dr. mihelcic honors chemistry unit 8 – gas laws. importance of gases airbags fill with n 2 gas in...
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Dr. Mihelcic Honors Chemistry Dr. Mihelcic Honors Chemistry
Unit 8 – GAS LAWSUnit 8 – GAS LAWS
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Importance of GasesImportance of Gases
Airbags fill with NAirbags fill with N22 gas in an accident. gas in an accident. Gas is generated by the decomposition of Gas is generated by the decomposition of
sodium azide, NaNsodium azide, NaN33..
2 NaN2 NaN33 ---> 2 Na + 3 N ---> 2 Na + 3 N2 2
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Three States of MatterThree States of Matter
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Characteristics of GasesCharacteristics of Gases
No definable No definable shape or shape or volumevolume
LowLow mass, with a lot of “free” mass, with a lot of “free” space (leads to space (leads to lowlow density) density)
Can be expanded Can be expanded infinitelyinfinitely and and placedplaced into a container if into a container if force is exerted.force is exerted.
Occupy containers Occupy containers uniformly uniformly and completelyand completely..
Escape Escape readilyreadily from from containers, mix containers, mix rapidlyrapidly..
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KINETIC MOLECULAR THEORY (KMT)
Definition:Definition:
Theory used to explain gas laws. Theory used to explain gas laws.
Treats gases as a Treats gases as a collection of collection of particles in rapid, random motionparticles in rapid, random motion..
Applies to Applies to ALLALL gases, regardless of gases, regardless of chemical identitychemical identity..
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Molecular ModelMolecular Model
Gas molecules are relatively far apart (mostly Gas molecules are relatively far apart (mostly empty space).empty space).
Gas molecules are in Gas molecules are in continuous, rapid, random continuous, rapid, random motion.motion.
All collisions between gas molecules are All collisions between gas molecules are elasticelastic (no energy lost or gained in a collision).(no energy lost or gained in a collision).
Gas pressure is caused by Gas pressure is caused by collisionscollisions of molecules of molecules with the walls of the container.with the walls of the container.
Average Temperature of a gas sample is related Average Temperature of a gas sample is related to its to its kinetic energykinetic energy..
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Properties of GasesProperties of Gases
Gas properties can be Gas properties can be modeledmodeled using math. using math. Model depends on—Model depends on—
1.1. V = volume of the gas (L)V = volume of the gas (L)
2.2. T = temperature (K)T = temperature (K)
3.3. n = amount (moles)n = amount (moles)
4.4. P = pressureP = pressure (atmospheres) (atmospheres)
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Gas PressureGas Pressure
Caused by gas molecules Caused by gas molecules hitting hitting container walls.container walls.
Definition:Definition: Force per unit area, or
ForceArea
Image from: Image from: www.indiana.edu/.../PressGasLaws.htmlwww.indiana.edu/.../PressGasLaws.html
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Pressure UnitsPressure Units
SI unit: SI unit:
pascal (Pa)pascal (Pa) (equal to (equal to
N/mN/m22))
1 kPa = 1000 Pa1 kPa = 1000 Pa
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Additional Units of Pressure Additional Units of Pressure
Will also see problems with:Will also see problems with:atmospheres atmospheres (atm)(atm)
millimeters of mercury millimeters of mercury (mm Hg)(mm Hg)
inches of Hg inches of Hg (in Hg)(in Hg)
torr ( = torr ( = 1 mm Hg1 mm Hg))
Less commonly used:Less commonly used:pounds per square inch (psi)pounds per square inch (psi)millibars (mb)millibars (mb)
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Conversion Factors and STPConversion Factors and STP
Conversion Factors and STPConversion Factors and STP
1 atm = 1 atm = 760760 mm Hg = mm Hg = 760760 torr = torr = 101.3101.3 kPakPa
= = 29.92129.921 in Hg = 1013.25 mb = 14.969 in Hg = 1013.25 mb = 14.969 psipsi
STP – STP – Standard Temperature (0ºC) and Pressure (1 Standard Temperature (0ºC) and Pressure (1 atm)atm)
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PressurePressure
BAROMETERBAROMETER (developed by (developed by Torricelli in 1643)Torricelli in 1643)
Use: Use: Measures pressure
of air
Image from Image from Dr. Walt Volland, all rights reserved Dr. Walt Volland, all rights reserved 1998-20051998-2005
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Barometric Barometric PressurePressure
Column height Column height measures the pressure measures the pressure
of the atmosphereof the atmosphere
1 standard atm1 standard atm= 760 mm Hg= 760 mm Hg
= 29.921 inches Hg= 29.921 inches Hg
= about 34 feet of = about 34 feet of waterwater
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ManometersManometers
Use: Use:
Measures the Measures the pressure of a gas pressure of a gas in a closed system.in a closed system.
