Ch5.Gases - Mr. Fischer.com
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Transcript Ch5.Gases - Mr. Fischer.com
Gases
Chapter 5
1
Gas Properties
Four properties determine the physical behavior of
any gas:
Amount of gas
Gas pressure
Gas volume
Gas temperature
2
Gas pressure
Gas molecules
exert a force on the
walls of their
container when
they collide with it
3
Gas pressure
Gas pressure can support a column of liquid
Pliquid = g•h•d
g = acceleration due to the force of gravity (constant)
h = height of the liquid column
d = density of the liquid
4
Atmospheric
pressure
Torricelli barometer
In the closed tube, the liquid
falls until the pressure exerted
by the column of liquid just
balances the pressure exerted
by the atmosphere.
Patmosphere = Pliquid = ghd
Patmosphere liquid height
Standard atmospheric
pressure (1 atm) is
760 mm Hg
5
Units for pressure
In this course we usually convert to atm
6
Gas pressure
Pliquid = g•h•d
Pressure exerted by a column
of liquid is proportional to the
height of the column and the
density of the liquid
Container shape and volume
do not affect pressure
7
Example
A barometer filled with perchloroethylene
(d = 1.62 g/cm3) has a liquid height of 6.38 m.
What is this pressure in mm Hg (d = 13.6 g/cm3)?
P = ghd = g hpce dpce = g hHg dHg
hpce dpce = hHg dHg
hHg = hpce d pce = (6.38 m)(1.62 g/cm3) = 0.760 m
dHg
13.6 g/cm3
hHg = 760 mm Hg
8
Gas pressure
A manometer compares the pressure of a gas in a
container to the atmospheric pressure
9
Gas Laws: Boyle
In 1662, Robert Boyle
discovered the first of
the simple gas laws
PV = constant
For a fixed amount of gas at
constant temperature, gas pressure
and gas volume are inversely
proportional
10
Gas Laws: Charles
In 1787, Jacques Charles discovered a relationship
between gas volume and gas temperature:
• relationship between volume
and temperature is always linear
• all gases reach V = 0 at same
temperature, –273.15 °C
volume (mL)
• this temperature is
ABSOLUTE ZERO
temperature (°C)
12
A temperature scale for gases:
the Kelvin scale
A new temperature scale was invented: the Kelvin
or absolute temperature scale
K = °C + 273.15
Zero Kelvins = absolute zero
13
Gas laws: Charles
Using the Kelvin scale, Charles’ results is
For a fixed amount of gas at constant pressure, gas
volume and gas temperature are directly proportional
V
constant
T
A similar relationship was found for pressure and
temperature:
P
constant
T
14
Standard conditions for gases
Certain conditions of pressure and temperature
have been chosen as standard conditions for gases
Standard temperature is 273.15 K (0 °C)
Standard pressure is exactly 1 atm (760 mm Hg)
These conditions are referred to as STP
(standard temperature and pressure)
16
Gas laws: Avogadro
In 1811, Avogadro proposed that equal volumes of
gases at the same temperature and pressure contain
equal numbers of particles.
At constant temperature and pressure, gas volume is
directly proportional to the number of moles of gas
V
constant
n
Standard molar volume: at STP, one mole of gas
occupies 22.4 L
17
Putting it all together:
Ideal Gas Equation
Combining Boyle’s Law, Charles’ Law, and
Avogadro’s Law give one equation that includes all
four gas variables:
PV
R
nT
or PV nRT
R is the ideal or universal gas constant
R = 0.08206 atm L/mol K
19
Using the Ideal Gas Equation
Ideal gas equation may be expressed two ways:
One set of conditions: ideal gas law
PV nRT
Two sets of conditions: general gas equation
P1V1 P2V2
n1T1 n2T2
20
Ideal Gas Equation and molar mass
Solving for molar mass (M)
PV nRT
m
n
M
mRT
PV
M
mRT
M
PV
22
Ideal Gas Equation and gas density
mRT
PV nRT
M
mRT
P
VM
d
dRT
P
M
m
V
MP
d
RT
24
Gas density
Gas density depends directly
on pressure and inversely on
temperature
Gas density is directly
proportional to molar mass
MP
d
RT
25
Mixtures of Gases
Ideal gas law applies to pure gases and to mixtures
In a gas mixture, each gas occupies the entire
container volume, at its own pressure
The pressure contributed by a gas in a mixture is
the partial pressure of that gas
Ptotal = PA + PB
(Dalton’s Law of Partial Pressures)
27
Mixtures of
Gases
When a gas is collected over water, it is always
“wet” (mixed with water vapor).
Ptotal = Pbarometric = Pgas + Pwater vapor
Example: If 35.5 mL of H2 are collected over water at
26 °C and a barometric pressure of 755 mm Hg, what is
the pressure of the H2 gas? The water vapor pressure at
26 °C is 25.2 mm Hg.
28
Gas mixtures
The mole fraction represents the contribution of
each gas to the total number of moles.
XA = mole fraction of A
nA
XA
ntotal
29
Gas Mixtures
For gas mixtures,
nA
PA
VA
ntotal Ptotal Vtotal
mole fraction
equals
pressure fraction
equals
volume fraction
Each gas occupies
the entire container.
The volume fraction describes
the % composition by volume.
32
Gases in Chemical Reactions
PV
To convert gas volume into moles for
n
RT
stoichiometry, use the ideal gas equation:
If both substances in the problem are gases, at the
same T and P, gas volume ratios = mole ratios.
n2
n1
P2 V2
RT2
P1V1
RT1
V2
V1
P2 = P1 and T2 = T1
34
A Model for Gas Behavior
Gas laws describe what gases do, but not why.
