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CHM426H1 Lecture Notes - Kinetic Theory Of Gases, Pneumatic Trough, Partial Pressure

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A J Bonner

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Chapter Six
Properties of Gases: Gas Pressure
Gases expand to fill their container and assume the shape of their containers
They diffuse into one another and mix in all proportions.
Four properties determine the physical behaviour of a gas:
1. The amount of the gas (in
2. The volume of the gas (in L)
3. The temperature of the gas (in
4. Pressure of gas (in atm or KPa)
The Concept of Pressure:
Consider this. A balloon expands when inflated with air, but what maintains the
balloon’s shape? One good argument is that the molecules of the gas within the
balloon are in constant motion and thus colliding with each other as well as the walls
of the container, the balloon, keeping the balloon in shape.
However it is difficult to measure the total force exerted by a gas. So in
chemistry, we speak in terms of pressure. Pressure is the force per unit area. In
translation, it is the force divided by the area over which the force is distributed.
Liquid Pressure:
It is difficult to measure the pressure of gas directly. So it is done indirectly by
comparison with liquid pressure. Liquid pressure depends only on the height of the
liquid column and the density of the liquid. Thus the formula, g x h x d, can be
derived. Since g is a constant, liquid pressure is directly proportional to the liquid
density and the height of the liquid column.
Barometric Pressure: (read experiment briefly, not important) the height of
mercury in a barometer, a measure of barometric pressure, varies with
atmospheric conditions and altitude. The standard atmosphere (atm) is defined as
the pressure exerted by a mercury column of exactly 760 mm in height when the
density of mercury = 13.5951 g/cm3 (at 0 ºC). Therefore, it is justified to say 1 atm =
760 mmHg.
Manometers: just remember how that thing looks like, and these three situations:
1. Pgas = Pbar. 2. Pgas = P bar. +
P, ( P>0)Δ Δ
3. Pgas = P bar. +
P, ( P<0)Δ Δ
Boyle’s Law: For a fixed amount of gas at a constant temperature, the gas volume is
inversely proportional to the gas pressure.
P1V1 = n = P2V2
Charles’ Law: The volume of a fixed amount of gas at constant pressure is directly
proportional to the Kelvin (absolute temperature)*
V1/T1 = V2/T2
*All gases condense to liquids/solids before the temperature approaches absolute zero.
0ºC = 273 K and the standard pressure is 1 atm = 760 mmHg.
Avogadro’s equal volumes – equal numbers hypothesis can be stated in two ways:
1. Equal volumes of different gases compared at the same temperature and
pressure contain equal numbers of molecules.
2. Equal numbers of molecules of different gases compared at the same
temperature and pressure occupy equal volumes.
This can be restated in one general phrase known as the Avogadro’s Law:
At a fixed temperature and pressure, the volume of a gas is directly
proportional to the amount of gas. Therefore, 1 mol gas = 22.4 L gas (at STP).
The Ideal Gas Equation: combination of the previous three laws.
PV = nRT
A gas whose behaviour conforms to the ideal gas equation is called an ideal or
perfect gas.
R is a gas constant. Depending on the situation of the reaction, R can have four
different values:
1. 0.082057 L atm mol-1 k-1
2. 62.364 L Torr mol-1 k-1
3. 8.3145 m3 Pa mol-1 k-1
4. 8.3145 J mol-1 k-1
The General Gas Equation
(P1V1/n1T1) = (P1V1/n1T1)
If one or more of the variables remain constant during the reaction, it is acceptable to
remove them from the equation, thus having a more simplified equation and then
continue forward in achieving the final result.
Molar Mass Determination
PV = (mRT/M)
Gas Densities
d = m/V = (n x M)/ V = (n/V) x M
Therefore: d = m / v = (MP/RT)
The density of gases differs from that of solids and liquids in two important ways.
1. Gas densities depend strongly on pressure and temperature, increasing as the
gas pressure increases and decreasing as the temperature increases. Densities
of liquids and solids also depend somewhat on temperature, but they depend
far less on pressure.
2. The density of a gas is directly proportional to its molar mass. No simple
relationship exists between density and molar mass for liquids and solids.
Mixture of Gases
John Dalton proposed that in a mixture, each gas expands to fill the container and
exerts the same pressure (partial pressure) that with if it were alone in a container.
This was the basis of Dalton’s law of partial pressures. It states that the total
pressure of a mixture of gases is the sum of the partial pressures of the components
of the mixture. This rule also formed the basis of a shared principle.
nA/ntot = PA/Ptot = VA/Vtot = xA
The term nA/ntot is given a special name, the mole fraction of A, xA.
Collecting a gas over liquid (definition not important, but known the mathematics
of it.)
Water collected in a pneumatic trough is said to be collected over water and is “wet.”
It is a mixture of two gases – The desired gas and water vapour, both filling a
container with partial pressure.
Gas is composed of a very large number of extremely small particles
(molecules or, in some cases, atoms) in constant, random, straight-line motion)
Molecules of a gas are separated by great distances. The gas is mostly empty
space (the molecules are treated as so-called point masses, as though they
have mass but no volume).
Molecules collide only fleetingly with one another and with the walls of their
container, and most of the time, molecules are not engaged in collisions.
There are assumed to be no forces between molecules except very briefly
during collisions. That is, each molecule acts independently of all others and is
unaffected by their presence, except during collisions.
Individual molecules may gain or lose energy as a result of collisions. In a
collection of molecules at constant temperature, however, the total energy
remains constant.
Deriving the kinetic-molecular theory equation depended on several factors:
1. The amount of translational kinetic energy of the molecules. Translational
kinetic energy is energy possessed by objects moving through space. The
faster the molecule moves, the greater their translational kinetic energies and
the greater the forces exerted between molecules during collisions.
2. The frequency of molecular collisions. Collision frequency increases with the
number of molecules per unit volume and with molecular speeds.
3. When a molecule hits the wall of a vessel, momentum is transferred as the
molecule reverses direction. This momentum transfer is called an impulse. The