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Open Manometer: Two CasesOpen Manometer: Two Cases
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Sample Manometer Problem
An open manometer is filled with Hg and connected to a container of hydrogen. The mercury level is 40.0 mm lower in the arm of the tube connected to the air. Air pressure is 1.00 atm. What is the pressure of the hydrogen gas in mm of Hg?
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RELATIONSHIP BETWEEN PRESSURE AND VOLUME
Boyle’s Law
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Boyle’s Law in Real Life
Popping a balloon As you squeeze the balloon, what happens
to the pressure and volume inside the balloon?
Are pressure and volume directly proportional or inversely proportional?
P V
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Boyle’s Law in Real Life
Operating a syringe As you pull back on the plunger, are you
increasing or decreasing the volume? How does the pressure change?
Are P and V directly or inversely proportional?
P V
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Boyle’s Law in Real Life
Marshmallow/balloon in a vacuum As we evacuate the chamber, what do you
think will happen to the pressure? What do you think will happen to the volume of the marshmallow?
Are P and V directly or inversely proportional?400 Marshmallows in a Vacuum
P V
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Boyle’s Law
When temperature is held constant, pressure and volume increase and decrease as opposites If pressure increases, volume decreases If pressure decreases, volume increases
P1V1 = P2V2
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Practice with Boyle’s Law
A balloon contains 30.0 L of helium gas at 103 kPa. What is the volume of the helium when the balloon rises to an altitude where the pressure is only 25.0 kPa? (Assume temperature is held constant)P1V1 = P2V2
P1 =
V1 =
P2 =
V2 =
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Practice with Boyle’s Law
At room temperature, 10.01 L of a gas is found to exert 97.0 kPa. What pressure (in atm) would be required to change the volume to 5.00 L?P1V1 = P2V2
P1 =
V1 =
P2 =
V2 = 1 atm = 101.3 kPa
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Practice with Boyle’s Law
Nitrous oxide (N2O) is used as an anesthetic. The pressure on 2.50 L of N2O changes from 105 kPa to 40.5 kPa. If the temperature does not change, what will the new volume be?P1V1 = P2V2
P1 =
V1 =
P2 =
V2 =
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CHARLES’ LAW:
Relating Volume and Temperature
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Charles’ Law in Real Life
Balloons popping when kept outdoors As the balloons sits outside, what happens to
the temperature of the gas inside the balloon? What happens to the volume of the balloon?
Are volume and temperature directly proportional or inversely proportional?
V T
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Charles’ Law in Real Life
A ball outside on a cold day You pump the ball up indoors. After
going outside where it’s colder, what happens to the volume of the ball?
Are volume and temperature directly or inversely proportional?
V T
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Charles’ Law in Real Life
Liquid Nitrogen demo video When the balloon is placed in the liquid
nitrogen, what happened to the temperature of the gas inside the balloon? What happened to the volume?
Are volume and temperature directly or inversely proportional?
V T
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Charles’ Law
If pressure is held constant (doesn’t change), volume and temperature increase or decrease together If volume increases, so does the
temperature If temperature decreases, so does the
volume
2
2
1
1
T
V
T
V ***T must
be in Kelvin!!!
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Practice with Charles’ Law
A balloon inflated in a room at 24 ºC has a volume of 4.00 L. The balloon is then heated to a temperature of 58 ºC. What is the new volume if the pressure remains constant?
