Title: Gases
1Gases
2Substances That Exist as a Gas
- Ionic compounds do not exist as gases at 25and 1
atm, because cations and anions in an ionic
compound are held together by strong
electrostatic forces.
3Substances That Exist as a Gas
- The majority of molecular compounds are liquids
or solids at 25and 1 atm. - The stronger the attractive forces between the
molecules (intermolecular forces) the less likely
the material is a gas.
4Substances That Exist as a Gas under normal
atmospheric conditions
5Properties of gases
- Gases assume the volume and shape of their
container - Gases are the most compressible of the states of
matter - Gases will mix evenly and completely when
combined in the same container - Gases have much lower densities than liquids or
solids.
6Variables that Describe a Gas
- Pressure (P) measured in kilopascals
- Volume (V) measured in liters
- Temperature (T) - measured in Kelvin
- Number of moles (n)
7Deriving units of Pressure
- Velocity is change of distance with elapsed time
vd/t - The SI unit for velocity is m/s
- Acceleration is the change in velocity with time
av/t - The SI unit for velocity is m/s2
8Deriving units of Pressure
- Pressure is a force and is dependent on mass.
According to Newtons second law - force mass x acceleration
- The SI unit for force is the Newton, where N
1 kg m/s2 - Finally, pressure is the force applied per unit
area p f/a - The SI unit for velocity is the pascal (Pa)
defines as one Newton per square meter, or 1 Pa
1 N/m2
9Atmospheric Pressure
- The gases in the atmosphere are subject to
Earths gravitational pull. - Air is denser at low altitudes, and less dense at
high altitudes. - The denser the air, the greater the pressure that
it exerts.
10Atmospheric Pressure
- The force experienced by any area exposed to the
Earths atmosphere is equal to the weight of the
column of air above it. The actual value depends
on location, temperature and weather conditions.
11Gas Pressure
- Barometer
- Measures atmospheric pressure
- Dependent on the weather
- Standard atmospheric pressure is equal to the
pressure that supports a column of mercury
exactly 760 mm high at 0C at sea level.
12Units of pressure
- Pascal (Pa)
- torr
- Millimeters mercury (mm Hg)
- Atmospheres (atm)
-
- 1 atm 760 mm Hg 760 torr 101.325 kPa
13Example 1
- The pressure outside a jet plane flying at high
altitudes is considerably lower than standard
atmospheric pressure. Therefore, the air inside
of the planes cabin is pressurized to protect
the passengers. What is the pressure in
atmospheres if the barometer reading in the cabin
is 688 mm Hg?
14Example 2
- The weatherman often reports the barometric
pressure. The barometric pressure in San
Francisco on a certain day was 732 mm Hg or 732
torr. What is the pressure in kPa?
15Gas Pressure
- A manometer is a device used to measure the
pressure of a fixed amount of gas separate from
the atmosphere.
16Closed Manometer
17Open Manometer
18The Gas Laws
- Boyles Law
- Robert Boyle (1627-1691)
- Boyle studied the effect of pressure on the
volume of a contained gas at constant temperature - For a given mass of a gas at constant
temperature, the volume of the gas varied
inversely with pressure.
19Boyles Law
- Notice that for both conditions, the product of
the pressure and volume was the same - P1V1 100 mmHg x 10 L 1000 mmHgL
- P2V2 200 mmHg x 5 L 1000 mmHgL
20Boyles Law
PV k1
P2V2
P1V1
P3V3
21Boyles Law
P k1 x 1/V
22Boyles Law
- P1V1 k1 P2V2
- Or
- P1V1 P2V2
23Example 3
- A child is given a balloon filled with 25 L of
helium gas at 103 kPa. What will the volume of
the balloon be if the child lets it go and it
floats up to an altitude where the pressure is
only 35 kPa?
24The Gas Laws
- Charles's Law
- Jacques Charles (1746-1823)
- Charles studied the effect of temperature on the
volume of a gas at constant pressure - For a given mass of a gas at constant pressure,
the volume of the gas varied directly with
temperature.
25Charless Law
- Notice that for both conditions, the ratio of the
volume and temperature was the same - V1/T1 10L / 300 K 0.03 L/K
- V2/T2 20L / 600 K 0.03 L/K
- V1/T1 V2/T2
26Charless Law
Gas A
Gas B
-273.15 C
Gas C
27Example 4
- A child is given a balloon filled with 25 L of
helium gas at 25 C. What will the volume of the
balloon be if the child goes outside where the
temperature is -15 C?
28The Gas Laws
- Gay-Lussac's Law
- Joseph Gay-Lussac (1778-1850)
- Gay-Lussac studied the effect of temperature on
the pressure of a gas at constant volume - For a given mass of a gas at constant volume, the
pressure of the gas varied directly with
temperature.
29Gay-Lussacs Law
- Notice that for both conditions, the ratio of the
pressure and temperature was the same - P1/T1 100 mm Hg / 300 K
- 0.3 mm Hg/K
- P2/T2 200 mm Hg / 600 K
- 0.3 mm Hg/K
- P1/T1 P2/T2
30Example 5
- You filled your bicycle tire to a pressure of 103
kPa early in the morning when the temperature was
only 17 C. What will be the pressure in the
tire when the temperature outside reaches 35 C?
