G10_Gas-Laws last lesson for third quearter

KINETIC MOLECULAR THEORY (KMT)
Kinetic Molecular
Theory of gases attempts
to explain the properties of
gases such as pressure,
temperature, or volume, by
looking at what they are
made up of and how they

 Kinetic refers to motion
 The energy an object has
because of its motion is
called kinetic energy
◦ Example: A ball rolling
down a hill has kinetic
energy

There are three main
components to kinetic theory:
1. Perfectly elastic collisions,
no energy is gained or lost
when gas molecules collide
2. Gas molecules take up no
space they are so small
3. Gas molecules are in
constant, linear, random

How does Kinetic Theory explain Gas
Pressure?
 Gas Pressure results from fast-moving gas
particles colliding with the sides of a
container
 More Collisions = Higher Pressure

How does Temperature relate to Kinetic
Theory?
 Temperature is a measure of the average
kinetic energy of all the particles in a gas
 Higher Energy = Higher Temperature

Through KMT, several Laws were developed to help calculate
the changes in pressure, temperature, and volume of gases.
There are 6 Basic Laws:
1. Boyle’s Law
2. Charles’ Law
3. Gay-Lussac’s Law
4. Avogadro’s Law
5. Ideal Gas Law – volume liters only
6. Dalton’s Law
Combined Gas Law

UNITS USED TO DESCRIBE GAS SAMPLES:
Volume
Liter (L)
Milliliter (mL)
1000 mL = 1L
Temperature
Kelvin ONLY
K = ºC + 273
Pressure
Atmosphere (atm)
Kilopascale (kPa)
Torr (torr)
mm of mercury (mm
Hg)
1 atm = 101.3 kPa
1 atm = 760 mm Hg
1 atm = 760 torr
Standard Temperature and Pressure (STP)
Standard Temperature = 273K
Standard Pressure = 1 atm

BOYLE’S LAW
Boyle’s Law – at constant temperature, the volume of
the gas increases as the pressure decreases. (and the
volume of the gas decreases and the pressure
increases). They are inversely related
P1V1 = P2V2
V↑ P↓
Volume (L)
Pressure
If you squeeze a
gas sample, you
make its volume
smaller.

Moveable
piston
↕
Now . . . a container
where the volume can
change (syringe)
Same
temperature
Volume is 100
mL at 25°C
Volume is 50
mL at 25°C
In which system is the pressure higher? (Which has
the greater number of collisions with the walls and
each other?)

Boyle’s Law Example
A 2.00 L of a gas is at 740.0 mmHg pressure. What is
its volume at 760.0 mm Hg pressure?
P1V1 = P2V2
2.00L x 740.0 mm Hg = 760.0 mm Hg x V2
2.00L x 740.0 mm Hg = 760.0 mm Hg x V2
760.0 mm Hg 760.0 mm Hg
1.95 L = V2
Solution:

CHARLES’ LAW
Charles’ Law – at a constant pressure, the volume of a gas
increases as the temperature of the gas increases (and the
volume decreases when the temperature decreases). They
are directly related.
V
o
l
u
m
e
L
Temperature (K)
V1 V2
T1 T2
=
• increasing the temperature
of a gas increases the speed
of gas particles which collide
more often and with more
force causing the walls of a
flexible container expand.
Think of hot air balloons!

Charles’ Law Example:
A 4.40 L of a gas is collected at 50.0°C. What will
be its volume upon cooling to 25.0°C?
First you must convert temperatures from Celsius to Kelvin.
Temperature must always be in Kelvin
K = 273 + °C
T1 = 273 + 50.0°C = 323K
T2 = 273 + 25.0°C = 298K

GAY-LUSSAC’S LAW
Gay-Lussac’s Law – at a constant volume, the pressure of a
gas increases as the temperature of the gas increases (and
the pressure decreases when the temperature decreases).
They are directly related.
Pressure
(atm)
Temperature (K)
P1 P2
T1 T2
=

Steel cylinder (2L)
contains 500
molecules of O2 at
400 K
Steel cylinder (2L)
contains 500
molecules of O2 at
800 K
1.In which system do the O2 molecules have the highest average kinetic
energy (temperature)?
2.In which system will the particles collide with the container walls with
the greatest force and the most often?
3.In which system is the pressure higher?
B
B
B

Example: In a rigid container a gas has a pressure of 1.3 atm
at 25°C. What is the pressure of the gas if it is heated to
45°C?
First you must convert temperatures from Celsius to Kelvin.
Temperature must always be in Kelvin
K = 273 + °C
T1 = 273 + 25.0°C = 298K
T2 = 273 + 45.0°C = 318K
1.3 atm = P2
298K 318K
X (318K)
1
(318K) X
1 P2 = 1.39 atm
1.4 atm (2 sig figs)

COMBINED GAS LAW
P1V1 P2V2
T1 T2
=
Note that all temperatures must be in Kelvin!
A combination of Boyle’s, Charles’, and Gay-Lussac’s
Laws

