Gases
Chapters 13.1 & 14
Where are gases found?
• Atmosphere is made of gases:– 78% nitrogen (N2)
– 21% oxygen (O2)
– 1% other gases, including carbon dioxide
Kinetic-Molecular Theory
• Describes the behavior of gases
• Makes several assumptions about the size, motion, and energy of gas particles.
Assumptions of Kinetic theory:
• There is a lot of empty space in a gas between particles
• Gas molecules are tiny compared to the distances between them– Gas does have a volume
• Particles are in constant, random motion• They move in a straight line until they
collide with other particles or the wall of the container
Assumptions of Kinetic theory:
• No kinetic energy is lost in the collisions– Called elastic collisions – b/c energy is
transferred but the total energy does not change
• All gases have the same average kinetic energy at a given temperature.– There is a direct relationship between temp.
and total energy of a gas system
Properties of All Gases
• Most compressible of the states of matter– b/c it has a low density
• Assume the volume & shape of their container– Fill containers uniformly and completely
• Diffuse and mix rapidly– Will mix evenly & completely when confined
And now, we pause for this commercial message from STP
OK, so it’s really not THIS kind of STP…
STP in chemistry stands for Standard Temperature and
Pressure
Standard Pressure = 1 atm (or an equivalent)
Standard Temperature = 0 oC
(273 K)
STP allows us to compare amounts of
gases between different pressures and temperatures
STP allows us to compare amounts of
gases between different pressures and temperatures
• V = volume of the gas (mL or L)V = volume of the gas (mL or L)• T = temperature (K)T = temperature (K)
–ALL temperatures when dealing ALL temperatures when dealing with gases MUST be in Kelvin!!! with gases MUST be in Kelvin!!! No Exceptions!No Exceptions!
• n = amount (moles)n = amount (moles)• P = pressure (Units will change)P = pressure (Units will change)
What is Pressure?
• The amount of “push” that occurs in a certain area.
• We are surrounded by pressure all the time but we have evolved to “ignore” it. What pressure is that?– Air pressure or Atmospheric Pressure
• Gas particles exert pressure when they collide with the walls of a container.
Pressure• Pressure of air is measured Pressure of air is measured
with a with a BAROMETERBAROMETER (developed by Torricelli in (developed by Torricelli in 1643)1643)
• Hg rises in tube until force of Hg rises in tube until force of Hg (down) balances the force Hg (down) balances the force of atmosphere (pushing up). of atmosphere (pushing up). (Just like a straw in a soft (Just like a straw in a soft drink)drink)
• P of Hg pushing down related P of Hg pushing down related to to • Hg densityHg density• column heightcolumn height
PressureColumn height measures Column height measures
pressure of the pressure of the atmosphereatmosphere
• 1 standard atmosphere 1 standard atmosphere (atm) (atm)
= 760 mm Hg (or torr)= 760 mm Hg (or torr)= 29.92 inches Hg= 29.92 inches Hg= 14.7 pounds/in= 14.7 pounds/in2 2 (psi)(psi)= about 34 feet of water= about 34 feet of water= 101.3 kPa (SI unit is = 101.3 kPa (SI unit is
PASCAL) PASCAL)
Pressure Conversions
A. What is 475 mm Hg expressed in atm?
B. The pressure of a tire is measured as 29.4 psi. What is this pressure in mm Hg?
= 1.52 x 103 mm Hg
= 0.625 atm
Effect of Air Pressure
Boyle’s Boyle’s LawLaw
Robert BoyleRobert Boyle• Investigated the Investigated the
relationship between relationship between pressure and volume of pressure and volume of a gas when the a gas when the temperature and amount temperature and amount of a gas is held constantof a gas is held constant
Robert Boyle Robert Boyle (1627-1691). Son of (1627-1691). Son of Earl of Cork, Earl of Cork, Ireland.Ireland.
Boyle’s Law and Kinetic Boyle’s Law and Kinetic Molecular TheoryMolecular Theory
Boyle’s Law and Kinetic Boyle’s Law and Kinetic Molecular TheoryMolecular Theory
How are pressure & volume related?How are pressure & volume related?
Boyle’s Boyle’s LawLawP P αα 1/V 1/V
This means Pressure and Volume This means Pressure and Volume are INVERSELY are INVERSELY PROPORTIONAL if moles and PROPORTIONAL if moles and temperature are constant (do not temperature are constant (do not change).change).
