Post on 03-Apr-2022
UNIVERSIDAD CARLOS III DE MADRIDUNIVERSIDAD CARLOS III DE MADRID
ChemistryChemistry
TOPIC 2
1TopicTopic 22.. StatesStates ofof MatterMatter (I)(I) -- GasesGases.. 1
States of Matter (I) - Gases
UNIVERSIDAD CARLOS III DE MADRIDUNIVERSIDAD CARLOS III DE MADRID
General Chemistry General Chemistry
Contents1. Introduction2. Pressure measurement3. The Ideal Gas equation4. Efusion and Diffusion
2TopicTopic 22.. StatesStates ofof MatterMatter (I)(I) -- GasesGases.. 2
4. Efusion and Diffusion5. Kinetic Molecular Theory6. Dalton’s Law of Partial Pressure7. Real Gases: van der Waals equation
UNIVERSIDAD CARLOS III DE MADRIDUNIVERSIDAD CARLOS III DE MADRID
General Chemistry General Chemistry
1. IntroductionStates of Matter
Distances Interactions Movement
3TopicTopic 22.. StatesStates ofof MatterMatter (I)(I) -- GasesGases.. 3
Solid Short Very strong Highly restricted
Liquids Short Strong Restricted
Gases Long Weak Almost Free
General Chemistry: Principles and Moderns ApplicationsR.H. Petrucci
UNIVERSIDAD CARLOS III DE MADRIDUNIVERSIDAD CARLOS III DE MADRID
General Chemistry General Chemistry
1. Introduction Where do we find gases?
4TopicTopic 22.. StatesStates ofof MatterMatter (I)(I) -- GasesGases.. 4
http://en.wikipedia.org/wiki/File:Michael_Schumacher_Ferrari_2004.jpg
http://en.wikipedia.org/wiki/File:Automobile_exhaust_gas.jpg
UNIVERSIDAD CARLOS III DE MADRIDUNIVERSIDAD CARLOS III DE MADRID
General Chemistry General Chemistry
2. Pressure Measurement
P = d·g·h
d = densityg = gravityh = height
Barometer
Column of
Vaccum
5TopicTopic 22.. StatesStates ofof MatterMatter (I)(I) -- GasesGases.. 5
h = height
1 atm = 760 mmHg ⇒⇒⇒⇒
atmospheric pressure at sea level
1 Torr = 1 mmHg
Pa = N/m2 <> 1/133.322 Torr
Standard Atmospheric Pressure 1.00 atm760 mm Hg, 760 Torr101.325 kPa1.01325 bar1013.25 mbar
Atmospheric pressure
Column of mercury
760 mmHg for standard atmosphere
UNIVERSIDAD CARLOS III DE MADRIDUNIVERSIDAD CARLOS III DE MADRID
General Chemistry General Chemistry
Manometer
2. Pressure Measurement
Closed end
Open end
Patm
6TopicTopic 22.. StatesStates ofof MatterMatter (I)(I) -- GasesGases.. 6
(a)
Pgas = Ph
Pgas
(b)
Pgas = Patm + Ph
Pgas
Ph = ρ(Hg)·g·h
ρ(Hg)= density of mercury13.6 g·cm3.
g = 9.8 m·s-2.h = distance B-N (in m).
UNIVERSIDAD CARLOS III DE MADRIDUNIVERSIDAD CARLOS III DE MADRID
General Chemistry General Chemistry
Boyle’s LawBoyle’s Law
3. Gases LawsP∝∝∝∝ 1/V when T & n are constant
P·V = k
7TopicTopic 22.. StatesStates ofof MatterMatter (I)(I) -- GasesGases.. 7
P·V = k
P1·V1 = P2·V2 = P3·V3 = · · · ·
For a fixed amount of an ideal gas at a constant temperature, pressure and volume areinversely proportional.
http://www.grc.nasa.gov/WWW/K-12/airplane/boyle.html
UNIVERSIDAD CARLOS III DE MADRIDUNIVERSIDAD CARLOS III DE MADRID
General Chemistry General Chemistry
3. Gases Laws
V ∝∝∝∝ T
V1/T1=V2/T2=k (P& n constant)
V = a(t + 273) where:
Charles and Gay-Lussac’s Law
8TopicTopic 22.. StatesStates ofof MatterMatter (I)(I) -- GasesGases.. 8
V = a(t + 273) where:
- V=volume
- t=temperature in Celsius
- a= slope of the straight line.
T = 273.15 + t
T=Absolute temperature (K)
Image from: http://www.unizar.es/lfnae/luzon/CDR3/charles.jpg
For a fixed amount of an ideal gas at a constant pressure, the volume is directlyproportional to the temperature. V = c· T
UNIVERSIDAD CARLOS III DE MADRIDUNIVERSIDAD CARLOS III DE MADRID
General Chemistry General Chemistry
TheThe Gas Gas ConstantConstant
• Boyle’s law V ∝ 1/P
• Charles’s law V ∝ T
• Avogadro’s law V ∝ n
nT
PV ∝ PV = nRTPV = nRT
The Ideal Gas equationThe Ideal Gas equation
3. Gases Laws
9TopicTopic 22.. StatesStates ofof MatterMatter (I)(I) -- GasesGases.. 9
TheThe Gas Gas ConstantConstant
R = 8,206�10-2 atm�l�mol-1�K-1
<> 8.314 J�mol-1�K-1 <> 1,987 cal�mol-1�K-1
At STP (0 ºC and 1atm) 1 mol gas = 22.4 L gas
Kmol
atmL
Kmol
Latm
nT
pVR 082.0
15.273*1
4.22*1 ===
UNIVERSIDAD CARLOS III DE MADRIDUNIVERSIDAD CARLOS III DE MADRID
General Chemistry General Chemistry
Diffusion
4. Diffusion and Efusion
10TopicTopic 22.. StatesStates ofof MatterMatter (I)(I) -- GasesGases.. 10
M
1R
1R
∝
∝ρ
Graham’s Law
Graham's law states that the rate of diffusion of a certain gas isinversely proportional to the square root of its molecular weight.
