Download a Gas

Gases
States of Matter
A Solid
- occupies a definite volume and has a definite shape..
-atoms are in close contact
A Liquid
- has a specific volume but it assumes the shape of its container.
- it has a ability to flow -the distances between atoms are greater than in a
solid
a Gas
- has neither a shape of its own nor fixed volume. It takes the shape and
volume of its container.
- Gas mixtures are always homogeneous
- Gases are highly compressible.
- The molecules of a gas are relatively far away each other.
- Individual gas molecules have little interaction with their neighbors.
- Gas molecules move freely in every dimension of space randomly
Number of gas substances are few,
Pressure is a force per unit area.
For gas,
P=
F
------A
Force = (mass*acceleration) or F=ma
F orce is expressed in Newtons (N) and area is expressed in square meters (m2)
The SI unit of pressure is N/m2 is called Pascal (Pa)
For liquid
P = g ·h ·d
g = gravitational force 9.81 m/s2
h = height of a column
d = density of a liquid
Atmospheric pressure is measured by a mercury barometer.
At sea level, The standard atmospheric pressure
is the pressure sufficient to support a column of
mercury 760mm in height.
1.0 atm = 760 mmHg = 760 torr = 1.01325 bar = 1.01325x105 Pa
In the laboratories, the gas pressures is measured by manometer.
question : what is the height of a column of water that exerts the same pressure as
acolumn of mercury 76.00cm high? Density of mercury is 13.6g/ml
question:
a) convert to 0.357 atm to bar.
b) convert 147200 Pa to torr
Gas laws
Amount of gas, volume of gas, temperature and pressure are the fundamentals
properties to determine the physical behavior of a gas.
Boyle’s law
(the pressure-volume relationship)
Charles’s Law
The temperature - volume relationship
For a fixed amount of gas at a constant temperature,
the gas Volume is inversely proportional to the gas
Pressure.
The Volume of a fixed amount of a gas at a constant
pressure is directly proportional to its absolute
(Kelvin) Temperature.
•Boyle 1662
Pinitial . Vinitial = constant = Pfinal . Vfinal
Charles 1787
Gay-Lussac 1802
Vinitial
Vfinal
----------- = ---------Tinitial
Tfinal
In 1848 William Thomson (Lord Kelvin) proposed an
absolute temperature scale known as Kelvin scale. On
this scale 0°K is called absolute zero, equals -273.15°C.
T (K) = t ( C) +273.15
the standard temperature for gases is defined as 0 C=273.15K and the
standard pressure is defined as 1atm=760mmHg.
These Standard conditions are usually abbreviated as STP.
P = 1 atm = 760 mm Hg
T = 0°C
= 273.15 K
At 1.0 atmosphere pressure and 0°C,
1 mole of any gas (i.e. 6.02 x10over23 gas molecules) occupies approximately
22.4 liters volume.
At STP
1 mol gas = 22.4 L gas
If the proportionality constant is called "R",
This equation is known as the ideal-gas equation . An ideal gas is a gas
whose physical behavior is accurately described by the ideal-gas equation.
Values for the gas constant R
Units
Value
0.08206
Temperature, T, must always be expressed on
an absolute-temperature scale (K)
cal/mol K
1.987
The quantity of gas, n, is normally expressed in
moles
J/mol K
8.314
m3 Pa/mol K
8.314
L atm/mol K
The units chosen for pressure and volume are
typically atmospheres (atm) and liters (l),
however, other units may be chosen
have the units of energy:
PV can
question : what is the pressure exerted by
0.508 mol O2 in a 15.0L container at 303
K?
question : what is the mass of propane,
C3H8 in a 50.0L container of the gas at
STP?
Molar Mass and Gas Densities
PV = nRT
and
m
m
, n=
d=
M
V
m
RT
PV =
M
m
=d=
V
MP
RT
question: calculate the molar mass of a liquid that
vaporized at 100°C and 755 Torr yields 185mL of
vapor with a mass 0.523g
Mixtures of Gases
Dalton’s law The total pressure of a mixture of gases equals the sum of
the pressures that each would exert if it were present alone.
Pt is the total pressure of a sample which contains a mixture of gases
