Download 2 - TrimbleChemistry

UNIT 4
GAS LAWS
Chemistry
CDO High School
Important Characteristics of Gases
1) Gases are highly compressible
An external force compresses the gas sample and decreases its
volume, removing the external force allows the gas volume to
increase.
2) Gases are thermally expandable
When a gas sample is heated, its volume increases, and when it is
cooled its volume decreases.
3) Gases have high viscosity
Gases flow much easier than liquids or solids.
4) Most Gases have low densities
Gas densities are on the order of grams per liter whereas liquids
and solids are grams per cubic cm, 1000 times greater.
5) Gases are infinitely miscible
Gases mix in any proportion such as in air, a mixture of many gases.
THE NATURE OF GASES
Three basic assumptions of the kinetic
theory as it applies to gases:
1. Gas is composed of particlesusually molecules or atoms
 Small, hard spheres
 Insignificant volume; relatively far
apart from each other
 No attraction or repulsion between
particles
THE NATURE OF GASES
2. Particles in a gas move rapidly
in constant random motion
 Move
in straight paths, changing
direction only when colliding with
one another or other objects
 Average speed of O2 in air at 20 oC is
an amazing 1660 km/h!
(1.6km=1mile)
THE NATURE OF GASES
3. Collisions are perfectly elasticmeaning kinetic energy is transferred
without loss from one particle to
another- the total kinetic energy
remains constant
THE KINETIC THEORY OF GASES
Remember the assumptions
 Gas
consists of large number of particles
(atoms or molecules)
 Particles make elastic collisions with
each other and with walls of container
 There exist no external forces (density
constant)
 Particles, on average, separated by
distances large compared to their
diameters
 No forces between particles except when
they collide
VARIABLES THAT DESCRIBE A GAS
The
four variables and their common
units:
1. pressure (P) in kilopascals
2. volume (V) in Liters
3. temperature (T) in Kelvin
4. amount (n) in moles
1. PRESSURE OF GAS
a
measure of the force
exerted by the gas on the
walls of a container
The
greater the number of
collisions between gas
particles and the wall the
greater the pressure
PRESSURE CONVERSIONS
1
atm = 101.3 kPa = 760 mmHg =
760 torr
 The
pressure in Tucson 668
mmHg, what is that pressure in:
 atm
 kPa
 torr
2. AMOUNT OF GAS
Increasing
the number of gas
particles increases the number of
collisions
 thus, the pressure increases
PRESSURE AND THE NUMBER OF
MOLECULES ARE DIRECTLY
RELATED
Gases
naturally move from areas of
high pressure to low pressure,
because there is empty space to
move into
3. VOLUME OF GAS
As
volume decreases, pressure
increases.
Thus,
volume and pressure are
inversely related to each other
4. TEMPERATURE OF GAS
Raising
the temperature of a gas increases
the pressure, if the volume is held constant.
(Temp. and Pres. are directly related)
DENSITY OF GAS AT STP



One mole of any gas at STP occupies 22.4 L.
The mass of one mole of a substance can be used
with the molar volume to calculate the density of
the gas as a g/L value.
What is the density of SO2 gas at STP, in g/L?
PRACTICE

What is the density, in g/L, of C2H6 at STP?
PRACTICE

What is the molar mass of a gas that has a
density of 0.890 g/L at STP?
THE GAS LAWS
#1. BOYLE’S LAW
Gas pressure is inversely proportional to the
volume, when temperature is held constant.
#2. CHARLES’S LAW
The volume of a fixed mass of gas is
directly proportional to the Kelvin
temperature, when pressure is held
constant.
CONVERTING CELSIUS TO KELVIN
•Gas law problems involving
temperature will always require that
the temperature be in Kelvin.
Kelvin = C + 273
and
°C = Kelvin - 273
#3. GAY-LUSSAC’S LAW
•The pressure and Kelvin temperature of
a gas are directly proportional, provided
that the volume remains constant.
#5. THE COMBINED GAS LAW
The combined gas law expresses the
relationship between pressure, volume
and temperature of a fixed amount of
gas.
P = Initial Pressure
1
P1V1 P2V2

T1
T2
V1 = Initial Volume
T1 = Initial Temperature in Kelvin
P2 = Final Pressure
V2 = Final Volume
T2 = Final Temperature in Kelvin
The
combined gas law contains
all the other gas laws!
If the temperature remains
constant...
P 1 x V1
T1
=
P2 x V2
T2
Boyle’s Law
The
combined gas law contains
all the other gas laws!
If the pressure remains constant...
P 1 x V1
T1
=
P2 x V2
T2
Charles’s Law
The
combined gas law contains
all the other gas laws!
If the volume remains constant...
P 1 x V1
T1
=
P2 x V2
T2
Gay-Lussac’s Law
EXAMPLES

The volume of some amount of a gas was 1.00 L
when the pressure was 10.0 atm; what would the
volume be if the pressure decreased to 1.00 atm?