PP11VV11 = P = P22 V V22
PP11VV1 1 = Initial conditions of the gas= Initial conditions of the gas
PP22VV2 2 = Changed conditions of the gas= Changed conditions of the gas
Robert Boyle Robert Boyle (1627-1691). Son of (1627-1691). Son of Earl of Cork, Earl of Cork, Ireland.Ireland.
Effect of Pressure on Volume = Boyle’s Law
5
1
3
1 atm
1
3
2 atm
5
1
3
5 atm
5
Which picture represents what the gas willlook like when the pressure is doubled?
(Assume constant n, T)
Charles’s LawCharles’s Law
Low Temperature High Temperature
Charles’s original balloonCharles’s original balloon
Modern long-distance balloonModern long-distance balloon
Charles’s Law and Kinetic Charles’s Law and Kinetic Molecular TheoryMolecular Theory
Charles’s Law and Kinetic Charles’s Law and Kinetic Molecular TheoryMolecular Theory
How are volume and temperature related?How are volume and temperature related?
Effect of Temperature on Volume
Charles’s Law• If n and P are If n and P are
constant, constant, then then
• V and T are V and T are DIRECTLY DIRECTLY proportionalproportional Jacques Charles (1746-Jacques Charles (1746-
1823) – from France1823) – from FranceIsolated boron and Isolated boron and studied gases studied gases BalloonistBalloonist
1 2
1 2
V V
T T
TEMPS. have to be in KELVIN!!
The volume of a gas increases with and increase in temperature.
Introductory Chemistry; 2nd Ed; by Nivaldo Tro; Prentice Hall Publishing 2006, p356
Which picture represents what the gas willlook like when the temperature is increased?
(Assume constant n, P)
Example of Charles’s Law
• Putting fully blown up balloons in a car during a hot summer’s day.
• What will happen?
• Why?
What happens to the pressure if volume What happens to the pressure if volume were kept constant and temp. was were kept constant and temp. was
changed?changed?What happens to the What happens to the
motion of the motion of the particles?particles?
This is Gay-Lussac’s This is Gay-Lussac’s LawLaw
Joseph Louis Gay-Joseph Louis Gay-Lussac (1778-1850)Lussac (1778-1850)
Kinetic Molecular Theory and Kinetic Molecular Theory and Gay-Lussac’s LawGay-Lussac’s Law
Kinetic Molecular Theory and Kinetic Molecular Theory and Gay-Lussac’s LawGay-Lussac’s Law
Gay-Lussac’s LawGay-Lussac’s Law• If n and V are constant, If n and V are constant,
thenthen• P and T are DIRECTLY P and T are DIRECTLY
proportional.proportional.
Joseph Louis Gay-Joseph Louis Gay-Lussac (1778-1850)Lussac (1778-1850)
1 2
1 2
P P
T T
TEMPS. have to be in KELVIN!!
Combined Gas Law• The good news is that you don’t have to
remember all three gas laws! Since they are all related to each other, we can combine them into a single equation. BE SURE YOU KNOW THIS EQUATION!
No, it’s not related to R2D2
1 1 2 2
1 2
PV P V
T T
Combined Gas Law
If you should only need one of the other gas laws, you can cover up the item that is constant and you will get that gas law!
= P1 V1
T1
P2 V2
T2
Boyle’s Law
Charles’ Law
Gay-Lussac’s Law
Combined Gas Law Problems:
Combined Gas Law ProblemA sample of neon gas is collected at a pressure of 2.7 atm and a temperature of 295.0 K. It has a volume of 2.25 L. What would be the volume of this gas at STP?
F:
P1 = 2.7 atm V1 = 2.25 L T1 = 295.0 K
P2 = 1 atm V2= ? T2 = 0oC
Calculation
• P1 = 2.7 atm V1 = 2.25 L T1 = 295.0 K
• P2 = 1 atm V2= ? T2 = 0oC = 273 K
P1 V1 P2 V2
= P1 V1 T2 = P2 V2 T1
T1 T2
V2 = P1 V1 T2
P2 T1
V2 = 2.7 atm x 2.25 L x 273 K
1 atm x 295.0 K
= 5.62 L5.62 L
A student collects a 3.5 L sample of hydrogen gas at 22.0oC and 91.9 kPa. What pressure would the hydrogen be at when the temperature is held constant but the volume decreases to 2.0L?
