Chapter 10
Gases
No…not that kind of gas
Kinetic Molecular Theory of Gases
Kinetic Molecular Theory of Gases –
Based on the assumption that gas
molecules are always moving.
Assumptions of Gas Molecules
1. Gases consist of lots of tiny particles that
are very far apart. Caron dioxide
particles take up 1000x space of liquid or
solid.
2. Collisions of the gas particles are elastic
– no net loss of energy.
3. Gas particles are in constant
random motion.
4. No attraction or repulsion between
gas particles.
5. Average energy of gas depends on
temperature of gas.
Ideal Gases
Ideal gases follow all 5 assumptions of the kinetic
molecular theory.
Real gases act like ideal gases at 1 atm and room
temperature.
Real gases don’t follow the assumptions of KMT at
very low temperatures and at very high
pressures because these gases at low temp.
and high press. are becoming a liquid or solid.
Therefore, will not act like a gas.
Properties of Gases
Gases don’t have definite shape or volume.
They flow, have low density, are
compressible and can diffuse and effuse.
Diffusion – mixing of two gases by random
motion
Effusion – process where a gas passes
through a small opening.
Pressure
Pressure = force per unit area
Calculate the force for getting your foot
stomped on by a) athletic shoe heel
b) stiletto high heel.
Measurements of Pressure
Barometer measures atmospheric
pressure.
Units for Pressure (memorize)
1 atm = 760 mm Hg = 760 torr = 101.3 kPa
atm = atmosphere
kPa = kilopascal
mm Hg = millimeters of mercury
STP = standard temp and press = 1 atm, 0C
Pressure
For gases in a container…
Pressure is caused by gas molecules
colliding with the WALL of the container
The more collisions with the wall, the
higher the pressure.
Gas Laws
Gas laws relates 4 variables of gases to
each other:
1. pressure , P
2. temp, T must be in kelvin
3. volume , V
4. amount of gas, n must be in moles
Boyle’s Law
Boyle’s Law: The pressure is inversely
proportional to the volume.
PV = k
OR P1V1 = P2V2
Illustrate and graph. Pg 314
Boyle's Law, As the pressure increases the
volume decreases proportionally
http://www.grc.nasa.gov/WWW/K-12/airplane/aboyle.html
Charles’ Law
Charles Law – volume of gas is directly
proportional to the Kelvin temp.
V =k
T
OR V1 = V2
T1
T2
Illustrate by example and graph p318.
Charles' Law, As the temperature
increases the volume increases
proportionally
Gay Lussac’s Law
Gay Lussac’s Law: Pressure of a gas is
directly proportional to the Kelvin
temperature.
P = k
T
OR P1 = P2
T1
T2
Illustrate by example and graph pg 319
Gay Lussac's Law, At constant volume as
the temperature increases the pressure
increases proportionately
Avogadro’sLaw
Avogadro’s Law - Gas volume is directly
proportional to the amount of gas.
V = k
n
OR V1 = V2
n1
n2
Illustrate by example and graph.
Combined Gas Law – shows the relationship
between pressure, volume, temperature,
and amount of gas.
Combined Gas Law
P1V1 = P2V2
n1T1 n2T2
P = pressure in mmHg, torr, kPa, as long as P1 &
P2 are same units.
V = volume in L, mL as long as V1 & V2 are same
units
n = number of moles
T = temperature in Kelvin K = °C + 273
must be Kelvin in all gas law calculations.
Demonstrate what happens to the combined gas
law when a variable does not change.
Therefore, any variable held constant or not
mentioned can be dropped from the combined
gas law equation.
Practice Problems
1. A fixed amount of helium gas is
compressed from 4 L to 2.5 L at a constant
temperature. If the pressure of a gas in
the 4.0 L volume is 210 kPa, what will the
pressure be at 2.5 L?
