Kinetic Theory of Gases Gases exert pressure because their
particles frequently collide with the walls of their container.
These collisions must be perfectly elastic (no loss of energy)
Adding more particles of gas increases pressure more particles =
more collisions more collisions = more force more force on area of
wall = more pressure
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More Kinetic Theory Increased temperature causes particles to
move faster As temperature increases, pressure increases Explains
why temperature affects pressure faster movement = more collisions
more collisions = more force more force on area of wall = more
pressure Also faster movement = more forceful collisions more
forceful collisions = more force on area of wall more force on area
of wall = more pressure
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Four Variables for Gases Amount of Gas (n) Measured in moles
Volume (V) Measured in Liters space Temperature (T) hot or cold
Measured in Kelvin Pressure (P) Force/area Measured in atmospheres,
kilopascals, millimeters of mercury, torr, bar, etc (whew!)
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Temperature Conversions What is 22 degrees C in Kelvin? What is
398 K in degrees C?
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Common Pressure Conversions 1000 Pa (pascal) = 1 kPa
(kilopascal)
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1 atm (atmosphere) = 760.0 mmHg (mm of Mercury) = 101.3 kPa = 760.0
Torr
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Atmospheric Pressure Atmospheric Pressure The pressure exerted
by the air in the atmosphere. Atmospheric pressure varies with
altitude because at different altitudes there are different amounts
of air above the earth. Tool for Measurement Barometer measures
atmospheric pressure Invented by Torricelli
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STP S tandard T emperature and P ressure Standard Pressure 1
atm = 760.0 mmHg = 101.3 kPa Standard Temperature 0 o C = 273
K
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Boyles Law Volume is inversely proportional to pressure. As
volume decreases, pressure increases (with temperature and amount
of gas held constant) P 1 V 1 = P 2 V 2
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To do a Gas Law Problem Each gas law problem will give initial
values and will ask for values under different conditions From the
question, list all initial variables known and record their
numerical value and unit Next to these variables (not the numbers),
write a 1 for their subscript Re-write the SAME variables (without
numbers) near the original ones and put a 2 for their subscript
Using the numbers and variables you are given, choose the gas law
relationship that fits the situation Initial values go with the 1s,
changed values go with the 2s
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Example Boyles Law Problem A gas at a pressure of 712 mmHg is
held in a container with a volume of 56.2 L. If the volume of the
container is decreased to 29.3 L, what will be the new pressure of
the gas if the temperature is held constant. P 1 = 712 mmHg P 2 = ?
V 1 = 56.2 L V 2 = 29.3 L P 1 V 1 = P 2 V 2
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Charles Law Temperature is directly proportional to volume As
temperature increases, volume increases (with pressure and amount
of gas held constant)
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Example Charles Law Problem The volume occupied by an inflated
ball during a cold winter day (T = -12 o C) is 21.3 L. What will
its volume be when the temperature reaches 44 o C? Assume constant
pressure. T 1 = -12 o C = 261 K T 2 = 44 o C = 317 K V 1 = 21.3 L V
2 = ? V 1 / T 1 = V 2 / T 2
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Gay-Lussacs Law Pressure is directly proportional to
temperature As pressure decreases, temperature decreases (with
volume and amount of gas held constant) What if we decrease
pressure indefinitely? The temperature will drop to the point where
particles cease to move. This temperature is known as absolute zero
(0 K)
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Example Gay-Lussacs Law Problem A sample of a gas has a
pressure of 1.0 atm at 27 C. What will the pressure be at 927 C ? P
1 / T 1 = P 2 / T 2
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Ideal Gases, Partial Pressure, and Gas Stoichiometry
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The Ideal Gas Law What is an ideal gas? An ideal gas is one
that obeys the kinetic- molecular theory. Gas particles not
attracted to each other Gas particles take up negligible space
Gases behave almost ideally most of the time. They deviate from the
kinetic theory at very high pressures and very low
temperatures.