UNIVERSIDAD CARLOS III DE MADRIDUNIVERSIDAD CARLOS III DE MADRID
General Chemistry General Chemistry
4. Diffusion and Efusion Why do tyres deflate?
Efusion
11TopicTopic 22.. StatesStates ofof MatterMatter (I)(I) -- GasesGases.. 11
A
B
B
A
M
M
R
R
B ofeffusion of rate
A ofeffusion of rate == Graham’s Law
UNIVERSIDAD CARLOS III DE MADRIDUNIVERSIDAD CARLOS III DE MADRID
General Chemistry General Chemistry
� Particles are point masses (with no volume) in constant,
random and straight line motion.
� Particles are separated by great distances, almost infinite.
� Collisions are elastic.
� There are no intermolecular forces between the particles.
5. Kinetic Molecular Theory Why do tyres deflate?
12TopicTopic 22.. StatesStates ofof MatterMatter (I)(I) -- GasesGases.. 12
� The total energy of the system remains constant.
V
NyProbabilit ∝
V
N=ion Concentrat
2umcollisionper Energy =
3liberty of Degrees =
V
uNmp
3
2
=
0 1000 2000 3000 4000 5000
No.
Mol
ecul
es (
%)
Speed (m/s)
um is the modal speed
uav is the simple average
urms2u=
umuav
urms
UNIVERSIDAD CARLOS III DE MADRIDUNIVERSIDAD CARLOS III DE MADRID
General Chemistry General Chemistry
5. Kinetic Molecular Theory
umN3
1PV 2
A=Let’s consider 1 mol of gas:
If PV = RT (for n= 1 mol):
Oxygen at 273 KM
3RTu rms =
Rel
ativ
e nu
mbe
r o
f M
olec
ules
(%)
13TopicTopic 22.. StatesStates ofof MatterMatter (I)(I) -- GasesGases.. 13
M
3RTu
uM3RT
umN3RT
rms
2
2
A
=
=
=
Considering that NAm = M:
0 1000 2000 3000 4000 5000
Hydrogen at 273 K
Oxygen at 1000 KR
elat
ive
num
ber
of
Mol
ecul
es (%
)
Speed (m/s)
UNIVERSIDAD CARLOS III DE MADRIDUNIVERSIDAD CARLOS III DE MADRID
General Chemistry General Chemistry
The total pressure of a mixture of gases is the sum of the pressures that each gas would
exert if it were present alone.
V , T constant∑=+++==
N
iiCBAT ppppp
1
···= Tii
where
pp χ:
6. Dalton’s Law of Partial Pressure
14TopicTopic 22.. StatesStates ofof MatterMatter (I)(I) -- GasesGases.. 14
P1 = 3.1 atm
P2 = 6.4 atmPtotal = P1 + P2 = 9.5 atm
V
RTnp ii =
pressure total
fraction mole
==
T
i
p
where
χ:
Example : Calculate the total pressure of a mixture of H2 and O2 whose partial pressures are PH2 =2.9 atm and PO2 = 7.2 atm respectively
UNIVERSIDAD CARLOS III DE MADRIDUNIVERSIDAD CARLOS III DE MADRID
General Chemistry General Chemistry
7. Real Gases
The factor “Z = PV/NRT” is known as COMPRESSIBILITY FACTOR and should be one for an ideal gas.
For exactly one mole of an ideal gas:
For exactly one mole of a real gas:
a) Effect of the nature of the gas b) Effect of the temperature
15TopicTopic 22.. StatesStates ofof MatterMatter (I)(I) -- GasesGases.. 15
0
1
2
0 200 400 600 800 1000 1200
NH3
CH4
H2
Ideal Gas
a) Effect of the nature of the gas b) Effect of the temperature
0
1
2
3
0 300 600 900
1000 K
500 K
200 K
Ideal Gas
0.1=RT
PV
P(atm)
0.1=RT
PV
P(atm)
UNIVERSIDAD CARLOS III DE MADRIDUNIVERSIDAD CARLOS III DE MADRID
General Chemistry General Chemistry
7. Real Gases
P + (V – nb) = nRTan2
V2( )
P · V = n·R·T The Ideal Gas Equation
The van der Waals Equation(a real gas equation)
16TopicTopic 22.. StatesStates ofof MatterMatter (I)(I) -- GasesGases.. 16
P + (V – nb) = nRTV2( )
PressureCorrection
VolumeCorrection
(a real gas equation)
a: Effect of intermolecular forces(i.e. nature of the gas)
b: Effect of molecular volume ���� Particles are NOT point masses (with no volume asstates the kinetic molecular theory).