2. The pressure of a fixed amount of gas in
a tank is 3.20 atm at 22.0 ºC. If the
temperature rises to 60 ºC, what is the
new gas pressure in the tank if the volume
is constant?
3. A fixed mass of gas at 40ºC occupies a
volume of 2.32 L. If the temperature is
raised to 75ºC, what is the new volume if
the pressure remains constant?
4. A gas at 110 kPa and 30C fills a flexible
container with an initial volume of 2 L. If
the temperature is raised to 80ºC, and the
pressure is increased to 440 kPa, what is
the new volume?
5. The volume of a sample of gas is 200 mL
at 275 K and 92.1 kPa. What is the
temperature of the gas if the volume
increases to 450 mL and the pressure
increases to 98.5 kPa?
Dalton’s Law of Partial Pressure
Dalton’s Law of partial pressures – the total
pressure of a gas mixture is equal to the
pressures of each of the individual gases added
together.
Pt = P1 + P2 + P3 + …
Illustrate how a gas is collected by water
displacement. Appendix A table gives water
vapor pressure at different temperatures. Pg.
899
Examples
1.
A mixture of a gases contains argon and
neon. If the partial pressure of neon is
1.84 atm, what is the partial pressure of
argon at 1816.4 mm Hg?
2.
888 mL of oxygen is collected
over water with a temperature
of 27C. The total pressure of
the gases is 55.8 kPa. What is
the partial pressure of the dry
gas?
3. Some hydrogen gas is
collected over water at 20C.
The levels of water inside and
outside the gas collection
bottle are the same. The partial
pressure of hydrogen is 742.5
torr. What is the barometric
pressure at the time the gas
collected?
Chapter 11
Gases Part II
Avogadro’s Law
Avogadro’s Law – Equal
volumes of gases at the
same temp and press have
the same number of
molecules. Illustrate.
Standard Molar Volume of
a Gas –
Volume of mole of gas at
STP = 22.414 L
1 mole gas = 22.4 L (STP)
Examples
1. A chemical reaction produced 0.0680
moles of oxygen gas. What is the volume
at STP?
2. What is the mass of 98 mL of sulfur
dioxide at STP?
Ideal Gas Law
Ideal Gas Law – relationship between P, V,
n, T for one gas alone.
PV = nRT
P = press in atm
V = volume in L
n = moles
R = universal gas constant
= 0.0821 Latm
molK
T = Kelvin
Memorize the value and units of R
See different values of R on pg. 342
1. What is the volume, in liters, of
0.250 moles of oxygen gas at 20C
and 0.974 atm?
2. What is the volume of 25.36 g
of nitrogen gas, N2, at 0C and
765 mm Hg?
3.
a. What is the molar mass of a
1.00 liter gas at 28C and 0.974
atm. The gas has a mass of
5.16 g?
b. What is the density of the
gas?
Gas Stoichiometry
Review the 4 steps of stoichiometry
problems:
Step 1
Step 2
Step 3
Step 4
Volume – Volume Calculations
1. What will be the volume of
oxygen at STP needed for
the complete combustion of
0.350 L of propane, C3H8?
Volume – Mass Calculations
2. How many grams of calcium
carbonate must be
decomposed to produce 5.00 L
of carbon dioxide at STP?
CaCO3  CaO + CO2
Gas Stoichiometry with New Conditions
1. Tungsten is produced for light
bulbs by this reaction:
WO3 + 3H2  W + 3H2O
How many liters of hydrogen at
35C and 0.980 atm are needed to
react completely with 875 g of
tungsten oxide?
2. What volume of chlorine gas
at 38C and 1.63 atm is needed
to react completely with 10.4 g
of sodium to form NaCl?
Graham’s Law of Effusion
The rates of effusion of gases at the same
temp and press are inversely proportional
to the square roots of their molar masses.
Rate of effusion of A = MB = densityB
Rate of effusion of B = MA
densityA
Examples
1. Compare the rates of effusion of
hydrogen and oxygen at the same temp
and press.