Transcript 11 Gaseous Elements

Macroscale Chemistry
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Ch 5 Gases—transition to macroscale
Ch 6-8 Equilibrium
Ch 9 Thermochemistry
Ch 10 Thermodynamics
Ch 15 Kinetics
Applications
Gases
Ch 5
IMF and Gases
11 Gaseous Elements
Gases: Macroscopic Observation
• Gases fill the container
into which they are
placed
• Gases are compressible
• Gases mix completely
and evenly when
confined to the same
container
• Gases have much lower
densities than solids or
liquids (g/L)
Gases: Molecular View
• Fill space evenly and completely:
randomly, fast moving particles
• Low density and compressibility: large
distances between particles
• Idealized assumptions
– Gas particles have no volume
– Gas particles have no interaction, so identity of
gas particle is inconsequential
Gases: Historical View
• Molecular basis
– Kinetic energy of
molecules much
greater than
intermolecular forces
• Historical studies
precede the atom
– First we will look at
non-molecular
properties
Torricelli (1608-1647)
1 atm = 760 torr
Pressure
• Velocity = distance / time
(m/s)
• Acceleration = change in velocity / time
(m/s2)
• Force = mass x acceleration (kg m/s2
= N)
• Pressure is the force of the gas pressing
on a given area P = F/A (N/m2 = Pa)
– Ability to cut with a knife doesn’t depend
simply on amount of force
Test the concept
Pressure
• Pressure = Force/Area
• Force = mass * acceleration
– Acceleration = g = pull of gravity
– mass = r*V = r*h*A
where r=density of Hg, h= height
of Hg, A = cross-sectional area of
column
• Force = r*h*A*g
• Pressure=(r*h*A*g)/A = r*h*g
• P  height and density
If the density of
mercury is 13.6g/ml,
what is the height of a
column of water under
vacuum at atmospheric
pressure? (76 cm =2.5
ft)
Pressure Conversions
1 atm = 14.7 lb/in2 = 760 mmHg = 760 torr = 101.325 kPa
Manometer
Experimenting with Gases
Robert Boyle (1627-1691)
As P (h) increases
V decreases
Plot of Pressure vs Volume
Boyle’s Law
V =k/P
Boyle’s Law
• P  1/V , when one sample is kept at
constant temperature
• Acts as an “Ideal Gas”
Ideal Gas
• Pressure is inversely proportional to volume
at a range of constant temperatures and
sample sizes
– k changes value at different temperatures, but is
constant…well, almost constant
Also notice that identity
of gas matters little, and
all approach same ideal
(all data from 1 mol
samples at 0 oC)
Ideal Gas
• Molecular perspective
• Assumptions
– Molecules occupy no
space
– Molecules do not interact
with each other
• Good assumptions?
Test your Understanding
• When you blow up your tire, you increase
the pressure and volume simultaneously.
According to Boyle, pressure and volume
are inversely proportional. What gives?
Charles’s Law
• Jacque Charles (17461823)
• Solo balloon flight
• At constant pressure,
volume increases
linearly with
temperature
• Write Law
Charles’s Law (1783)
• VT
– T in Kelvin
– K = oC + 273
• Absolute zero
Pressure and Temperature
Draw Pressure as a function of Temperature at constant volume
Avagadro’s Law (1811)
• In light of Dalton’s Atomic Theory (1808)
• Based on Gay-Lussac
– Law of combining volumes
Avogadro’s Law
• At constant P and T, the volume of a gas is
proportional to the amount of gas
• molar volume Vm = V/n
• Vn
Little known historical fact:
Junior High nickname
happened to be “The Mole”
Combined Ideal Gas Law
• V proportional to 1/P
• V proportional to T
• V proportional to n
• 𝑉=𝑅
𝑛𝑇
𝑃
• PV = nRT
Problem Types
• If three variables known, calculate fourth
• Some conditions change—how does it
affect others?
• Stoichiometry
• Determine a molar mass
Molar Volume
• Molar Volume = Vm
– Defined as the volume taken
up per mole of gas
• Vm at STP = 22.41 L/mol
• Standard Pressure is 1 atm
• What is standard
temperature in Celcius?
A flask that can withstand an internal pressure of 2500 torr,
but no more, is filled with a gas at 21.0 oC and 758 torr and
heated. At what temperature will it burst?
Strategy/Sketch:
Answer: 7.0 x 102 oC
Change in State of Ideal Gas
If the stopcock is
opened, the total
pressure is 0.975 atm.
What was the original
pressure of the red bulb?
2.00L Ar at
360 torr
1.00 L Ar
unknown pressure
Strategy:
Assumption Check: According to ideal gas,
would the total pressure change if the right
bulb were filled with 1 L of carbon dioxide?