V1 =
T1 =
V2 =
T2 =2
2
1
1
T
V
T
V
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Practice with Charles’ Law
Exactly 5.00 L of air at -50 ºC is warmed to some temperature so that the volume was 8.36 L. What temperature was the system warmed to?
V1 =
T1 =
V2 =
T2 =2
2
1
1
T
V
T
V
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Practice with Charles’ Law
A 50.0 mL sample of a gas is cooled from 119 ºC to 353 K. If the pressure remains constant, what is the final volume of the gas?
V1 =
T1 =
V2 =
T2 =2
2
1
1
T
V
T
V
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Avogadro’s HypothesisAvogadro’s Hypothesis
Equal Equal volumesvolumes of gases at the same T and of gases at the same T and P have the same P have the same number of molecules.number of molecules.
V = knV = kn
V and n are V and n are directly relateddirectly related..
twice as many twice as many moleculesmolecules
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Image from Image from
library.thinkquest.library.thinkquest.org/12596/org/12596/avogadro.htmlavogadro.html
1 mol gas @ STP = 1 mol gas @ STP = 22.422.4 L L(a new conversion factor for (a new conversion factor for
moles!!)moles!!)
Avogadro’s Hypothesis & Molar Avogadro’s Hypothesis & Molar VolumeVolume
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Sample ProblemSample Problem
Example 5.3 Example 5.3 What is the mass of propane gas, C3H8, that can be held in a 5.0 L container at STP?
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Combined Gas Law
Combining all four Combining all four variables:variables:
PP11VV11 = = PP22VV22
nn11TT11 n n22TT22
If any one of these variables does not change in the problem, you can eliminate it from the
equation before starting!
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Imploding Can Demo
What happened to the volume of the can?
What happened to the temperature of the gas inside the can?
How did pressure play a role in the can imploding?
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IDEAL GAS LAWIDEAL GAS LAW
P = pressureP = pressure
V = volumeV = volume
n = # of molesn = # of moles
R = Ideal gas constantR = Ideal gas constant
T = temperature (in Kelvin)T = temperature (in Kelvin)
P V = n R TP V = n R T
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Gas Law Constant (R)Gas Law Constant (R)
RR: Universal or ideal gas : Universal or ideal gas constantconstant
Can be in different units, Can be in different units, depending on units used in the depending on units used in the
equation!equation!
0.082058 L atm/mol K0.082058 L atm/mol K62.364 L torr/mol K62.364 L torr/mol K8.3145 J/mol K8.3145 J/mol K
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Sample ProblemSample Problem
Example 5.4 Example 5.4 If a fixed amount of gas occupies 2.53 m3 at -15°C and 191 Torr, what will the volume of the same gas be at 25°C and 1142 Torr?
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Sample ProblemSample Problem
Example 5.5 Example 5.5 A gas cylinder is filled with 100 g of CO2 at 25oC and a pressure of 1000 mmHg. If 50 more grams of CO2 are added and the cylinder is stored at a temperature of 50oC, calculate the new pressure inside the cylinder.
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Using PV = nRTUsing PV = nRTHow much N2 is required to fill a small room with a volume of 960 cubic feet (27,000 L) to a pressure of 745 mm Hg at 25°C?
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Sample ProblemSample Problem
Example 5.7 Example 5.7 If 0.623 g of ethane, C2H6, is introduced into an evacuated 2.00 liter container at 23°°C, what is the pressure, in atmospheres, in the container?
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Sample ProblemSample Problem
Example Example 5.8 How much gas can be placed in a gas cylinder with a volume of 10.0 L and which is designed to store gas at a maximum pressure of 75.0 atm and at a maximum of 50°°C?
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Gas Density and Molar Mass
PV = nRTPV = nRTPV = nRTPV = nRT
nV
= P
RT
nV
= P
RTm
M• V =
PRT
where M = molar mass
mM• V
= P
RT
where M = molar mass
d = mV
= PMRT
d = mV
= PMRT
d and M proportionald and M proportional
and density (d) = m/Vand density (d) = m/V
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Sample ProblemSample Problem
Example 5.9 Example 5.9 A sample of phosgene (a highly toxic gas) is collected in a flask with a volume of 247 mL at a pressure of 751 mmHg and a temperature of 21°°C. If the mass of the gas is 1.00 g, what is the molar mass of phosgene?
