KINETIC THEORY OF GASES - Bowen University
Transcript of KINETIC THEORY OF GASES - Bowen University
Gases • Rather than considering the atomic
nature of matter we can classify it based on the bulk property: gaseous, liquid or solid.
• Gases are the most easily understood form of matter (we shall see why).
Air is an example of a complex mixture of gases: gases form homogeneous mixtures regardless of identities or proportions (unlike liquids and solids).
Gases expand to fill any container, and are highly compressible (unlike liquids and solids)
These characteristics arise because the molecules of gas are very far apart and don’t (mostly) interact. Different gases thus behave similarly.
Component Symbol Volume
Nitrogen N2 78.084%
99.998% Oxygen O2 20.947%
Argon Ar 0.934%
Carbon Dioxide CO2 0.033%
Neon Ne 18.2 parts per million
Helium He 5.2 parts per million
Krypton Kr 1.1 parts per million
Sulfur dioxide SO2 1.0 parts per million
Methane CH4 2.0 parts per million
Hydrogen H2 0.5 parts per million
Nitrous Oxide N2O 0.5 parts per million
Xenon Xe 0.09 parts per million
Ozone O3 0.07 parts per million
Nitrogen dioxide NO2 0.02 parts per million
Iodine I2 0.01 parts per million
Carbon monoxide CO trace
Ammonia NH3 trace
Physical Characteristics of Gases
Physical Characteristics Typical Units
Volume, V liters (L)
Pressure, P atmosphere
(1 atm = 1.015x105 N/m2)
Temperature, T Kelvin (K)
Number of atoms or
molecules, n
mole (1 mol = 6.022x1023
atoms or molecules)
Pressure • Pressure is the force that acts on a given area (P=F/A).
• Gravity on earth exerts a pressure on the atmosphere:
atmospheric pressure.
• We can evaluate this by calculating the force due to
acceleration (by gravity) of a 1m2 column of air extending
through the atmosphere (this has a mass of ~10,000kg).
25
2
5
22
/1011
101/
/000,100/8.9000,10
.
mNm
NAFP
skgmsmkgF
amF
This unit is a Newton (N)
This unit is a Pascal (Pa)
Units of Pressure S.I. unit of pressure is the N/m2, given the name Pascal (Pa).
A related unit is the bar (1x105 Pa) used because atmospheric
pressure is ~ 1x105 Pa (100 kPa, or 1bar).
Torricelli (a student of Galileo) was the first to recognise that the
atmosphere had weight, and measured pressure using a barometer
Standard atmospheric pressure was thus defined
as the pressure sufficient to support a mercury
column of 760mm (units of mmHg, or torr).
Another popular unit was thus introduced to
simplify things, the atmosphere (atm =
760mmHg).
Pressure • Atmospheric pressure and relationship between units
1 atm = 760 mmHg = 760 torr = 101.325kPa = 1.01325 bar)
Measuring Pressure: the manometer
Exercise:
On a certain day a barometer gives the atmospheric pressure as 764.7 torr. If a
metre stick is used to measure a height of 136.4mm in the open arm, and
103.8mm in the gas arm of a manometer, what is the pressure of the gas sample?
(give in torr, atm, kPa and bar).
Result
Difference in height is 32.6 mm. Gas inside has greater pressure than prevailing atmospheric pressure: 764.7 + 32.6 mmHg = 797.3 mmHg (Torr)
Convert to atm: divide by 760 = 1.049 atm
Convert to kPa: multiply by 101.325 = 106.3 kPa
Convert to bar: divide by 100 = 1.063 bar
Gas Laws
• A large number of experiments have determined that 4
variables are sufficient to define the physical condition (or
state) of a gas: the gas laws.
Boyle’s Law,
Charles’ Law,
Avogadro’s hypothesis
Boyle’s Law
• Boyle investigated the variation of the volume occupied by a
gas as the pressure exerted upon it was altered and noted that
the volume of a fixed quantity of gas, at constant temperature
is inversely proportional to the pressure
constantor 1
constant PVp
V
Charles’ Law • A century later, a French scientist, Jacques Charles discovered that the
volume of a fixed amount of gas, as constant pressure, is proportional to the absolute temperature. Cool a balloon, or a sealed plastic bottle, to verify this!
constantor constant T
VTV
It was recognised (by William
Thomson, Lord Kelvin, a Belfast
born physicist) that if the graph was
extrapolated to zero volume, an
absolute zero of -273.15 oC is
obtained.
