Phy351 ch 1 ideal law, gas law, condensed, triple point, van der waals eq
Condensed Matter-solid and liquid
Van der Waals of State Equation
Gases are a state of matter characterized by
two properties which are lack of exact volume
and lack of exact shape.
There are three properties of gases:
The Gas Laws and Absolute
The relationship between the volume,
pressure, temperature, and mass of a gas is
called an equation of state.
The gases law that we will cover for this
Pressure law or Gay-Lussac law
The volume of a gas depends on the pressure exerted on
it. When you pump up a bicycle tire, you push down on a
handle that squeezes the gas inside the pump. You can
squeeze a balloon and reduce its size (the volume it
In general, the greater the pressure exerted on a gas,
the less its volume and vice versa.
This relationship is true only if the temperature of the
gas remains constant while the pressure is changed.
to the volume.
Boyle‟s law definition:
..’The volume of a given
amount of gas is inversely
proportional to the absolute
pressure as long as the
temperature is constant’..
We can see that the data fit into a
pattern called a hyperbola.
If, however we
plot pressure against 1/volume
we get a linear (straight line)
PV = constant
P1V1 = P2V2
Charles‟s law definition:
..’ the volume of a given
amount of gas is directly
proportional to the absolute
temperature (Kelvin) when the
pressure is kept constant’..
V/T = constant
V1/T1 = V2/T2
By extrapolating, the volume becomes zero at
−273.15°C; this temperature is called absolute
zero (refer figure).
Therefore, absolute temperature:
T(K) = T(C) + 273.15
..’The absolute pressure of a given amount of gas
is directly proportional to the absolute temperature
(K) when the volume is kept constant’..
P/T = constant
P1/T1 = P2/T2
Known as the Kelvin scale. Degrees are same
size as Celcius scale.
Absolute zero = 0°C = 273.15 K
At standard atmospheric pressure :
Room temperature is about 293 K (20°C)
Standard temperature is 273 K
Water freezes at 273.15 K and boils at 373.15
T (K) = T (°C) + 273.15
If any gas could be cooled to -273°C, the volume would
The Ideal Gas Law
This three gas laws can be combined to produced a single
more general relation between absolute pressure, volume
and absolute temperature; that is:
Where PV/T = constant
P1V1/T1 = P2V2/T2
Now we are looking to a simple experiment where the
balloon is blown up at a constant pressure and temperature
It is found that, the volume, V of a gas increases in direct
proportion to the mass, m of a gas present:
Hence we can write:
A mole (mol) is defined as the number of grams of a
substance that is numerically equal to the molecular mass of
1 mol H2 has a mass of 2 g.
1 mol Ne has a mass of 20 g.
iii. 1 mol CO2 has a mass of 44 g; where the molecular
mass for CO2 = [12 + (2 x 16)] = 44 g/mol
Where the number of moles in a certain mass of material
is given as:
law can be written as:
the equation for IDEAL GAS
Where n is the number of moles and R is the universal gas
constant and its value is given as:
The ideal gas law often refers to “standard conditions” or
standard temperature and pressure (STP). Where at STP:
T = 273 K
P = 1.00 atm
= 1.013 x 105 N/m2
= 101.3 kPa
1 mol STP gas has:
Volume = 22.4L
ii. No. of molecule/moles = 6.023 x 1023 molecules
When using and dealing with all this three gas laws and also
ideal gas law; the temperature must in Kelvin (K) and the
pressure must always be absolute pressure, not gauge
Absolute pressure = gauge pressure + atmospheric pressure
1. Determine the volume of 1.00 mol of any gas, assuming
it behaves like an ideal gas, at STP.
(ans: 0.0224 m3)
2. An automobile tire is filled to a gauge pressure of 200
kPa at 10°C. After a drive of 100 km, the temperature
within the tire rises to 40°C. What is the pressure within
the tire now?
(ans: 333 kPa)
Ideal Gas Law in Terms of
Molecules: Avogadro’s Number
Since the gas constant is universal, the number of
molecules in one mole is the SAME for all gases. That number
is called Avogadro‟s number:
The number of molecules in a gas is the number of moles
times Avogadro‟s number:
Therefore we can write:
Where k is called Boltzmann‟s constant
Kinetic Theory and the Molecular
Interpretation of Temperature
The force exerted on the wall by the collision of one
Then the force due to all molecules colliding with that
(a)Molecules of a gas moving about
in a rectangular container.
(a) Arrows indicate the momentum
of one molecules as it rebounds
from the end wall.