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Sample ProblemSample Problem
Example 5.10 Example 5.10 What is the density of methane, CH4, at 0.940 atm and 23°°C?
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Gases in Reaction Gases in Reaction StoichiometryStoichiometryReview of steps in Stoichiometry
Problems:
1. Balance equation & convert to moles for known.
2. Convert moles of known to moles of unknown quantity using coefficient ratio.
3. Convert moles of unknown to required unit (g, L)
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Short-cut when dealing with all Short-cut when dealing with all gases in an equationgases in an equation
1.1. If have all gases in an equation, can go If have all gases in an equation, can go directly from V of the given to V of the directly from V of the given to V of the asked for quantity using the coefficients.asked for quantity using the coefficients.
2.2. ONLY works for equations with all gases!ONLY works for equations with all gases!
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Sample ProblemSample Problem
Write the balanced equation for the synthesis of gaseous water from gaseous hydrogen and oxygen. If we start with 5.4 L of oxygen, how much water in Liters is produced?
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Sample ProblemSample Problem
What is the mass, in grams, of potassium chlorate that must be used to produce 1.50 L of oxygen gas measured at 18°°C and 0.950 atm?
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Sample ProblemSample Problem
How many liters of oxygen, measured at 725 mmHg and 21°C are required to burn 1.00 g of butane gas, C4H10, to produce water and carbon dioxide?
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GRAHAM’S LAW &
DALTON’S LAW
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Racing Gases Demo:If concentrated HCl is at one end
of the tube and concentrated NH3 is at the other end, which
gas do you think will move farthest and fastest down the
tube?
Racing Gases Demo
HCl (g)
NH3 (g)
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RACING GASES DEMOThe gases will diffuse down the tube
Diffusion – tendency of molecules to move from areas of higher concentration towards areas of lower concentrationExample: spraying perfume and
smelling it across the room
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DIFFUSION
Originally
Over Time
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RACING GASES DEMOThe gases diffused at different rates
If the white ring forms closer to the HCl end of the tube, which gas moved farthest and fastest?
What if it was closer to the NH3 end?
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RACING GASES DEMOWhat happened in the tube?
Was the reaction closer to the HCl or NH3 end of the tube?
Calculate the molar mass of NH3(g) and HCl(g). Did the lighter or heavier gas move faster?
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GRAHAM’S LAW OF EFFUSION
The demo is related to Graham’s Law of Effusion – gases of lower molar masses effuse faster than gases with higher molar massesEffusion – when a gas escapes through a
tiny hole in its containerExample: Helium balloons shrinking
compared to normal balloons
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GRAHAM’S LAWGraham’s Law can also be applied to the
diffusion of a gasGases with lower molar masses (lighter
gases) diffuse faster than gases with higher molar masses (heavier gases)
The lighter the gas, the faster it moves
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GRAHAM’S LAWWhich gas would both diffuse and
effuse faster…Methane (CH4) or carbon dioxide
(CO2)?Chlorine (Cl2) or oxygen (O2)?Hydrogen sulfide (H2S) or carbon
monoxide (CO)?
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GAS DIFFUSION AND GAS DIFFUSION AND EFFUSIONEFFUSION
Graham’s law calculates: Graham’s law calculates:
rate of effusion and rate of effusion and diffusion of gas diffusion of gas molecules.molecules.
Thomas Graham, 1805-1869. Thomas Graham, 1805-1869. Professor in Glasgow and London.Professor in Glasgow and London.
Rate of effusion is Rate of effusion is inversely proportional inversely proportional
to its molar mass.to its molar mass.
Rate of effusion is Rate of effusion is inversely proportional inversely proportional
to its molar mass.to its molar mass.
M of 1
M of 2
Rate(Gas 2)
Rate (Gas 1)
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Sample ProblemSample ProblemIf they are compared under the same conditions, how much faster than helium does hydrogen effuse through a tiny hole?
