many moles of Hydrogen are present?

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Volume Ratios

• The coefficients in balanced equations can be
  mole and volume ratios
• From the ideal gas law
• VnRT/P
• Therefore Volume and Moles are directly related

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Volume Ratios

• The equation
• 2H2(g) O2(g) ? 2H2O(g)
• Means
• 2 mol H2 and 1 mol O2 ? 2 mol H2O
• OR
• 2 L H2 and 1 L O2 ? 2 L H2O

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Calculate This

• What volume does 1.00 mol of a gas at STP occupy?

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Molar Volume

• Volume occupied by 1 mole of a gas
• At STP 1 mole of a gas occupies 22.4L

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Molar Volume

• What does this mean?
• One mole of any gas at the same temp and pressure
  occupies the same volume!
• Gas volume is independent of identity

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More Ideal Gas Law Fun!

• Ideal gas law can be used to find two more items.
• Density
• Mass/Volume
• Molar Mass
• Grams/Moles

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Molar Mass

• Molar mass can be found two different ways
• 1) Solve for moles then divide grams/moles
• 2) Rearrange the ideal gas law
• Molar mass is hiding in the equation

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Density

• Density can be found two ways
• 1) Divide Mass/Volume
• 2) Rearrange the ideal gas law
• Mass/Volume is hiding in the equation

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1 mol He
1 mol H2
1 mol O2
1 mol N2
1 mol Ne
1 mol CO2
1 mol Cl2
1 mol CH4
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Mole Fraction

• Ratio of the number of moles of a given component
  to the total moles in a mixture
• Xa na/ntotal Pa/Ptotal

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Homework

• P.418 s 51,53,56

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Explain

• Why pressure and volume are inversely related.
  (Moles and Temp. constant)
• Why volume and temperature are directly related.
  (Pressure and Moles constant)
• Why pressure and moles are directly related.
  (Volume and Temp. constant)
• Why pressure and temperature are directly
  related. (Volume and Moles constant)

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Kinetic Energy

• Energy of motion
• KE 1/2mv2
• m mass
• v velocity
• Speed

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Kinetic Energy Temperature

• All gases at the same temperature have the same
  kinetic energy
• Assumption of Kinetic Molecular Theory
• Temp. directly related to Kinetic Energy
• All gases at the same temp. do not have the same
  velocity
• Gases have different masses

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Kinetic Energy Temperature

• According to the equation
• KE 1/2mv2
• KE depends on mass on velocity
• If two gases have the same KE
• m1v12 m2v22
• The gas with the SMALLER mass has the LARGER
  velocity

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All gases are at 298K and 1.00 atm. Which gas has
Greatest KE? Highest Velocity? Smallest Velocity?
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Kinetic Energy of a Gas per Mole

• R 8.314 J/Kmol
• T Temperature in Kelvins
• As temperature goes up so does KE

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Root Mean Speed

• Speed of the AVERAGE gas particles at a given
  temperature
• At a given temp gas particles have a range of
  speeds.
• As temp goes up the speed of the average particle
  goes up

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Root Mean Speed

• R 8.314 J/Kmol
• T Temp in Kelvin
• MM Molar Mass in kg/mol

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• 73 Page 235
• Compare the KE and Root Mean Speed and KE of O2
  and N2 at 0 degrees C

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Effusion

• The process of a gas entering a vacuum
  thru a small opening.
• The rate of effusion varies with molar mass
• Molar mass changes the velocity

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Image from http//itl.chem.ufl.edu/2045_s00/lectu
res/lec_d.html
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Grahams Law of Effusion

• 1 and 2 designate the gases
• MM is molar mass
• Usually the lighter gas is designated as 1
• Rates can be relative or velocities

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Example

• Compare the rates of effusion for oxygen and
  helium gas

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Diffusion

• Random movement of gas particles among other
  particles
• Process is similar to effusion
• Larger gases diffuse slower than smaller gases
• Due to velocity

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Real Gases

• Real Gases do not behave exactly like ideal gases
• Corrections must be made for gas particle volume
  and intermolecular forces
• Observed pressure is smaller that ideal pressure
• Observed volume is smaller that ideal volume

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Pressure and Volume Corrections

• Pressureobs Pressureideal-a(n/V)2
• VolumeobsVolumeideal-nb
• Corrections are placed into the Real Gas Law
• Called van der Waals Equation

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van der Waals Equation

• a and b are constants for given gases
• On page 224 in your text

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Homework

• P. 235 s 73,77,80,81,85