Gases Chapter 10 very loosely of Brady

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GasesChapter 10 (very loosely)of Brady
Senese 5TH ed)

• Dr. C. Yau
• Fall 2009

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Properties of Gases Macroscopic View

• Gases can be compressed
• Gases exert a pressure.
• The pressure of a gas depends on how much gas is
  confined.
• Gases fill completely any container into which
  they are placed.
• Gases mix freely and quickly with each other.

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Kinetic Molecular Theory of GasesView at the
Particulate Level

• A gas is made of an extremely large number of
  very tiny particles that are in constant, random
  motion.
• The gas particles themselves occupy a net volume
  so small in relation to the volume of their
  container that their contribution to the total
  volume can be ignored.
• The particles often collide in perfectly elastic
  collisions with themselves and with the walls of
  the container.

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Kinetic Molecular Theory of GasesView at the
Particulate Level (cont'd.)
4. The particles move in straight lines neither
attracting nor repelling each other. 5. The
pressure of a gas is due to the frequency and
force of collisions of the particles with the
sides of the container. 6. The particles within a
sample of gas have different kinetic energy (KE),
but for samples at a given temperature, the
average kinetic energy is the same. It is
affected only by temperature.
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The Ideal Gas Law
This is the law for the ideal gas. It's the gas
that is ideal, not the law. There are "real
gases" that do not follow this law. KNOW THIS
WELL! PV nRT where P pressure of gas in
atm V volume of gas in L n moles of
gas T temp. of gas in Kelvin R 0.08206 atm
L mol-1 K-1 or (no need to memorize R)
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Parameters of a Gas
To describe a gas, one must specify the P, V and
T as they are all interdependent on each
other. Pressure Units 1 atm 760 mmHg 760
torr 1 mmHg 1 torr What has P to do
with mm and mercury? The barometer measures the P
of the atmosphere. It is constructed with a tube
of mercury, and the height of the mercury column
is measured in millimeters, hence, mm Hg.
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Parameters of a Gas (cont'd.)
The column of Hg is affected by the pressure of
the atmosphere pressing down on the reservoir of
Hg. Which day has the higher atmospheric
pressure? A taller column means a higher P. Day 1
has the higher atmospheric pressure (or
barometric pressure). 752 mm Hg means a higher P
than 750 mm Hg.
Day 1 Day 2
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Parameters of a Gas (cont'd.)
Which barometer(A or B) is at the top of a tall
mountain, and which is at sea level? The air is
thinner at the top of a tall mountain and so the
P is lower. Barometer B is at the top of a tall
mountain.
Barometer A Barometer B
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Parameters of a Gas (cont'd.)

• Pressure
• The manometer measures the P of a gas sample.
• Temperature
• The Celsius scale was arbitrarily based on the fp
  of water to be zero.
• The behavior of gases cannot be based on
  something arbitrary. Instead it is based on the
  absolute zero being the lowest temp possible.
• The Kelvin scale TK ToC 273.15 KNOW THIS!
• V of gas decrease with T. Theoretically when V
  zero, T is at lowest (zero K).
• KE of gas particles decreases with T.
• At 0 K, theoretically gas particles have zero KE
  (motionless).

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Parameters of a Gas (cont'd.)
Volume If we want to convey to someone how much
solid is produced, we would want to specify its
mass. If we want to convey how much liquid is
produced, we would want to specify its
volume. For a gas, we would not weigh it because
its density is too low and not feasible to
weigh. If we specify its volume we would have to
specify the temperature and pressure as well,
because the volume would change with T and P.
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STP (Standard Temperature Pressure)
KNOW THIS WELL! STP means "standard temperature
pressure)0oC (273.15 K)and 1 atm (760 mm Hg)
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Molar Volume at STP
For ease of comparison, we usually give the
volume of a gas at STP. For an ideal gas, since
the gas particles have negligible volume and do
not sense the presence of neighboring particles
(no attraction nor repulsion) the volume does NOT
depend on the type of gas we have. "Molar volume"
refers to the V of one mole of gas. Molar Volume
of any ideal gas at STP 22.4 L Do not forget
this is ONLY at STP, for ideal gas.
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Gas Calculations
TWO types of Gas Problems dealing with
PVnRT 1) One set of parameters given Use
PVnRT 2) Two sets of parameters givenRearrange
equation so only R is on one side of eqn Since
R is a constant, this means that under any
conditions, PV/nT must always equal to each
other
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• Example 1 (from handout)
• What is the volume of one mole of gas at STP?
• Example 2
• What does "molar volume of a gas" refer to?
• Example 3
• Sulfur hexafluoride SF6 is a colorless, odorless,
  very unreactive gas. Calculate the pressure (in
  atm) exerted by 1.82 moles of the gas in a steel
  vessel of volume 5.43 L at 69.5?C.