Avogadro’s Law • Relationship between quantity of gas and volume established by
Gay-Lussac (balloon science!) and Avogadro in the 19th Century.
Result was Avogadro’s hypothesis: equal volumes of gases at the same temperature and pressure contain equal numbers of molecules
Experiments show that 22.4L of gas at 0oC and 1atm
(STP), or 24.8L of gas at 298.15 K and 1 bar (SATP),
contains 6.022 x 1023 molecules (Avogadro’s number, NA)
Avogadro’s law: volume of gas at constant temperature and
pressure is proportional to the number of moles of gas (n)
constant nV Remember:
1 mole = Avogadro’s
number of objects
Putting it all together
nRTPV
P
nTRV
P
nTV
nVTVP
V
, ,1
Boyle, Charles, Avogadro
Combine
Call proportionality constant R
(gas constant)
Ideal Gas Equation
At constant volume,
pressure and absolute
temperature are
directly related.
P = k T
P1 / T1 = P2 / T2
Gay-Lussac Law
The total pressure in a container
is the sum of the pressure each
gas would exert if it were alone
in the container.
The total pressure is the sum of
the partial pressures.
PTotal = P1 + P2 + P3 + P4 + P5 ...
(For each gas P = nRT/V)
Dalton’s Law
Water evaporates!
When that water evaporates, the vapor has a
pressure.
Gases are often collected over water so the vapor
pressure of water must be subtracted from the
total pressure.
Vapor Pressure
Units and dimensional analysis
SI unit for R is J/mol.K or m3.Pa/mol.K (R=8.315 of these units)
Need to use the units of Pa for pressure and m3(=1000L) for volume in any calculation.
Alternatively you can use units of kPa and L.
If you wish to use atm and L
R=0.0826 L.atm/mol/K.
Always use absolute temperature scale (K)
Gas mixtures • Dalton’s Law of partial pressures
The total pressure of a mixture of gases equals the
sum of the pressures that each would exert if it
were present alone
PT=P1+P2+P3+….Pn
Mole Fractions
• The ratio n1/nT is called the mole fraction (denoted x1), a
dimensionless number between 0 and 1.
T
T
TTT
Pn
nP
n
n
VRTn
VRTn
P
P
11
111
/
/
Mole fraction of N2 in air is 0.78, therefore if the total
barometric pressure is 760 torr, the partial pressure of N2 is
(0.78)(760) = 590 torr.
Kinetic –Molecular Theory
Theory describing why gas laws are obeyed (explains both pressure and temperature of gases on a molecular level).
• Complete form of theory, developed over 100 years or so, published by Clausius in 1857.
Gases consist of large numbers of molecules that are in continuous, random motion
Volume of all molecules of the gas is negligible, as are attractive/repulsive interactions
Interactions are brief, through elastic collisions (average kinetic energy does not change)
Average kinetic energy of molecules is proportional to T, and all gases have the same average kinetic energy at any given T.
Because each molecule of gas will have an individual kinetic energy, and thus
individual speed, the speed of molecules in the gas phase is usually characterised
by the root-mean-squared (rms) speed, u,(not the same though similar to the
average speed). Average kinetic energy є = ½mu2
Application to Gas Laws
• Increasing V at constant T:
Constant T means that u is unchanged. But if V is increased the likelihood of collision with the walls decreases, thus the pressure decreases (Boyle’s Law)
• Increasing T at constant V:
Increasing T increases u, increasing collisional frequency with the walls, thus the pressure increases (Ideal Gas Equation).
Molecular speeds and mass • The average kinetic energy of gases has a specific value at
a given temperature. The rms speed of gas composed of light particles, He, is higher than that for heavier particles, Ne, at the same temperature.
• Can derive an expression for the rms speed (from kinetic theory)
M
RTu
3 M is the molar mass
This gives rise to interesting consequences:
effusion
Effusion • Thomas Graham (1846)
discovered that effusion is inversely proportional to the square root of molar mass.
1
2
2
1
M
M
r
r
Derived from comparison
of rms speeds
REAL GASES
Deviations from ideal gas law
WHY? 1. Molecules have volume
2. Molecules have attractive forces
(intermolecular)
1. V-nb
2. -a(n/V)2
Van der Waals Equation of State
2
V
na
nbV
nRTP