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The Ideal Gas Equation R Ideal Gas Constant
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What is R? Lets consider speed. Speed = distance / time Miles
per hour = miles / hour works out! Also, distance = speed x time
Miles = miles / hour x hours works out!
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More on R P V = n R T If we take R out, we have the following
units: atmospheres (P) x liters (V) = moles (n) x kelvin (T) BUT
WAIT! atmospheres x liters moles x kelvin So, we fix the units
Throw in R, which is
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Ideal Gas Law Example 1 If a container has 39.2 moles of gas at
a pressure of 1.33 atm and a temperature of 301 K, what is the
volume of the container?
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Ideal Gas Law Example 2 Identify this gas from the P.T given
the following information: It has a mass of 41.9 grams. At 27
degrees Celsius it occupies 6.2 liters of space and exerts a
pressure of 2.0 atm.
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Gas Stoichiometry The ideal gas equation can be used with any
gas, as long as it acts ideally (almost all do) If this is case,
then any gas should take up the same volume of space (as long as n,
T, and P stay the same) P V = n R T use this to calculate the
volume of a gas under STP
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Gas Stoichiometry (cont.) One mole of gas, under STP, takes
up
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Adding that to our roadmap
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Example Problem #1: In the reaction: Mg + 2HCl H 2 + MgCl 2 If
2 moles of magnesium are used, how many moles of hydrogen gas will
be produced? How many liters of hydrogen gas is that at STP?
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Example Problem #2: Mg + 2HCl H 2 + MgCl 2 (same rxn) How many
moles of magnesium are needed to produce 11.2 liters of hydrogen
gas at STP? How many grams of magnesium is that?
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Daltons Partial Pressure Law Earths atmosphere is made of
different gases 78% Nitrogen 21% Oxygen ~1% Carbon Dioxide, Water,
Argon, Carbon Monoxide At standard pressure, all of these combined
gases have a pressure of 1 atm (or 760 torr) Question: What would
happen to the atmospheric pressure if nitrogen was taken out of the
mix?
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Partial Pressure Answer: the atmospheric pressure would
decrease Why? Each gas in a mixture of gases exerts a pressure The
combined pressure of each gas equals the total pressure Partial
pressure the pressure that one gas contributes to the total
pressure Alternate definition: the pressure that one gas would
exert as if it were alone in the container
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Calculating Partial Pressure moles of gas 1 moles of gas 1 Mole
ratio of gas 1= ------------------------ total moles of gas total
moles of gas Mole ratio of gas 1 x total pressure = partial
pressure of gas 1 (continue for all gases if needed) (continue for
all gases if needed)
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Collecting Gas One of the most common ways scientists collect
gas to study is by water displacement Collected over water Because
water vaporizes, the gas that is collected has some water molecules
in it In order to study only the gas desired, you must account for
the partial pressure due to water (subtracting it)
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Collecting Gas
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Sample Problem #1 A container holds 1.7 moles of oxygen, 2.3
moles of nitrogen, and 1.5 moles of carbon dioxide. What are the
partial pressures of each gas if the total pressure is 2.5 atm?
mole ratios: mole ratios: Oxygen Nitrogen Carbon dioxide 1.7 2.3
1.5 ----------- =.31 -------------- =.42 ------------ =.27 5.5 5.5
5.5
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Sample problem #1 (cont.) Mole fractions(s) x total pressure =
P.P. Oxygen =.31 x 2.5 = 0.78 atm Nitrogen =.42 x 2.5 = 1.1 atm
Carbon dioxide =.27 x 2.5 = 0.68 atm
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Sample Problem #2 A sample of gas is collected over water at 25
o C at 850 torr of pressure. If the vapor pressure of water at 25 o
C is 23.8 torr, what is the pressure of the dry gas alone?
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Sample #2 (follow up) If the same dry gas was brought down to
-10 o C, how much pressure would it exert? (hint: use a gas
law)