P1, P2, P3, etc. are the partial pressures of the gases in the mixture
Partial pressure
– Each component of a gas mixture exerts a pressure that it
would exert if it were in the container alone.
The partial pressure of a gas is equal to its mole
fraction times the total pressure
the term (X1 = n1 / nt ) is the mole fraction of a substance in the gaseous
mixture.
The mole fraction of a component expresses the ratio of the number of moles of
one component to the total number of moles in the mixture.
question : A gaseous mixture made from 10 g of oxygen and 15 g of methane is
placed in a 10.0 L vessel at 25°C. What is the partial pressure of each gas, and
what is the total pressure in the vessel?
question : the main component of dry air by volume N2 78.08%, O2 20.95% Ar
0.93% and CO2 0.04%. what are the partial pressures of each of the four gases in
a sample of air at 1.00atm.
question : the total pressure of a gas mixture which containing 0.2 mol of CH4,
0.3 mol of N2 and 0.5 mol of H2, is 2atm. Calculate the partial pressures of
each gases in atm.
• Question: the reaction of aluminum with HCl produces
Hydrogen gas,
Al (s) + HCl (aq) → AlCl3 (aq) + H2 (g)
if 35.5ml of H2 is collected over water at 26 °C and barometric pressure
of 755.0mmHg, how many moles of HCl must have been consumed
Pwater= at 26 C is 25.2mmHg
0,37gr KClO3 was heated and O2 produced in this reaction wwas collected over water.
The temperatuer of water is 23°C ve atmosferic pressure is 751mmHg. What is the
volume of O2 collected over water. Vapor pressure of water at 23°C is 21,1mmHg
P tot= P gas
+
P H2O
Kinetic Molecular Theory
• Particles are point masses in constant, random, straight line
motion.
• Particles are separated by great distances. the actual volume of
molecules is negligible.
• Collisions are rapid and elastic.
• No force between particles.
• Total energy remains constant.
• The average kinetic energy of the molecules is proportional to
absolute temperature
• Translational kinetic
energy,
1
e k  mu 2
2
• Frequency of
collisions,
N
vu
V
• Impulse or momentum
transfer,
I  mu
• Pressure proportional
to impulse times
frequency
N
P  mu 2
V
• Three dimensional systems lead to:
P
1N
m u2
3V
1
2
PV  N A m u
3
3RT  N A m u
3RT  M u
u rms 
2
3RT
M
2
Molecular Speed
The root mean square speed urms
u rms 
3RT
M
Units
for R must be 8.314 joule mol/K
for M must be in kg
question: determine the urms of O2 and H2 at 0C.
Diffusion is the process of the mixing of gases with one another. Each gas
spreads throughout the mixture until its partial pressure is the same everywhere
Effusion is a process in which a gas escapes from its container through a tiny hole.
At a given temperature, the rates of effusion of a gas molecules are inversely
proportional to the square roots of their molar masses.
Effusion time and rates are inversely related.
rate of effusion of A (u rms ) A
3RT/M A
MB



rate of effusion of B (u rms ) B
3RT/M B
MA
Ratio used can be:
– Rate of effusion (as above) – Distances traveled by
molecules
– Molecular speeds
– Amounts of gas effused.
– Effusion times
question: if an unknown gas has a effusion rate 0.468 times the rate of
O2 at the same temperature, what is the molecular weight of the unknown
gas?
rate of effusion of A (u rms ) A
3RT/M A
MB



rate of effusion of B (u rms ) B
3RT/M B
MA
Nonideal (Real ) gases
• An ideal gas is a gas in which the volumes of the
molecules, intermolecular attractive forces and the
loss of kinetic energy in collisions are neglected.
• Compressibility factor PV/nRT=1 for ideal gases.
• Gases tend to behave ideally at high temperatures and low
pressures, and tend to behave nonideally at low temperatures
and high pressures.
Deviations occur for real gases.
PV/nRT > 1 - molecular volume is significant.
PV/nRT < 1 - intermolecular forces of attraction.
Substance
a (L2 atm/mol2)
He
0.0341
0.0237
H2
0.244
0.0266
O2
1.36
0.0318
b(L/mol)