Logic Check:
Answer: 1.50 x 103 torr
Gas Density
• 𝑃𝑉 = 𝑛𝑅𝑇
•
•
𝑃𝑉
𝑚
𝑃
𝜌
=
=
𝑚
𝑉
𝑚
𝑛
𝑛𝑅𝑇
𝑚
where m = mass in grams
= density in grams/Liter
= molar mass in g/mol
𝑅𝑇
𝑀
where ρ = density & M = molar mass
Experimental Importance
•
𝑃
𝜌
=
𝑅𝑇
𝑀
• If you had a sample of an unknown gas,
what could you measure experimentally?
What could you determine about the gas?
Dalton’s Law of Partial Pressures
• Extension of ideal gas
assumptions
• For a mixture of two gases A
and B, the total pressure, PT,
is PT = PA + PB
• “Partial Pressure”
• Since two gases by definition
𝑛𝑎
𝑃𝑎
are at same V and T, =
𝑛𝑏
• Useful case:
𝑛𝑎
𝑛𝑡𝑜𝑡𝑎𝑙
=
𝑃𝑏
𝑃𝑎
𝑃𝑡𝑜𝑡𝑎𝑙
An example of early utility
of Dalton’s atomic theory
Mole Fraction
• Mole fraction (χ) is the number of moles of
one component of a mixture divided by the
𝑛𝑎
total moles in the mixture:
𝑛𝑡𝑜𝑡𝑎𝑙
• χA+χB+χC=1
• The partial pressure of any gas, A, in a
mixture is given by: PA = χ A ( PT )
Collecting a Gas Over Water
• Gases collected by water displacement are a
mixture of the gas and water vapor.
• All liquids have a certain amount in the gas
phase. This is known as the Vapor Pressure
of the liquid. It is temperature dependent.
• PT = Pgas + PH2O
Experimental Determination of R
Name
Joe Dirk
Joe Dirk
Joe Dirk
Anne Marie, Emily
Anthony Nick
Jon Josh
mike jeremy
mike jeremy
mike jeremy
Marissa, Natalie,
Katie
Kim, Dave
Marshall, Brian
Alysha, Ashley
Ryan, Valerie
Toni, Bryson
Mass Mg (g)
0.0295
0.03
0.0291
0.0293
0.03
0.0295
0.0302
0.0287
0.0285
0.0301
0.0313
0.0319
0.0305
0.0302
0.0298
0.0295
0.0313
0.0297
0.0296
0.0291
0.0293
0.028
0.0285
0.029
0.0279
0.0277
0.0274
0.029
0.0299
0.0302
0.0279
0.0286
0.0282
Moles Mg
Moles H2
T (Celsius)
21.8
21.8
21.8
21.0
20.0
20.0
22.0
22.7
23.3
21.5
21.0
20.5
23.5
24.2
23.8
23.0
21.5
21.0
22.0
22.0
21.5
24.0
23.5
23.0
23.0
23.0
23.0
24.0
22.8
22.0
24.5
23.5
22.9
T (Kelvin)
PT (mm Hg)
731
731
731
731
731
731
731
731
731
731
731
731
731
731
731
PH2O (mm Hg)
19.59
19.59
19.59
18.65
17.54
17.54
19.83
20.57
21.32
19.32
18.65
18.08
18.50
18.50
18.50
731
731
731
731
731
731
731
731
731
731
731
731
731
731
731
731
731
731
21.07
19.35
18.65
19.83
19.83
19.11
22.38
21.58
21.07
21.07
21.07
21.07
22.38
20.82
19.83
22.92
21.58
21.07
PH2 (mm Hg)
PH2 (atm)
VH2 (mL)
30.5
30.5
30.5
31.5
31.6
31.1
31.9
30.2
30.0
32.0
33.4
33.4
31.9
32.5
31.7
30.0
32.6
31.4
31.0
31.1
31.5
29.9
30.8
32.1
29.8
29.2
28.4
30.3
31.7
31.4
28.0
28.8
28.5
VH2 (L)
R (L-atm/mol-K)
Kinetic Molecular Theory
• Describes gases at the molecular level
• 1. Gases consist of small particles separated by large
distances (assume no volume.)
• 2. Constant, random motion. Collisions with wall cause
pressure
• 3. Gas particles have no interaction with one another (no
intermolecular forces.) Collisions occur continuously and
are elastic (no gain/loss of KE).
• 4. KE  T, average kinetic energy only changes when
temperature changes.
