The Definition of a Gas Gas - a substance that is characterised
by widely separated molecules in rapid motion. Mixtures of gases
are uniform. Gases will expand to fill containers.
Slide 4
Examples of Gaseous Substances Common gases O 2 and N 2, the
major components of "air" Other gases F 2, Cl 2, H 2 gaseous
diatomic molecules H 2 and He are the lighter than air gases N 2 O
(laughing gas)
Slide 5
Three States of Matter SolidsLiquidsGases
Slide 6
Gases (contd) Most molecular compounds are solids or liquids at
room temperature, but they can be converted to a gas relatively
easily Important exception ionic solids (e.g., NaCl) can't be
easily coverted to gases
Slide 7
Gases and Vapours What is the difference between a gas and a
vapour? Gases normally in the gaseous state at 25C and 1 atm
pressure A vapour is the gaseous form of any substance that is
normally in the liquid or solid state at normal temperatures and
pressures
Slide 8
The Definition of Pressure The pressure of a gas is best
defined as the forces exerted by gas on the walls of the container
Define P = force/area The SI unit of pressure is the Pascal 1 Pa =
N/m 2 = (kg m/s 2 )/m 2
Slide 9
The Measurement of Pressure How do we measure gas pressure?
Barometer - invented by Torricelli Gas pressure conversion factors
1 atm = 760 mm Hg = 760 Torr 1 atm = 101.325 kpa = 1.01325 bar
Slide 10
The Barometer
Slide 11
The Gas Laws Four variables were sufficient to fully describe
the state of a gas Pressure (P) Volume (V) Temperature (T) The
amount of the gas in moles (n)
Slide 12
Boyle's Law The gas volume/pressure relationship The volume
occupied by the gas is inversely proportional to the pressure V 1/P
Temperature and the amount of the gas are fixed V = k 1 / P or PV =
k 1 k 1 is a proportionality constant
Slide 13
Boyle's Law
Slide 14
Charles and Gay-Lussac's Law Defines the gas volume/temperature
relationship V T (constant pressure and amount of gas) Note T
represents the temperature on Lord Kelvin's temperature Scale V = k
2 T k 2 proportionality constant
Slide 15
Charles and Gay-Lussac's Law
Slide 16
An Aside The Kelvin temperature scale - Lord Kelvin recognised
the significance of the intercept in the volume/temperature
relationship All temperature (C) vs. volume plots extrapolated to 0
volume at -273.15C Kelvin - absolute 0 all thermal motion
ceases
Slide 17
The Kelvin Temperature Scale Relating Kelvin scale and the
Celcius scale T (K) = [ t c (C) + 273.15C] K/C Freezing point of
water: t c = 0 C; T = 273.15 K Boiling point of water: t c = 100 C;
T = 373.15 K Room temperature: t c = 25 C; T = 298 K NOTE t c = C;
T (K) = K NO DEGREE SIGN
Slide 18
Amontons Law The pressure/temperature relationship For a given
quantity of gas at a fixed volume, P T P = k 3 T P 1 = k 3 T 1 P 2
= k 3 T 2 P 1 / T 1 = P 2 / T 2 Amonton's law
Slide 19
Amontons Law P / atm t / C t = -273.15 C V1V1 V2V2 V3V3
V4V4
Slide 20
Avogadros Law The volume of a gas at constant T and P is
directly proportional to the number of moles of gas V = k 4 n =>
n = number of moles of gas
Slide 21
Avogadros Law
Slide 22
The Ideal Gas Equation of State We have four relationships V
1/P; Boyles law V T; Charles and Gay-Lussac's law V n; Avogadros
law P T; Amontons law
Slide 23
Ideal Gas Equation of State We combine these relationships into
a single fundamental equation of state the ideal gas equation PV =
nRT R is the universal gas constant R = 0.082057 L atm / (K mol) =
8.314 J / (K mol)
Slide 24
The Definition of an Ideal Gas An ideal gas is a gas that obeys
totally the ideal gas law over its entire P-V-T range Ideal gases -
molecules have negligible intermolecular attractive forces Occupy a
negligible volume compared to the container volume
Slide 25
Standard Temperature and Pressure Define:STP (Standard
Temperature and Pressure) Temperature 0.00 C = 273.15 K Pressure
1.000 atm The volume occupied by 1.000 mole of an ideal gas at STP
is 22.41 L!
Slide 26
Gas Density Calculations A simple expression for calculating
the molar mass of an unknown gas. Molar mass and gas density M =
(dRT) / P d = the gas density
Slide 27
Partial Pressures Let's consider two ideal gases (gas 1 and gas
2) in a container of volume V. 1 2 22 2 2 1 1 1 1 1 1 2 2
Slide 28
Dalton's Law of Partial Pressure In a gaseous mixture, each gas
exerts the same pressure as if it was alone and occupied the same
volume. the partial pressure of each gas, P i, is related to the
total pressure by P i = X i P T X i is the mole fraction of gas
i.