The averages of the squares of the speeds in all three
directions are equal:
So the pressure is:
The average translational kinetic energy of the
molecules in an ideal gas is directly proportional to the
temperature of the gas.
We can invert this to find the average speed of
molecules in a gas as a function of temperature:
Distribution of Molecular
These two graphs show the distribution of speeds of
molecules in a gas, as derived by Maxwell. The most
probable speed, vP, is not quite the same as the rms
Figure 13.17: Distribution of speeds of molecules in an ideal gas.
vrms is not at the peak of the curve because the curve is skewed to the right (not symmetrical).
vp is called the „most probable speed.
As expected, the curves shift to the right with temperature.
Figure 13.18: Distribution of molecular speeds for two different temperature
The ideal gas law equation is given as;
The term of “ideal” refers to characteristics/behavior of gas
where at “ideal”, the pressure of gas is too high and the
temperature of gas close/near the liquefaction point (boiling
However, at pressures less than an atmosphere or so (not
too high), and when temperature is not close to the boiling
point of the gas, it is refers to behavior of real gases.
Figure below is the curve of P vs V at temperature
constant for ideal gas (Boyle`s law).
And figure below is the curves represent the behavior of
the gas at different temperatures (not constant) for real
gases. Where TA TB TC TD
It is found that, the cooler (temperature decrease @
farther from boiling point) it gets, the further the gas is from
Below the critical temperature (the gas can liquefy if the
pressure is sufficient; above it, no amount of pressure
The dashed curve A` and B`
represents the behavior of a gas as
predicted by the ideal gas law (Boyle`s
law) for several different values of the
We see that, the behavior of gas
deviates even more from the curves
predicted by ideal gas law (curves A
and B), and the deviation is greater
when the gas is closer to liquid-vapor
region (curve C and D).
Figure 13.19: PV diagram for
In curve D, the gas becomes liquid; it begins condensing
at (b) and is entirely liquid at (a).
Curve C represent the behavior of the substance at its
critical temperature, and the point (c) is called the critical
At temperature less than the critical temperature, a gas
will change to the liquid phase if sufficient pressure is
The behavior of a substance can be diagrammed not only
on a PV diagram but also on a PT diagram.
A PT diagram is called a phase diagram; it shows all
three phases of matter:
The solid-liquid transition (in equilibrium) is melting
The liquid-vapor transition is boiling or condensing
The solid-vapor transition is sublimation. Where
sublimation refers to the process whereby at low
pressures a solid changes directly into the vapor
phase without passing through the liquid phase.
The intersection of the three curves is called the triple
point. Where it is only at triple point that the three phases
can exist together in equilibrium.
Figure 13.20: Phase diagram of water.
Figure 13.21: Phase diagram of carbon dioxide.
23. CO2exists in what phase when the pressure is 30 atm and the
temperature is 30°C (Fig. 18–6)?
24. (a) At atmospheric pressure, in what phases can exist?
(b) For what range of pressures and temperatures can be a liquid?
Refer to Fig. 18–6.
25. Water is in which phase when the pressure is 0.01 atm and the
26. You have a sample of water and are able to control temperature and
(a) Using Fig. 18–5, describe the phase changes you would see if you
started at a temperature of 85°C, a pressure of 180 atm, and
decreased the pressure down to 0.004 atm while keeping the
(b) Repeat part (a) with the temperature at 0.0°C. Assume that you
held the system at the starting conditions long enough for the system
to stabilize before making further changes.
Van Der Waals of State
To get a more realistic model of a gas, we
include the finite size of the molecules and the
range of the intermolecular force beyond the
size of the molecule.
Molecules of radius, r colliding.
The van der Waals equation is:
P = pressure (atm)
n = number of moles (mol)
R = ideal gas constant
V = volume (liter)
T = temperature (Kelvin,K)
a and b = constants
The PV diagram for a Van der Waals gas fits most
experimental data quite well.
PV diagram for a van der Waals gas, shown for four different temperature.
For TA, TB and TC (TC is chosen equal
to the critical temperature), the curves
fit the experimental data very well for
The curves labeled TD, a temperature
below the critical point, passes through
the liquid-vapor region.
The maximum (poin b) and minimum (point d) would seem to be
artifacts, since we usually see constant pressure, as imdicated by
the horizontal dashed line.
However, for very pure supersaturated vapors or supercooled
liquids, the sections ab and ed respectively, have been observed.
The section bd would be unstable and has not been observed.
41.For oxygen gas, the van der Waals equation of
state achieves its best fit for and Determine
the pressure in 1.0 mol of the gas at 0°C if its
volume is 0.70 L, calculated using
(a) the van der Waals equation
(b) the ideal gas law.