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Chapter 11
Gas Laws
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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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Assumptions of Gases
• We are going to make a few assumptions about gases to study them.
• These assumptions are bases on years of study.
• They work well at normal temperatures and pressures
– Especially well at high temps and low pressures. (In case you were wondering)
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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 (To be Cont.)
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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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What’s 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 are treatment of gases
• Corrections for real gases are fairly small
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How do you know this is an ideal gas?
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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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Torricelli’s 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
• PV=nRT– P,V,n,T have been discussed
– What is R?
– Universal Gas Constant
• Same for ALL gases
• But can change with pressure unit
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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 (L*kPa)/(mol*K)
• R = 0.08206 (L*atm)/(mol*K)
– 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
• PV=nRT• 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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Solve for V
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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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Homework
• p.418 # 18,24,27 41,44,49,51,52,53
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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
• PV=nRT
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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
• PV=nRT
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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
• PV=nRT
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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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More Ideal Gas Law Fun!
• Ideal gas law can be used to find three more items.
• Density
– Mass/Volume
• Molar Mass
– Grams/Moles
• Molar Volume
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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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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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1 mol N2
1 mol Cl2 1 mol CH4
1 mol Ne 1 mol CO2
1 mol He1 mol H2 1 mol O2
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Homework
• P.418 #’s 58,60,62
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Objectives
• Perform gas stoichiometry calculations
• Describe volume ratios
• Relate gas temperature to Kinetic Energy
• Perform calculations using Grahams Law of Effusion
• Describe the dependence of gas variables
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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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Dalton’s 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/digital_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 evaporting
• 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/digital_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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Volume Ratios
• The coefficients in balanced equations can be mole and volume ratios
• From the ideal gas law
– V=nRT/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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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 = m2v2
2
– The gas with the SMALLER mass has the LARGER velocity
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1 mol N2
1 mol Cl2 1 mol CH4
1 mol Ne 1 mol CO2
1 mol He1 mol H2 1 mol O2
All gases are at 298K and 1.00 atm.
Which gas has
Greatest KE?
Highest Velocity?
Smallest Velocity?
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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/lectures/lec_d.html
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Graham’s Law of Effusion
1
2
2
1
MM
MM
rate
rate
• 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 smaller gases
– Due to velocity
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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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Homework
• Page 420 #’s 68-71