Kinetic Molecular Theory of Gases (KMT) is the
model that explains gas behavior.
developed by Maxwell & Boltzmann in the mid-1800s
based on the concept of an ideal or perfect gas
36
Ideal gas
Composed of tiny particles in constant, random, straight-line motion
Gas molecules are point masses, so gas volume is just the empty
space between the molecules
Molecules collide with each other and with the walls of their
container
The molecules are completely independent of each other, with no
attractive or repulsive forces between them.
Individual molecules may gain or lose energy during collisions, but
the total energy of the gas sample depends only on the absolute
temperature.
37
Molecular collisions and pressure
Force of molecular collisions depends on
collision frequency
molecule kinetic energy, ek
1 2
ek mu
2
ek
depends on molecule mass m and molecule speed u
molecules move at various speeds in all directions
38
Molecular speed
Molecules move at various speeds
Imagine 3 cars going 40 mph, 50 mph, and 60 mph
Mean speed = u = (40 + 50 + 60) ÷ 3 = 50 mph
Mean square speed (average of speeds squared)
u2 = (402 + 502 + 602) ÷ 3 = 2567 m2/hr2
Root mean square speed
urms = √2567 m2/hr2 = 50.7 mph
39
Distribution of molecule speeds
40
The basic equation
of KMT
1N
2
P
mu
3V
Combining collision frequency, molecule kinetic
energy, and the distribution of molecule speeds
gives the basic equation of KMT
P = gas pressure and V = gas volume
N = number of molecules
m = molecule mass
u2 = mean square molecule speed (average of speeds squared)
41
Combine the Equations of
KMT and Ideal Gas
1N
2
P
mu
3V
If n = 1,
N = NAAvogadro’s number
and
PV = RT
PV nRT
1 NA
2
P
mu
3 V
PV N A m u RT
1
3
2
42
Combine the Equations of
KMT and Ideal Gas
PV N A m u RT
1
3
2
N A mu 3RT M u
2
2
NA x m (Avogadro’s number x mass of one molecule)
= mass of one mole of molecules (molar mass M)
43
Combine the Equations of
KMT and Ideal Gas
3RT M u
2
u urms
2
3RT
M
We can calculate the root mean square speed
from temperature and molar mass
44
Calculating root mean square speed
To calculate root mean square speed from
temperature and molar mass:
Units must agree!
Speed is in m/s, so
urms
3RT
M
R must be 8.3145 J/mol K
M must be in kg per mole, because Joule = kg m2 / s2
Speed is inversely related to molar mass: light
molecules are faster, heavy molecules are slower
45
Interpreting temperature
Combine the KMT and ideal gas equations again
Again assume n=1, so N = NA and PV = RT
PV NAmu NA mu
2
1
3
PV N
2
3
mu
1
A 2
2
2
3
1
2
2
3
2
N A e k RT
R
ek
T constant T
NA
3
2
47
Interpreting
temperature
R
ek
T
NA
3
2
Absolute (Kelvin)
temperature is
directly
proportional to
average
molecular kinetic
energy
At T = 0, ek = 0
48
Diffusion and Effusion
Diffusion (a) is
migration or mixing
due to random
molecular motion
Effusion (b) is escape
of gas molecules
through a tiny hole
49
Rates of diffusion/effusion
The rate of diffusion or effusion is directly
proportional to molecular speed:
rat e of effusion of A (urms)A
3RT MA
rat e of effusion of B (urms)B
3RT MB
MB
MA
The rates of diffusion/effusion of two different
gases are inversely proportional to the square roots
of their molar masses (Graham’s Law)
50
Using Graham’s Law
rat e of effusion of A (urms)A
rat e of effusion of B (urms)B
MB
MA
Graham’s Law applies to relative rates, speeds,
amounts of gas effused in a given time, or
distances traveled in a given time.
51
Using Graham’s Law with times
Graham’s law can be confusing when applied to
times
rat
e
A
n
/t
M
A
A
B
rate = amount of gas (n)
time (t)
rat e B nB/t B
MA
For same amount s of A and B
tB
tA
MB
MA
52
Use common sense
with Graham’s Law
When you compare two gases, the lighter gas
escapes at a greater rate
has a greater root mean square speed
can effuse a larger amount in a given time
can travel farther in a given time
needs less time for a given amount to escape or travel
Make sure your answer reflects this reality!
53
Reality Check
Ideal gas molecules
constant, random,
straight-line motion
point masses
independent of each other
gain / lose energy during
collisions, but total energy
depends only on T ek)
Real gas molecules
same
are NOT points – molecules
have volume; Vreal gas > Videal gas
are NOT independent –
molecules are attracted to
each other, so Preal gas < Pideal gas
same (some energy may be
absorbed in molecular
)
56
Real gas corrections
For a real gas,
a corrects for attractions between gas molecules, which
tend to decrease the force and/or frequency of collisions
(so Preal < Pideal)
b corrects for the actual volume of each gas molecule,
which increases the amount of space the gas occupies
(so Vreal > Videal)
The values of a and b depend on the type of gas
57
An equation for real gases:
the van der Waals equation
2
n
a
P
V – nb nRT P V
re al
2
re al
ideal ideal
V
Add correction to Preal to make it equal to Pideal,
because intermolecular attractions decrease real pressure
Subtract correction to Vreal to make it equal to Videal,
because molecular volume increases real volume
58
When do I need
the van der Waals equation?
Deviations from ideality become significant when
molecules are close together (high pressure)
molecules are slow (low temperature)
}
non-ideal
conditions
At low pressure and high temperature, real gases
tend to behave ideally
At high pressure and low temperature, real gases
do not tend to behave ideally
59