Download Gases

Properties of Gases
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takes shape of container
takes volume of container
exerts pressure on its surroundings
particles are very far apart
exert no forces on each other
move in straight line random paths
Factors or measurements
that affect gases:

 Pressure- occurs from the force and number of
collisions with the walls of the container
 • Temperature- a measure of the average kinetic
energy of the particles therefore indirectly relates to
the motion of the particles
 • Volume- space occupied by a gas
 • Number of moles- amount of gas
Pressure
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Atmospheric pressure measured by a barometer; usually
contains mercury
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units of pressure: mm of Hg, torr, atmosphere, kPa
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defined as force/unit area; in SI Newtons/m2 = pascal
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1 atmosphere= 760 mm Hg = 760 torr= 101,325
pascals= 101.325 kPa=14.7 lbs/in2; standard pressure;
average pressure at sea level
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use these to convert from one to another
Ex. 723 mm Hg= _______ kPa
Pressure

 Manometer- instrument used to measure gas
pressure
 Two types of manometers Open- open to the atmosphere
 Closed-closed to the environment; barometer is a
 special type of closed manometer that measures
atmospheric pressure is called a barometer.
Using Liquids Other
than Mercury in

Manometers
 Use formula based upon density:

hb = ha x da
db
Using Liquids Other than
Mercury in Manometers

 Ex. A liquid with a density of 1.15
g/mL was used in an open-ended
manometer. In a particular
experiment, a difference in the
heights of the levels in the two arms
was measured to be 14.7 mm, with
the level in the arms connected to an
apparatus containing a trapped gas
lower than the level open to the
atmosphere. The barometric pressure
had been measured to be 756.00 torr.
What was the pressure of the trapped
gas?
:
Gas Laws: Boyle’s Law

Boyle’s Law- relates pressure and volume; inverse
relationship; gives hyperbola graph; true under low
pressures such as atmospheric pressure; used to
predict the new volume of a gas when the pressure is
changed
 PV = k ;true for any gas with constant temperature and
amount
 Therefore at different volumes for same gas
 PV= k
 P1 V 1 = P 2 V 2
Gas Laws: Charles’ Law

 Charles’ Law- relates volume of a gas to temperature
of a gas; direct relationship; gives straight line; based
upon absolute temperature which is the kinetic
energy of particles; must use Kelvin temperature
( K = oC + 273)
V = k
T
V1= V2
T1 T 2
Gas Laws: Gay-Lussac’s
Law

Relates pressure and temperature; direct
relationship; gives straight line; use any
pressure units and Kelvin temperature
P1 = P2
T1 T2
Gas Laws: Combined
Gas Law

Combined Gas Law- combines all three
effects
P1V1 = P1V1
T1
T2
Gas Laws: Avogadro’s
Law

Avogadro’s Law- involves volume and
amount of gas in moles
V = kn
V is volume; k is constant; n is symbol for #
of moles
Ideal Gases

 Ideal Gases- name given to gases that follow the
above laws at all temperatures and pressures. At
room temperature and pressure, most real gases
follow those of ideal. At high pressures and low
temperatures, we must make adjustments in our
formula to account for attractions between molecules
Ideal Gas Law

 Ideal Gas Law- incorporates all factors into one
formula
 PV= nRT
 P is pressure in atmospheres, V is volume in L, n is
moles, and T is temperature in K.
 R is a constant; known as the gas constant; can have
different values based upon units used in equation.
 R= 0.0821 L atm/mol K
 R= 62.4 mm Hg L/mol K
 R= 8.31 kPa dm3/mol K
Molar Gas Volume

When one mole of any gas is at STP the
volume will be 22.4 L. Known as molar gas
volume.
Gas Stoichiometry

 If conditions differ from STP use Combined Gas
Laws equations or Ideal Gas Law to determine the new
volume.
Ex. Calculate the volume of CO2 at STP produced from the
decomposition of 152 g of CaCO3 according to the reaction:
CaCO3 (s)  CaO (s) + CO2(g)
Gas Stoichiometry

 Ex. A sample of methane gas having a volume of 2.80
L at 25oC and 1.65 atm was mixed with a sample of
oxygen having a volume of 35.0 L at 31oC and 1.25
atm. The mixture was ignited to form carbon
dioxide and water. Calculate the volume of CO2
formed at a pressure of 2.50 atm and a temperature
of 125 oC.
Molar Mass of a Gas

 Molar Mass of a Gas
 Moles(n) = m___
MM ( molar mass)
 PV=nRT
P = nRT
V
 P= (m/MM) R T
V
 MM = mRT
PV
 Or
 Since D = m/V substitute
MM = D R T
P
Molar Mass of a Gas

 Ex. A student measured the density of a gaseous
compound to be 1.34 g/L at 25oC and 760 torr and
was told that the compound was composed of 79.8%
carbon and 20.0% hydrogen. A) What is the
empirical formula of the compound? B) What is its
molecular mass? C) What is the molecular formula
of the compound?
Gas Density

 To determine the density of a gas at STP simply take
the molar mass/ 22.4 L.
Dalton’s Law of Partial
Pressure

 For a mixture of gases in a container, the total pressure
exerted is the sum of the pressures that each gas would
exert if it were alone in the container.