31Avogadros Hypothesis
- Equal volumes of gases at the same temperature
and pressure contain equal numbers of particles. - At STP, 1 mol (6.02 x 1023 particles ) of any gas
occupies 22.414 L.
32The Gas Laws
- Avogadro's Law
- Amedeo Avogadro (1776-1856)
- Avogadro studied the effect of the amount of
particles on the pressure of a gas at constant
volume and temperature - For a given mass of a gas at constant volume, the
pressure of the gas varied directly with the
number of particles.
33Avogadros Law
- Notice that for both conditions, the ratio of the
pressure and temperature was the same - P1/n1 100 mm Hg / 1 mole
- 100 mm Hg/mole
- P2/n2 200 mm Hg / 2 mole
- 200 mm Hg/mole
- P1/n1 P2/n2
34Avogadros Law
- Notice that for both conditions, the ratio of the
pressure and temperature was the same - P1/n1 100 mm Hg / 1 mole
- 100 mm Hg/mole
- P2/n2 200 mm Hg / 2 mole
- 200 mm Hg/mole
- P1/n1 P2/n2
35Example 6
- A rigid 50-L container is used as reaction
vessel. When 3 moles of H2 and 1 mole of N2 are
added the initial pressure is 198 kPa. What will
be the pressure in the container when the
reaction is complete?
36Avogadros Law
- Avogadro also studied the effect of the amount of
particles on the volume of a gas at constant
pressure and temperature - For a given mass of a gas at constant pressure,
the volume of the gas varied directly with the
number of particles.
37Example 7
- When 3 L of H2 and 1 L of N2 are reacted at
constant pressure, what will be the volume of the
gas when the reaction is complete?
38I hear grumbling..
- Mrs. Rick, how are we supposed to memorize all
of these equations? - You dont! You only have to memorize one!
39The Combined Gas Law
- These four gas laws can be combined into a single
expression
40The Combined Gas Law
- Any variable which is held constant can be
factored out of the equation. - The combined gas law enables you to perform
calculations where none of the variables are
constant.
41Example 8
- You are flying in a hot air balloon in the middle
of the afternoon. The balloon has a volume of
2.24 x 103 L at an altitude of 1 km where the
temperature is 290 K and the pressure is 760 mm
Hg. What would the volume be if the balloon
ascended to 50 km where the pressure is 1.0 mm
Hg, and the temperature is 260K?
42The Ideal Gas Law
- A single equation can be derived which describes
the relationship between all four variables
43The Ideal Gas Law
- This equation relates two amounts at two
different sets of conditions. - It shows that the ratio of PV to Tn is constant
for gases that behave ideally
44The Ideal Gas Law
- This constant value can be calculated based on
some important facts about gases - Molar volume 22.414L at STP
- STP is defined as 273.15K and 101.325 kPa
45The Ideal Gas Law
- We can use this information to solve for R, the
ideal gas constant
46The Ideal Gas Law
- Rearranging the equation for R gives the usual
form of the ideal gas law - PV nRT
- The ideal gas law enables calculation of the
number of moles of a gas given P,V, and T
47Example 9
- Compressed gases are stored and transported in
steel cylinders. If a 250 L cylinder of N2 gas
has an internal pressure of 2500 kPa at 25.0 C,
what is the mass of nitrogen in the cylinder?
48Density Calculations
- Density is defined as mass/volume. The ideal gas
law can be rearranged to solve for density.
49Density Calculations
- The number of moles of a gas, n, can be given by
- Where m is mass, and M is molar mass, therefore
50Density Calculations
- Density, D, is mass per unit volume, resulting in
the following equation
51Example 10
- Calculate the density of carbon dioxide in grams
per liter at 0.990 atm and 55C
52Example 11
- The density of dry air at 30.0 C, 720 mm Hg, is
1.104 g/L. Calculate the average molecular
weight of the air.
53Gas Stoichiometry
- Gas laws are used to calculate moles when
conditions are not constant or not _at_ STP
- Remember the molar highway?
- When the reactants and/or products are gases we
can use the relationships between amounts and
volumes
54Example 12
- Calculate the volume of O2 (in Liters) required
for the complete combustion of 7.64 L of
acetylene (C2H2) at the same temperature and
pressure. - 2C2H2 (g) 5O2 (g) ? 4CO2 (g) 2 H2O (l)
55Example 13
- A 3.25 g sample of KClO3 is decomposed according
to the equation - 2KClO3(s) ? 2KCl(s) 3O2(g)
- Assuming 100 decomposition, what volume of O2
should be collected at 22C,740 mm Hg?
56Daltons Law
- Gas pressure is dependent only on the number of
gas particles in a container, and their kinetic
energy. - The total pressure of the system is the sum of
the pressures due to all particles.