F: L: I: P: S:
Avogadro’s PrincipleAvogadro’s PrincipleEqual volumesEqual volumes of gases at the of gases at the
samesame TT and and PP have the have the samesame number of molecules (we’ll number of molecules (we’ll use moles = n)use moles = n)..
VV and and nn are are directlydirectly related. related.
Also Also massmass and and nn are directly are directly related b/c of related b/c of molar massmolar mass..
•Twice as many Twice as many moleculesmolecules•Twice the massTwice the mass•Twice the volume Twice the volume @ STP@ STP
Which picture represents what the gas willlook like when the moles of gas is doubled?
(Assume constant P, T)
Experiments show that at STP, 1 mole of an ideal gas occupies 22.4 L
Practice Problems:
Determine the volume of a container that holds 2.4 mol of gas at STP.
How many moles of nitrogen gas will be contained in a 2.00 L flask at STP?
= 54 L
= 0.0893 mol
• What volume, in L, will 4.5 kg of ethylene gas occupy at STP?
= 3.6x103 L
What is an “Ideal” Gas?What is an “Ideal” Gas?• The particles take up NO space
and have NO intermolecular forces interact.
• MOST gases will behave like ideal gases under most conditions
Deviations from Ideal GasesDeviations from Ideal Gases• Real molecules have volume.The ideal gas consumes the entire
amount of available volume. It does not account for the volume of the molecules themselves.
• There are intermolecular forces.An ideal gas assumes there are no
attractions between molecules. Attractions slow down the molecules and reduce the amount of collisions.– Otherwise a gas could not
condense to become a liquid.
Conditions that cause Conditions that cause Deviations from Ideal GasesDeviations from Ideal Gases
Real gases are the LEAST like ideal gases under 2 conditions:
1. Extremely high pressures
2. Extremely low temperatures
• Under these circumstances the gas molecules are too close together to NOT interact and take up space.
IDEAL GAS LAWIDEAL GAS LAW
Brings together gas properties Brings together gas properties of pressure, volume, of pressure, volume, temperature and moles of temperature and moles of gas.gas.
BE SURE YOU KNOW THIS BE SURE YOU KNOW THIS EQUATION!EQUATION!
P V = n R TP V = n R T
Ideal Gas Law
5.4
Charles’s law: V T(at constant n and P)
Avogadro’s principle: V n(at constant P and T)
Boyle’s law: V (at constant n and T)1P
V nT
P
V = constant x = RnT
P
nT
PR is the gas constant
0.0821
is the one most commonly used
L atmR
mol K
Other Gas Law Relationships
• PV = nRT
• Remember
• Also density could be used b/c
If you rearrange the equation above:
M
mRT PV so
(M) massmolar
mn
mD
V
( ) substitute in density Mmolar mass
mRT DRTM
VP P
Using the Ideal Gas LawUsing the Ideal Gas Law
How many moles of NHow many moles of N22 are are required to fill a small required to fill a small room with a volume of room with a volume of 960 cubic feet (27,000 L) 960 cubic feet (27,000 L) to 745 mm Hg at 25 to 745 mm Hg at 25 ooC?C?
K: K: UK: nUK: nV = 27,000 LV = 27,000 L
T = 25 T = 25 ooC + 273 = 298 KC + 273 = 298 K P = 745 mm HgP = 745 mm Hg
= 0.98 atm = 0.98 atm (b/c 1 atm = 760 mmHg)(b/c 1 atm = 760 mmHg)And we always know And we always know ..
PV=nRT
0.0821L atm
Rmol K
PVn
RT
22 2
(0.98 *27000 )
((0.0821 )(298 ))
26461
24.4658
108 N 1.0x10 mol N
atm Ln
L atmK
mol K
mol
mol
Example problem:
Dinitrogen monoxide (N2O), laughing gas, is used by dentists as an anesthetic. If 2.86 mol of gas occupies a 20.0 L tank at 23°C, what is the pressure (mmHg) in the tank in the dentist office?