Ideal Gas Law from Theory:
Qualitative
• Connect Atomic level (velocity, mass,
collisions) to macroscopic (P, V, n, T)
• P∝
𝑚𝑜𝑚𝑒𝑛𝑡𝑢𝑚
𝑐𝑜𝑙𝑙𝑖𝑠𝑖𝑜𝑛
• P ∝ 𝑚𝑎𝑠𝑠
• P∝
• P∝
𝑐𝑜𝑙𝑙𝑖𝑠𝑖𝑜𝑛𝑠
(
)
𝑠𝑒𝑐𝑜𝑛𝑑
𝑎𝑣𝑒 𝑠𝑝𝑒𝑒𝑑(#𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒𝑠)
𝑎𝑣𝑒 𝑠𝑝𝑒𝑒𝑑 [
]
𝑣𝑜𝑙𝑢𝑚𝑒
(𝑚υ2 )(#𝑚𝑜𝑙𝑒𝑠)
𝑣𝑜𝑙𝑢𝑚𝑒
𝑇𝑛
𝑉
∝
𝑘𝑖𝑛𝑒𝑡𝑖𝑐 𝑒𝑛𝑒𝑟𝑔𝑦 (#𝑚𝑜𝑙𝑒𝑠)
𝑉𝑜𝑙𝑢𝑚𝑒
Is KMT consistent with
Observation?
•
•
•
•
•
Compressibility
Boyle – P and V
Charles – V and T, P and T
Avogadro – V and n
Dalton’s Partial Pressures
Ideal Gas Law from Theory:
Quantitative
• Error in text (total force does not equal
sum of component)
• 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 2 = 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦𝑥 2 + 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦𝑦 2 +
𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦𝑧 2
Derivation of KMT
See handout
The meaning of Temperature
•
•
𝑃𝑉
𝑛
2
𝑃𝑉
= (KE)ave and = RT
3
𝑛
3
KEave = RT where R = 8.314
2
J/mol K
• Kelvin temperature is measurable quantity
that is directly proportional to the random
motion (kinetic energy) of the particles
Velocity of particles in Gas
Velocity of particles in Gas
Maxwell-Boltzmann Distribution
f(u)= 4𝜋
𝑚
2𝜋𝑘𝑇
3/2
𝑒
𝑚𝑢2
(−
)
2𝑘𝑇
How does this function form
the shape of the distribution?
How does high mass shift curve?
How does high T shift curve?
Maxwell/Boltzmann Distribution
“Typical” Velocities at 298 K in m/s
These gases are at the same
temperature, so they have the same
__________ but they have different
average velocities because they have
different _________________.
Three ways to describe
a “typical velocity”
• Most probable
• Average
• RMS
Determination of RMS velocity
• KEave =
•
𝑢2
=
3
RT
2
=
1
Na 𝑚𝑢2
2
3𝑅𝑇
𝑚𝑁𝑎
• Root mean square velocity
Root Mean Square Speed
uRMS =
3RT
M
R = 8.314 J/K mol
M = molar mass in kg/mol
Test your understanding
uRMS =
3RT
M
R = 8.314 J/K mol
M = molar mass in kg/mol
Gas Motion on a Molecular Level
Diffusion
Effusion
Diffusion and Effusion
• Diffusion – mixing due to motion
• Effusion – passage of a gas through a small
hole into an evacuated space
Ratio of effusion or diffusion rates depends on
relative velocities of gases
𝑒𝑓𝑓 𝑜𝑟 𝑑𝑖𝑓𝑓 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑔𝑎𝑠 1
=
𝑒𝑓𝑓 𝑜𝑟 𝑑𝑖𝑓𝑓 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑔𝑎𝑠 2
3𝑅𝑇/𝑚1
3𝑅𝑇/𝑚2
=
𝑚2
𝑚1
Real Gases
Nitrogen gas
At 200K
Real Gases: Check Assumptions
• 1. Gases consist of small particles separated by large
distances (assume no volume.)
• 2. Constant, random motion. Collisions with wall cause
pressure
• 3. Gas particles have no interaction with one another (no
intermolecular forces.) Collisions occur continuously and
are elastic (no gain/loss of KE).
• 4. KE  T, average kinetic energy only changes when
temperature changes.
Assumptions that Fail
Gases have no contribution to volume. Is this
assumption equally valid at all states?
Assumptions that Fail
Gases velocity is unaffected by attraction
to other particles.
When Is a Gas Most Ideal?
Make a “Real Gas” Law
• Points to consider
– Volume: must factor in _________and
__________ of particles
– Pressure: must factor in ___________ and
___________ of interaction
Van der Waals equation
nonideal gas
2
an
( P + V2 ) (V – nb) = nRT
}
}
corrected
pressure
corrected
volume
Does this
experimental
data match
theory?