Download Determination of molar mass for ideal gas

13/14 Semester 2
Physical Chemistry I
(TKK-2246)
Instructor: Rama Oktavian
Email: [email protected]
Office Hr.: M.13-15, Tu. 13-15, W. 13-15, Th. 13-15, F. 09-11
Outlines
1. Review
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.)
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   mi
i 1
k
and
N m   Ni
i 1
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.
mf i 
mi
mm
and
yi 
Ni
Nm
Note that
k
 mf
i 1
k
i
=1
and
y
i
i 1
1
Dalton’s law
Ideal gas law for gas mixture
We define the partial pressure of each gas in the mixture as the pressure the
gas would exert if it were alone in the container of volume V at temperature T
Dalton’s law
Partial pressure
Dalton’s law
Dalton’s law
Dalton’s Law of Partial Pressures indicates
that
• pressure depends on the total number of gas
particles, not on the types of particles.
• the total pressure exerted by gases in a
mixture is the sum of the partial pressures of
those gases.
PT = P1 + P2 + P3 +.....
Dalton’s law
Dalton’s law
Partial pressures are simply related to the mole fractions of the gases
in the mixture
p1 n1 RT V

p nt RT V
Dalton’s law
Partial pressures are simply related to the mole fractions of the gases
in the mixture
Dalton’s law
Learning check
If I place 3 moles of N2 and 4 moles of O2 in a 35 L container at a temperature
of 25°C, what will the pressure of the resulting mixture of gases be?
What’s the partial pressure of carbon dioxide in a container that holds 5
moles of carbon dioxide, 3 moles of nitrogen, and 1 mole of hydrogen and
has a total pressure of 1.05 atm?
Dalton’s law
Learning check
A vessel of volume 22.4 dm3contains 1.5 mol H2and 2.5 mol N2 at
273.15 K. Calculate (a) the mole fractions of each component, (b) their
partial pressures, and (c) their total pressure
Dalton’s law
Dalton’s law application in atmosphere
This explains why people usually difficult to breathe in high altitude place
even the concentration of oxygen is same (21%)
The transfer of oxygen molecules from the lungs to the bloodstream is
dependent on a pressure gradient.
Exercise and learning check
Problems
Ch. 1 Atkin’s Physical chemistry 8th ed. Numerical problems no:
1.4
1.5
1.6
Take-home assignment – Theoretical problem 1.24
Chapter 2 Castellan Physical chemistry 3rd ed. Problems no:
2.9
2.13