The volume of some amount of a gas was 1800 mL
when the pressure was 98 kPa; what would the
volume be if the pressure decreased to 400
mmHg?

A gas occupied a volume of 6.54 mL at 25°C what
would its volume be at 100°C?

A gas occupied a volume of 3.2 L at 90oC what
would be the temperature of the gas if the volume is
increased to 5.0L ?
•
A gas has a pressure of 750 torr at 15oC. If the
pressure is increased 1025 torr, what is the new
temperature?

A gas has a pressure of 250 kPa at 100 K. If the
pressure is increased 3.5 atm, what is the new
temperature?

A 1.00 L balloon at 25.0oC has a pressure of 750
mmHg. If the temperature is increased to 37.0oC
and the pressure is decreased to 740 mmHg, what
is the new volume?

0.85 L of a gas 125.0oC has a pressure of 1.25
atm. If the temperature is increased to 237.0oC and
the pressure is decreased to 0.85 atm, what is the
new volume?
AVOGADRO'S LAW

The amount of gas, in moles, is directly related to
the volume of the gas.
𝑽𝟏
𝒏𝟏
=
𝑽𝟐
𝒏𝟐
n1 = Initial amount of
gas in moles
n2 = Final amount of gas
in moles

1.75 mol of gas occupies a volume of 1.5 L what
would be the volume if the amount of gas is
decreased to 0.68 mol?

3.5 mol of gas occupies a volume of 300 mL what
would be the volume if the amount of gas is
increased to 5.8 mol?
#6. THE IDEAL GAS LAW #1
Equation:
Ideal
R
PV = nRT
Gas Constant (R)
= 0.08206 (L atm) / (mol K)
The
other units must match the value of
the constant, in order to cancel out.
#7. IDEAL GAS LAW 2
PVmm
g
= gRT
= mass, in grams
mm = molar mass, in g/mol
IDEAL GAS EQUATION #3
Density
is mass divided by volume
PMr = dRT
d = density
Mr= Molar Mass
#8 DALTON’S LAW OF PARTIAL PRESSURES
For a mixture of gases in a container,
PTotal = P1 + P2 + P3 + . . .
represents the “partial pressure”,
or the contribution by that gas.
•Dalton’s Law is particularly useful in
calculating the pressure of gases
collected over water.
•P1
Connected
to gas
generator
Collecting a gas over water – one of the
experiments in this unit involves this.
 If
the first three containers are all put into the
fourth, we can find the pressure in that container
by adding up the pressure in the first 3:
2 atm
1
+ 1 atm
2
+ 3 atm
3
= 6 atm
4
Sample Problem 14.6, page 434
IDEAL GASES DON’T EXIST, BECAUSE:
1. Molecules
2. There
do take up space
are attractive forces between
particles
- otherwise there would be no liquids formed
REAL GASES BEHAVE LIKE IDEAL GASES...
When
the molecules are
far apart.
The molecules do not
take up as big a
percentage of the space

We can ignore the particle
volume.
This
is at low pressure
REAL GASES BEHAVE LIKE IDEAL GASES…
When
molecules are moving fast
 This is at high temperature
Collisions are harder and faster.
Molecules are not next to each
other very long.
Attractive forces can’t play a role.
DIFFUSION IS:
Molecules
moving from areas of high
concentration to low concentration.
Example:
perfume molecules spreading
across the room.
Effusion:
Gas escaping through a tiny
hole in a container.
Both
of these depend on the molar
mass of the particle, which
determines the speed.
•Diffusion:
describes the mixing
of gases. The rate of
diffusion is the rate
of gas mixing.
•Molecules move
from areas of high
concentration to low
concentration.
•Fig. 14.18, p. 435
Effusion: a gas escapes through a tiny
hole in its container
-Think of a nail in your car tire…
Diffusion
and effusion
are
explained
by the next
gas law:
Graham’s