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Sample Sample ProblemProblem
The rate of a volume of an unknown gas to effuse through a pinhole was 4.00 moles/sec. The rate calculated for the
same volume at the same temperature and pressure of oxygen was 2.00 moles/sec. Calculate the molar mass of
the unknown gas.
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REVIEW - PRESSURE OF A GAS If the gas molecules in a sample
collide more with the walls of the container, will the pressure increase or decrease?
If the number of gas molecules increases, what will happen to the pressure?
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DALTON’S LAW
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DALTON’S LAWPartial pressure – the contribution of each
gas in a mixture to the total pressureDalton’s Law of Partial Pressures – for a
mixture of gases, the total pressure is the sum of the partial pressure of each gas in the mixture
Ptotal = P1 + P2 + P3 + …
(at constant volume and temperature)
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PRACTICE – DALTON’S LAWDetermine the total pressure of a gas mixture that contains oxygen, nitrogen, and helium. The partial pressures are: PO2
= 20.0 kPa, PN2=46.7 kPa, and PHe=26.7 kPa.
Ptotal = P1 + P2 + P3 + …
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PRACTICE – DALTON’S LAWAir contains O2, N2, CO2, and trace amount of other gases. What is the partial pressure of oxygen (PO2
) if the total pressure of the system is
101.3 kPa and the partial pressures of N2, CO2, and the other gases are 79.10 kPa, 0.040 kPa, and 0.94 kPa, respectively?
Ptotal = P1 + P2 + P3 + …
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Vapor Pressure of WaterVapor Pressure of Water
PPtotaltotal = P(gas) + P(H = P(gas) + P(H22O) = 788 mm HgO) = 788 mm Hg
If the total pressure is 788 mm Hg at 25oC, what is the partial pressure of hydrogen collected over water?
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Deviations from Ideal Gas Law occur Deviations from Ideal Gas Law occur because of two main factors:because of two main factors:
1. Real molecules have 1. Real molecules have volumevolume..
2. There are 2. There are forces between forces between moleculesmolecules.. Otherwise a gas could not Otherwise a gas could not
become a liquid.become a liquid.
These factors are important These factors are important at at HIGHHIGH pressures and pressures and
LOW LOW temperatures.temperatures.
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Deviations from Ideal Gas Law occur because of two main factors:
1. Real molecules have 1. Real molecules have volumevolume..
2. There are 2. There are forces between forces between moleculesmolecules.. Otherwise a gas could not Otherwise a gas could not
become a liquid.become a liquid.
In general, the closer a gas is In general, the closer a gas is to theto the LIQUIDLIQUID state, the more state, the more it will deviate from the Ideal it will deviate from the Ideal
Gas Law.Gas Law.
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Deviations from Ideal Gas Deviations from Ideal Gas LawLaw
Account for volume of molecules Account for volume of molecules and intermolecular forces with and intermolecular forces with
VAN DER WAALS’s EQUATIONVAN DER WAALS’s EQUATION..
Measured V = V(ideal)Measured P
intermol. forcesvol. correction
J. van der Waals, J. van der Waals, 1837-1923, 1837-1923, Professor of Professor of Physics, Physics, Amsterdam. Amsterdam. Nobel Prize 1910.Nobel Prize 1910.
nRTV - nbV2
n2aP + ----- )(
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Deviations from Ideal Gas Deviations from Ideal Gas LawLawDeviations from Ideal Gas Deviations from Ideal Gas LawLaw
ClCl22 gas has gas has aa = 6.49, = 6.49, bb = 0.0562 = 0.0562
For 8.0 mol ClFor 8.0 mol Cl22 in a 4.0 L tank at 27 in a 4.0 L tank at 27 ooC.C.
P (ideal) = nRT/V = 49.3 atmP (ideal) = nRT/V = 49.3 atm
P (van der Waals) = 29.5 atmP (van der Waals) = 29.5 atm
Measured V = V(ideal)Measured P
intermol. forces
vol. correction
nRTV - nbV2
n2aP + -----