57Daltons Law
58Daltons Law
- The contribution each gas makes is called the
partial pressure. - In a mixture of gases, the total pressure is
equal to the sum of the partial pressures - Ptotal P1P2P3P4.
59Daltons Law
60Daltons Law
- The partial pressure of any component is equal to
the mole fraction of that component times the
total pressure. - Because the sum of all mole fractions is equal to
1
61(No Transcript)
62Example 14
- You have three tanks of equal volume. One
contains nitrogen at 200 kPa, the second contains
oxygen at 500 kPa, and the third contains an
unknown quantity of carbon dioxide. If the gases
are combined into one tank, and the final
pressure is 1100 kPa, what pressure is due to
carbon dioxide?
63Example 15
- Oxygen gas generated by the decomposition of
potassium chlorate is collected as shown. The
volume of oxygen collected at 24C and 762 mmHg
is 128 mL. Calculate the mass (in grams) of
oxygen gas obtained. - the vapor pressure of water at 24C is 22.4 mmHg
64Kinetic Molecular Theory of Gases
- Gas molecules are separated by great distances.
They possess mass, but have negligible volume. - Gas molecules are in constant, random motion.
The collide frequently and elastically. - Gas molecules exert no attractive or repulsive
forces. - The average kinetic energy of the molecules is
proportional to the absolute temperature of the
gas (K)
65Kinetic Molecular Theory of Gases
- Compressibility of gases
- Molecules can move into empty space
- Boyles Law
- Decreasing volume increases number density, which
increases the number of collisions per area. - Charles Law/Gay-Lussacs Law
- As the average KE increase, the rate of collision
increases - Avogadros Law
- At the same T,P, equal volumes of gas contain an
equal number of particles, having an equal number
of collision per area.
66Kinetic Molecular Theory of Gases
- At higher temperatures more molecules are moving
at higher speeds
67Kinetic Molecular Theory of Gases
- The distribution of speeds for four gases at 300
K. On average, the lighter molecules are moving
faster.
68Kinetic Molecular Theory of Gases
- Root mean square speed is an average molecular
speed - For one mole of a gas KE 3/2 RT
- For one molecule
- Therefore
69Kinetic Molecule Theory
- most probable speed
- proportionality constant
- root mean square speed
70Example 16
- Calculate the root mean square speed of nitrogen
molecules in m/s at 25C
71The Gas Laws
- Grahams Law
- Thomas Graham (1805-1869)
- Graham studied the diffusion of gases under the
same conditions of temperature and pressure. - Under the same conditions of temperature and
pressure, rates of diffusion for gases are
proportional to the square roots of their molar
masses.
72time
73Grahams Law of Diffusion
- For two gases of differing molar mass
74Example 17
- Helium particles are much smaller than nitrogen
particles. How much faster will they diffuse?
75Grahams Law
- Diffusion is the tendency for molecules to move
toward areas of lower concentration until
equilibrium is reached. - Effusion is the process by which a gas escapes
through a tiny hole in its container.
76Effusion of a gas
77Grahams Law
- Although effusion differs from diffusion in
nature, the rate of effusion follows the same
form as Grahams law of diffusion.
78Example 18
- A flammable gas composed of carbon and hydrogen
effuse through a porous barrier in 1.50 min. If
an equal volume of bromine gas effuses through
the same barrier under the same conditions in
4.73 min, what is the molar mass of the unknown
gas?
79Deviation From Ideal Behavior
- The laws that we have discussed assume that gases
behave in an ideal manner obeying the
assumptions of Kinetic Theory. - They Are Wrong!!
80Deviations from Ideal Behavior
- Assumptions of Kinetic theory
- Gas particles are not attracted to each other
- Particles have no volume
- Not True!!
81Deviations from Ideal Behavior
- Kinetic theory assumes gases are ideal.
- A truly ideal gas does not exist
- At many conditions (T,P) real gases behave
ideally - BUT, at low T or high P gases can condense or
even become solids
82Deviations from Ideal Behavior
- What is an ideal gas?
- No attractive or repulsive forces
- Volume of particles is negligible
- Under what conditions do these laws apply?
- Low pressure
- High temperature
83Deviations from Ideal Behavior
- No gas behaves ideally at all temperatures and
pressures. - For an ideal gas, the ratio
- (PV)/(nRT)1
- Deviation indicates non-ideal behavior.
84Pressure Influence on Ideal behavior
85Deviations from Ideal Behavior
- Real gases take up slightly less space than
predicted by the ideal gas law. - Indicates attractive forces
- Less space between particles decreases volume.
- Results in a ratio lt 1
86Deviations from Ideal Behavior
- Real gas particles do have volume.
- Causes ratio gt1
87Deviations from Ideal Behavior
- Corrections can be made for the pressure and
volume of a real gas - The van der Waals equation uses constants a and b
to adjust for the behavior of a real gas
88Van der Walls constants
89Example 19
- Given that 3.50 moles of NH3 occupy 5.20 L at
47C, calculate the pressure of the gas (in atm)
using the ideal gas law, and then the van der
Waals equation.