PT = P 1 + P 2 + P 3 + …
 Each P represents the partial pressure of each gas
 PT = P1 + P2 + P3 … = n1RT
V
(n1 + n2 + n3 +…) RT
V
+ n2RT + n3RT =
V
V
Ideal Gases

 Since the pressure of the ideal gas is not affected by the
identity of the gas particles, tells us that ideal gases
1) the volume of the individual gas particles must not be
important and
2) the forces among the particles must not be important.
Mole Fraction

 Concentration unit
 Mole Fraction (C)- moles of solute
Total moles of solution
 C = n2
nT
 P1= C x PT
= P1
PT
= n1
n1 + n2 + n3
Example

 Ex. Mixtures of helium and oxygen are used in
scuba diving tanks to help prevent “the bends.” For
a particular dive 46 L of O2 at 25oC and 1.0atm was
pumped along with 12L of He at 25oC and 1.0 atm
into a tank with a volume of 5.0 L. Calculate the
partial pressure of each gas and the total pressure in
the tank at 25oC.
Example

 Ex. The partial pressure of oxygen in air was
observed to be 156 torr when the atmospheric
pressure was 743 torr. Calculate the mole fraction of
O2 present.
Example

 Ex. The mole fraction of nitrogen in the air is 0.7808.
Calculate the partial pressure of N2 in air when the
atmospheric pressure is 760 torr.
Collecting gases by the
displacement of water

 Water vapor is always present when a gas is
collected over water. The water vapor becomes a
constant since equilibrium is obtained. Therefore to
find the pressure of the “dry gas” (gas pressure
without water vapor pressure present) subtract the
water vapor pressure from the total.

Pgas + PH20 = PT

PT - PH2O = Pgas
Collecting Gases over
Water

 The pressure of the water vapor is a constant
depending on the temperature. Usually this
information is given or on a table of water vapor
pressures by temperature.
 When calculating the pressure of the gas, the
pressure of the dry gas only must always be used.
The volume of the dry gas is the total volume of the
container.
Kinetic Molecular
Theory of Gases
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 explains the properties of an ideal gas
 specifically for behavior of the individual gas particles
 the volume of the individual particles can be assumed to
be negligible.
 particles are in constant motion; collisions of the particles
with the walls of the container cause the pressure of the
gas
 particles exert no forces on each other
 average kinetic energy of the gas particles is assumed to
be directly proportional to the Kelvin temperature
Kinetic Molecular
Theory of Gases
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 Real gases do not necessarily conform to these
assumptions; however at low pressures
(atmospheric) and high temperatures (normal
temperatures) they are very close.
Root Mean Square
Velocity
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 urms- root mean square velocity
 Derived: urms = 3RT/M




T- Temperature in Kelvins
M- molar mass in kilograms
R- 8.31 J/K mol if velocity is to come out in m/s
J (Joules- unit of energy = k m2/s2)
 Path of individual gas particles is very erratic
 Average distance a particle travels between collisions is very
small and is called the mean free path.
 Large number of collisions produces large range of velocities.
Therefore even if the root mean square velocity is given this is not
the velocity of the entire group of molecules.
Effects of temperature
on velocity
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 As temperature is increased, the curve peak moves
toward higher values and the range of velocities
becomes much larger. The peak of the curve reflects
the most probable velocity. Called MaxwellBoltzmann Distribution.
Effusion and Diffusion
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 Diffusion- describes the mixing of gases (The
movement of a substance from an area of high
concentration to an area of lower concentration)
 Effusion- the passage of a gas through a tiny orifice
into an evacuated chamber (vacuum)
Effusion and Diffusion

 Rate of diffusion is the rate at which gases mix.
 Rate of effusion is the speed at which a gas is transferred into the
chamber.
1/2 m 1v 12 = 1/2 m 2v22
for two particles at same temperature
m1v12 = m2v22
v12/v22 = m2/m1
 This is Graham’s Law of Effusion
Example

 Ex. The mole fraction of nitrogen in the air is 0.7808.
Calculate the partial pressure of N2 in air when the
atmospheric pressure is 760 torr.
Real Gases

 Corrections for real gases can be made using van der
Waal’s equation. It contains corrections for pressure
and volume.
Corrections for Read
Gases

 For pressure: In real gases there are some
attractions. These attractions will decrease the
frequency with which the molecules hit the walls of
the container. Therefore a correction has been made.
Pobs = Pcor pres - a (n/V)2
 Therefore
Pcor pres = Pobs + a(n/V)2
Corrections for Real
Gases

 For volume: In real gases molecules have volume
and therefore reduces the overall volume of the
container. A correction has been made.
V – nb is volume correction
Corrections for Real
Gases

 The variables a and b are constants which depend
upon the kind of molecule; specifically the
attractions between the molecules and the size of the
molecules. They can be found in a table in your
book.
Example

 Ex. For any given gas, the values of the constants a
and b can be determined experimentally. Indicate
which physical properties of a molecule determine
the magnitudes of the constants a and b. Which of
the two molecules, H2 or H2O, has a higher value for
a and which has the higher value for b? Explain.
Example

 Ex. Three volatile compounds X, Y and Z each contain element Q.
The percent by weight of element Q in each compound was
determined. Some of the data obtained are given in the next slide.
 a) The vapor density of compound X at 27o C and 750 mm Hg
was determined to be 3.53 g/L. Calculate the molecular weight of
compound X.
 b) Determine the mass of element Q contained in 1.00 moles of
each of the three compounds.
 c) Calculate the most probable value of the atomic weight of
element Q.
 d) Compound Z contains carbon, hydrogen, and element Q.
When 1.00 g of compound Z is oxidized and all of the carbon and
hydrogen are converted to oxides, 1.37 g of CO2 and 0.281 g of
water are produced. Determine the most probable molecular
formula.
Compound
X
Y
Z
Example

Percent by
Weight of
Element Q
64.8%
73.0%
59.3%
Molecular
Weight
?
104
64.0