= 2600 mmHg
Another Example Problem
A 5.0 L cylinder contains oxygen gas at 20.0°C and 735 mm Hg. How many grams of oxygen are in the cylinder?
n=PV/RT = (0.967atm*5.0L)/(0.0821 Latm/molK*293) =
0.201mol(32.00g/1mol) = 6.4g O2
Dalton’s Dalton’s LawLaw
John DaltonJohn Dalton1766-18441766-1844
Dalton’s Law of Partial Pressures
When V and T are constant
P1P2 Ptotal
5.6
++ ==
Kinetic theory of gases and …
• Dalton’s Law of Partial Pressures
Molecules of gases do not attract or repel one another
P exerted by one type of molecule is unaffected by the presence of another gas
Ptotal = sum of all the partial pressures of
individual gases = Pi
5.7
Dalton’s Law of Partial PressuresDalton’s Law of Partial Pressures
What is the total pressure in the flask?What is the total pressure in the flask?
PPtotaltotal in gas mixture = P in gas mixture = PAA + P + PBB + ... + ...
Therefore, Therefore,
PPtotaltotal = P = PHH22OO + P + POO22
PPtotaltotal = 0.32 atm + 0.16 atm = 0.48 atm = 0.32 atm + 0.16 atm = 0.48 atm
Dalton’s Law: total P is sum of Dalton’s Law: total P is sum of PARTIAL PARTIAL PRESSURESPRESSURES
2 H2 H22OO2 2 (l) (l) 2 H 2 H22O (g) + OO (g) + O2 2 (g)(g)The pressure of the water vapor is 0.32 atm and The pressure of the water vapor is 0.32 atm and the pressure of the oxygen gas is 0.16 atm.the pressure of the oxygen gas is 0.16 atm.
Gases in the AirThe % of gases in air Partial pressure (STP)
78.08% N2 593.4 mm Hg
20.95% O2 159.2 mm Hg
0.94% Ar 7.1 mm Hg
0.03% CO2 0.2 mm Hg
PAIR = PN + PO + PAr + PCO = 760 mm Hg 2 2 2
Total Pressure 760 mm Hg
Collecting a gas “over water”
• Animation of this concept
When a gas is collected over water; you always have a mixture of that gas and
water vapor.
Introductory Chemistry; 2nd Ed; by Nivaldo Tro; Prentice Hall Publishing 2006, p372
Table of Vapor Pressures for Water
Solve This!A student collects some
hydrogen gas over water at 20 oC and 768 torr. What is the pressure of the hydrogen gas?
GAS DIFFUSION AND EFFUSIONGAS DIFFUSION AND EFFUSION
• diffusiondiffusion is the is the gradual mixing of gradual mixing of molecules of different molecules of different gases.gases.
• effusioneffusion is the is the movement of movement of molecules through a molecules through a small hole into an small hole into an empty container.empty container.
Example: A leak in a balloon
GAS DIFFUSION AND GAS DIFFUSION AND EFFUSIONEFFUSION
Graham’s law governs Graham’s law governs effusion and diffusion effusion and diffusion of gas molecules.of gas 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 AM of B
Rate for B
Rate for A
GAS DIFFUSION AND GAS DIFFUSION AND EFFUSIONEFFUSION
Molecules effuse thru holes in a Molecules effuse thru holes in a rubber balloon, for example, at a rubber balloon, for example, at a rate (= moles/time) that israte (= moles/time) that is
• proportional to Tproportional to T
• inversely proportional to Minversely proportional to M..
Therefore, He effuses more rapidly Therefore, He effuses more rapidly than Othan O22 at same T. at same T.
HeHe
OO22
Gas DiffusionGas Diffusionrelation of mass to rate of diffusionrelation of mass to rate of diffusion
Gas DiffusionGas Diffusionrelation of mass to rate of diffusionrelation of mass to rate of diffusion
• HCl and NH3 diffuse from opposite ends of tube.
• Gases meet to form NH4Cl
• HCl heavier than NH3
• Therefore, NH4Cl forms closer to HCl end of tube.
• HCl and NH3 diffuse from opposite ends of tube.
• Gases meet to form NH4Cl
• HCl heavier than NH3
• Therefore, NH4Cl forms closer to HCl end of tube.
Which gas molecules will diffuse faster? Why?
a) CO2 or water vapor
b) Argon (Ar) or NH3
c) HCl (g) or SO2 (g)
The ones circled all have the smaller molar mass so their molecules move faster so they will diffuse faster than the other gases.