13/14 Semester 2
Physical Chemistry I
(TKK-2246)
Instructor: Rama Oktavian
Email: rama.oktavian86@gmail.com
Office Hr.: M.13-15, Tu. 13-15, W. 13-15, Th. 13-15, F. 09-11
Outlines
1. Ideal gas properties
2. Molar mass of gas
3. Molar mass of volatile component
4. Gas mixture
Review
Learning check
A sealed flask with a capacity of 1 dm3 contains 5 g of ethane. The flask is so
weak that it will burst if the pressure exceeds 1 MPa. At what temperature will the
pressure of the gas reach the bursting pressure ?
Review
Learning check
A perfect gas undergoes isothermal compression, which reduces its
volume by 1.80 dm3. The final pressure and volume of the gas are 1.97 bar and
2.14 dm3, respectively. Calculate the original pressure of the gas in (a) bar,
(b) Torr
Review
Learning check
A large cylinder for storing compressed gases has a volume of about 0.050 m3. If
the gas is stored under a pressure of 15 MPa at 300 K, how many moles of
gas are contained in the cylinder ?
What would be the mass of oxygen in such a cylinder ?
Review
Learning check
A manometer consists of a U-shaped tube containing a liquid. One side
is connected to the apparatus and the other is open to the atmosphere. The
pressure inside the apparatus is then determined from the difference in
heights of the liquid. Suppose the liquid is water, the external pressure is
770 Torr, and the open side is 10.0 cm lower than the side connected to the
apparatus. What is the pressure in the apparatus? (The density of water at
25°C is 0.99707 g cm−3.)
Ideal gas and Real gas
Ideal gas
The ideal gas law is used to describe the behavior of an ideal
gas.
Ideal gas: hypothetical gas that obeys kinetic molecular theory
and the ideal gas law
Ideal gas and Real gas
Ideal gas
p V  RT
The ideal gas law was useful in determining the properties of a specific
sample of gas at constant T, P, V, and n.
We often need to know how a change in one (or more) properties impacts the
other properties for a sample of a gas
Ideal gas and Real gas
Real gas
p V  RT
deviations from the perfect gas law because molecules interact
with one another
Repulsive forces are significant only when molecules are
almost in contact
Attractive intermolecular forces have a relatively long range and are
effective over several molecular diameters
Ideal gas and Real gas
Real gas
The compression factor
For ideal gas
Z
Z 1
P  Z  1
P moderate Z < 1
P  Z  1
Ideal gas and Real gas
Real gas
The compression factor
Z 
PV
RT
Z
Ideal gas and Real gas
Equation of state for Real gas
Virial equation of state
How to describe this P-V behavior?
Ideal gas and Real gas
Equation of state for Real gas
Virial equation of state
Z 
PV
RT
Ideal gas and Real gas
Equation of state for Real gas
Virial equation of state
Ideal gas and Real gas
Equation of state for Real gas
Virial equation of state
The second virial coefficient B′ can be obtained from measurements of the
density ρ of a gas at a series of pressures. Show that the graph of p/ρ against
p should be a straight line with slope proportional to B′.
Molar mass of ideal gas
Determination of molar mass for ideal gas
Ideal gas equation
PV  nRT
n
w
M
 w  RT
 
M  
   RT
V  P
P
Intensive properties and
measurable
Molar mass of ideal gas
Determination of molar mass for ideal gas
Gas density
 w  RT
 
M  
   RT
V  P
P
Density is higher
1. for gases with a higher molar mass Gases
2. at higher pressures
3. at lower temperatures
Molar mass of ideal gas
Determination of molar mass for ideal gas
Example
if chemical analysis of a gas yields an empirical formula (CH 2 )n, then the
molar mass must be some multiple of 14 g/mol ; the possibilities are 28, 42, 56,
70, and so on. If a molar mass determination using Eq. (2. 20) yields a
value of 54 g/mol, then we may conclude that n = 4 and that the material
is one of the butenes.
Molar mass of ideal gas
Determination of molar mass for ideal gas
Problem : Calculation of Molecular Weight of a
Natural Gas - Methane
A sample of natural gas is collected at 25.0 C in a 250.0 ml
flask. If the sample had a mass of 0.118 g at a pressure of 550.0 torr,
what is the molecular weight of the gas?
Use the ideal gas law to calculate n, then calculate the molar mass.
Molar mass of ideal gas
Determination of molar mass for ideal gas
Problem
At 100°C and 1.60 kPa, the mass density of phosphorus vapour is
0.6388 kg m−3. What is the molecular formula of phosphorus under these
conditions?
Molar mass of ideal gas
Determination of molar mass for ideal gas
Problem
A series of measurements are made in order to determine the molar mass of an
unknown gas. First, a large flask is evacuated and found to weigh 134.567 g. It is
then filled with the gas to a pressure of 735 torr at 31°C and reweighed; its mass
is now 137.456 g. Finally, the flask is filled with water at 31°C and found to weigh
1067.9 g. (The density of the water at this temperature is 0.997 g/mL.) Assuming
that the ideal-gas equation applies, calculate the molar mass of the unknown gas.
Gas mixture
Air is an example of an ideal gas mixture and has the following approximate
composition.
Component
N2
O2
Argon
CO2 + trace elements
% by Volume
78.10
20.95
0.92
0.03
Gas mixture
Properties of gas mixture
k gases
T = Tm
P = Pm
V = Vm
m = mm
The total mass of the mixture mm and the total moles of mixture Nm are
defined as
k
mm 
m
i 1
k
i
and
Nm 

i 1
Ni
Gas mixture
Properties of gas mixture
Volume concentration
Unit : mol/m3
Volume concentration  molarity
Gas mixture
Properties of gas mixture
The composition of a gas mixture is described by specifying either the mass
fraction mfi or the mole fraction yi of each component i.
mi
mfi 
and
mm
yi 
Ni
Nm
Note that
k
 mf
i 1
k
i
=1
and

i 1
yi  1