Example:
A gas occupies 2.0 L at 2.5 atm and 25ºC. What is it’s volume if the
temperature is increased to 33ºC and the pressure is decreased to
1.5 atm?
P1V1 P2V2
T1 T2
P1 = 2.5 atm
V1 = 2.0L
T1 = 25 + 273 = 298K
P2 = 1.5 atm
V2 = ?
T2 = 33 + 273 = 306K
(2.5 atm)(2.0L) (306K) = V2
(298K) (1.5 tm)
V2 = 3.4 L
=

Example:
A gas occupies 4.5 L at 1.3 atm and 35ºC. What is the final
temperature if the final volume of the gas is 3.2 L with a pressure
of 1.5 atm?
P1V1 = P2V2
T1 T2
P1 = 1.3 atm
V1 = 4.5L
T1 = 35 + 273 = 308K
P2 = 1.5 atm
V2 = 3.2L
T2 = ?K
(1.5 atm)(3.2L) (308K) = T2
(4.5L) (1.3 atm)
T2 = 250K
(1.3 atm)(4.5L) = (1.5atm)(3.2L)
(308k) T2

What is STP?
STP is the abbreviation for standard
temperature and pressure.
Standard temperature is 273K
Standard pressure is 1 atm
You must memorize the meaning of STP.

AVOGADRO’S LAW
Avogadro’s Law – equal volumes of gases at the same
temperature and pressure contain equal numbers of
molecules.
1 mole of ANY gas takes
up a volume of 22.4 L at
STP. This is called Molar
Volume
22.4L = 1 mole of gas at
STP
Memorize this!
H2 O2 CO2

AVOGADRO’S LAW:
One mole of ANY gas takes up a volume of 22.4 L
at STP.
So how many molecules of any gas are there in
22.4 L at STP?
One mole which is 6.022 x 1023

AVOGADRO’S LAW:
At STP, 1.0 L of Helium gas contains the same number of
atoms as:
A. 2.0 L of Kr
B. 1.0 L of Ne
C. 0.5 L of Rn
D. 1.5 L of Ar
Therefore equal _______________ of gas contain equal numbers of
__________ or ____________________.
volumes
atoms molecules

IDEAL GASES
• Gases whose behavior can be predicted by the kinetic molecular
theory are called ideal, or perfect, gases. No gases are truly ideal
because no gas totally obeys all of the gas laws.
• An ideal gas is an imaginary gas that is perfect and follows everything
perfectly.
•We assume that all gases behave like ideal gases so there is an ideal
gas law
◦ There are no intermolecular forces between the gas molecules.
◦ The volume occupied by the molecules themselves is entirely
negligible relative to the volume of the container.

IDEAL GAS LAW
PV = nRT
P = pressure in atmospheres (atm)
V = volume in Liters (L)
n = # of moles
T = temperature in Kelvin (K)
R =.08206 L·atm/mol·K

Ideal Gas Law Example:
How many moles of oxygen will occupy a volume of
2.50 L at 1.20 atm and 25°C?
PV = nRT
n = .123 moles of oxygen
n = (1.20)(2.50)
(.08206) (298K)
n = PV
RT

Ideal Gas Law Example:
What volume will 12.4 grams of O2 gas occupy at 756 torr and 17°C?
PV = nRT V = nRT
P
n = 12.4g
1
x 1 mol
32.00g n = .388 mol
V = (.388)(.08206) (290K)
.995 atm
P = 756 torr
1
X 1 atm
760.0 torr
P = .995 atm
V = 9.28L

What is STP? STP stands for standard temperature and pressure.
Standard temperature is always 273K. Standard pressure is always
1.00 atm.
Examples using STP:
At 1.80 atm of pressure and 30.0 °C temperature, a gas occupies a
volume of 65.5 mL. What will be the volume of the same gas at STP?
Which gas law should we use?
Combined Gas Law
P1V1 = P2V2
T1 T2
(1.80 atm) (65.5 mL) = (1.00 atm) V2
(303K) 273K
(1.80 atm) (65.5 mL) (273K) = V2
(303K) (1.00 atm)
V2 = 106 mL

Dalton’s Law of Partial Pressures -
In a mixture of gases, each gas exerts a certain pressure as if it were
alone. The pressure of each one of these gases is called the partial
pressure. The total pressure of a mixture of gases is the sum of all of
the partial pressures.
Ptotal = P1 + P2 + P3 …….
Pair = PO2 + PN2
+ Par + PH2O + PCO2

Example:
What is the total pressure of a mixture of gases made up of
CO2, O2, and H2 if the partial pressures are 22.3 kPa, 44.7 kPa,
and 112 kPa, respectively?
Ptotal = P1 + P2 + P3
PTOTAL = 22.3kPa + 44.7 kPa + 112 kPa
PTOTAL = 179 kPa

G10_Gas-Laws last lesson for third quearter

G10_Gas-Laws last lesson for third quearter

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G10_Gas-Laws last lesson for third quearter