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• Example 4
• A gas at 772 mmHg and 35.0?C occupies a volume of
  6.85 L. Calculate its volume at STP.
• Example 5
• If the volume of a gas is 5.0 L at 758 torr, what
  is the volume when the pressure is increased to
  1.23 atm. Assume the temperature remains
  constant.

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Example 6 A 2.0 L balloon filled with nitrogen
at 18C at a picnic. By noon, the temperature
has gone up to 28C. What is the volume of the
balloon at that point? Assume the atmospheric
pressure has not changed throughout the day.
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Example 7 Sodium azide (NaN3) is used in some
automobile air bags. The impact of a collision
triggers the decomposition of NaN3 as follows
2NaN3 (s) ?? 2Na (s) 3N2 (g) The
nitrogen gas produced quickly inflates the bag
between the driver and the windshield. Calculate
the volume of N2 generated at 80.0?C and 823 mmHg
by the decomposition of 60.0 g of NaN3.
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How would you rearrange PVnRT to give you the
density of the gas? How do you normally calculate
the density of an object? Which part of PV nRT
would give us density? Which part of the eqn
would give us molar mass (MM)? Rearrange the
equation to calculate MM.
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Example 8 The volume of a gas was determined to
be 200.0 mL at 99oC and 733 mmHg. It has a mass
of 0.970 g. What is its molar mass? Is it
chloroform (CHCl3) or carbon tetrachloride?
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Effusion Diffusion of Gases
Effusion is the gradual movement of gas particles
through a very tiny hole into a vacuum. Diffusion
is the spontaneous mixing of the particles of one
gas with those of another. Graham's Law of
Effusion The rate of effusion is inversely
proportional to the square root of its
density. The density of a gas is directly
proportional to its molar mass. Thus, rate of
effusion is inversely proportional to the square
root of its molar mass.
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Graham's Law of Effusion
Rate of effusion is inversely proportional to the
square root of its molar mass. where r
rate of effusion M molar mass The
heavier gas effuses slower at a given T. How does
T affect the rate of effusion? If a molecule B is
4X heavier than A, how much faster would A be
effusing?
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Ans. A is 2X as fast.
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Dalton's Law of Partial Pressures
This law concerns mixtures of gases. In a mixture
of gases (such as A and B), the total pressure is
the sum of the partial pressures of each
gas. PTOT p A p B p A
and p B Note Since they are in the same
container, T and V must be the same. R is also
the same.
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Dalton's Law of Partial Pressures (cont'd.)
Rearrangement of equation gives us What this
tells us is that the fraction in pressures is
equal to the mole fraction. REMEMBER This is
only for mixtures of gases.
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Real Gas vs. Ideal Gas
A real gas differs from an ideal gas 1) Gas
particles do have volume. 2) There are
interactions between particles in a gas
(attraction and repulsion). These are noticeable
only under these conditions 1) At VERY high P
particles are forced closely together and their
volume becomes significant.EFFECT Actual P is
higher than ideal. 2) At VERY low T, particles
are moving very slowly, and they have more time
to "socialize." EFFECT Actual V smaller than
ideal.
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Real Gas vs. Ideal Gas
You do not need to memorize this equation or do
any calculations with it. Know when and how real
gases deviate in the Ideal Gas Law (previous
slide).
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