Slide 29
Partial Pressures (contd) The pressure exerted by the gases is
the sum of the partial pressures of the individual gases Let P 1
and P 2 be the partial pressures of gas 1 and 2, respectively. P T
= P 1 + P 2 = n T (RT/V), P T = n 1 (RT/V) + n 2 (RT / V)
Slide 30
The Mole Fraction The mole fraction is defined as follows For a
two component mixture n 1 = moles of substance 1 n 2 = moles of
substance 2 n T = n 1 + n 2 X 1 = n 1 / n T ; X 2 = n 2 / n T
Slide 31
Gas Collection Over Water
Slide 32
Many gas measurements are carried out over water. Water vapour
is collected with the gas. P T = P gas + P H 2 O
Slide 33
Kinetic Molecular Theory of Gases Macroscopic (i.e., large
quantity) behaviour of gases. The kinetic molecular theory of gases
attempts to explain the behaviour of gases on a molecular
level.
Slide 34
Kinetic Theory of Gases Gases consist of molecules widely
separated in space. Volume of molecules is negligible compared to
total gas volume. Gas molecules are in constant, rapid, straight-
line motion. Collisions are elastic. Average kinetic energy (K.E.)
of molecules depends on absolute temperature (T) only. Attractive
forces between molecules are negligible.
Slide 35
Kinetic Theory of Gases
Slide 36
Gas Laws Explanations Gas pressure results from collisions of
gas molecules with the container walls. Pressure depends on the
number of collisions per unit time how hard gas molecules strike
the container wall!
Slide 37
Avogadros Law Let's increase the amount of gas in the container
(T, P constant) More collisions of gas with container wall. V n at
constant P, T.
Slide 38
Boyle's Law Let's decrease the volume of the container
(constant n and T). More collisions of the gas molecules with the
container wall and P increases. (V 1/P)
Slide 39
Charles and Gay-Lussacs Law Let container volume increase (P, n
are held constant). Low Temp. High Temp. The molecules must move
faster T must increase.
Slide 40
Molecular Speeds K.E. = 1/2 M U 2 M = the molar mass of the gas
U 2 =the mean square speed of the gas This speed is an average
speed (some will always be fast, some slow).
Slide 41
The Mean Square Speed Kinetic Molecular Theory of Gases allows
us to relate macroscopic measurements to molecular quantities P, V
are related to the molar mass and mean square seed, U 2 P V = 1/3 n
M U 2 = n R T
Slide 42
The Root Mean Square Speed 1/3 MU 2 = RT U 2 = 3RT / M (U 2 )
1/2 = u rms = (3RT/M) 1/2 u rms = the root mean square speed
Slide 43
The Root Mean Square Speed
Slide 44
The Mean Free Path Gas molecules encounter collisions with
other gas molecules and with the walls of the container Define the
mean free path as the average distance between successive molecular
collisions
Slide 45
The Mean Free Path
Slide 46
As the pressure of the gas increases, the mean free path
decreases, i.e., the higher the pressure, the greater the number of
collisions encountered by a gas molecule.
Slide 47
Diffusion Diffusion - gradual mixing of gas molecules caused by
kinetic properties. Graham's Law Under constant T, P, the diffusion
rates for gaseous substances are inversely proportional to the
square roots of their molar masses.
Slide 48
Grahams Law r 1 /r 2 = (M 2 / M 1 ) 1/2 r 1 and r 2 are the
diffusion rates of gases 1 and 2. M 1 and M 2 are the molar masses
of gas 1 and gas 2, respectively.
Slide 49
Effusion Effusion - the process by which a gas under pressure
goes (escapes) from one compartment of a container to another by
passing through a small opening.
Slide 50
Effusion
Slide 51
The Effusion Equation Grahams Law - estimate the ratio of the
effusion times for two different gases. t 1 /t 2 = (M 1 / M 2 ) 1/2
t 1 and t 2 are the effusion times of gases 1 and 2. M 1 and M 2
are the molar masses of gas 1 and gas 2, respectively.
Slide 52
Deviations from Ideal Gas Behaviour The ideal gas equation is
not an adequate description of the P,V, and T behaviour of most
real gases. Most real gases depart from ideal behaviour at
deviation from low temperature high pressure
Slide 53
Deviations from Ideal Gas Behaviour at Low Temperatures
Slide 54
Deviations from Ideal Gas Behaviour at High Pressures
Slide 55
Deviations from Ideal Behaviour Look at assumptions for ideal
gas Real gas molecules do attract one another. (i.e., P id = P obs
+ constant). Real gas molecules do not occupy an infinitely small
volume (they are not point masses). (V id = V obs - const.)
Slide 56
The Van der Waals Equation V id = V obs - nb where b is a
constant for specific different gases. P id = P obs + a (n / V) 2
where a is also different for different gases. Ideal gas Law P id V
id = nRT
Slide 57
The Van der Waal's Equation (contd) (P obs + a (n / V) 2 ) x (V
obs - nb) = nRT Van der Waalss equation of state for real gases.
Two constants (a, b) that are experimentally determined for each
separate gas Table 10.3 in text.