Transcript BEHAVIOR OF GASES Chapter 12

Unit 8 – GAS LAWS
Dr. Mihelcic
Honors Chemistry
Importance of Gases



Airbags fill with N2 gas in an accident.
Gas is generated by the decomposition of sodium azide,
NaN3.
2 NaN3 ---> 2 Na + 3 N2
Three States of Matter
Characteristics of Gases





No definable shape or volume
Low mass, with a lot of “free” space
(leads to low density)
Can be expanded infinitely and
placed into a container if force is
exerted.
Occupy containers uniformly and
completely.
Escape readily from containers, mix
rapidly.
KINETIC MOLECULAR THEORY
(KMT)
Definition:
Theory used to explain gas laws.
Treats gases as a collection of particles in rapid,
random motion.
Applies to ALL gases, regardless of chemical
identity.
Molecular Model

Gas molecules are relatively far apart (mostly
empty space).

Gas molecules are in continuous, rapid, random
motion.

All collisions between gas molecules are elastic (no
energy lost or gained in a collision).

Gas pressure is caused by collisions of molecules with
the walls of the container.

Average Temperature of a gas sample is related to
its kinetic energy.
Properties of Gases
Gas properties can be modeled using math. Model
depends on—
1.
2.
3.
4.
V = volume of the gas (L)
T = temperature (K)
n = amount (moles)
P = pressure
(atmospheres)
Gas Pressure


Caused by gas molecules hitting container walls.
Definition:
 Force per unit area, or
Force
Area
Image from: www.indiana.edu/.../PressGasLaws.html
Pressure Units
SI unit:
pascal (Pa)
(equal to N/m2)
1 kPa = 1000 Pa
Additional Units of Pressure
Will also see problems with:
atmospheres (atm)
millimeters of mercury (mm Hg)
inches of Hg (in Hg)
torr ( = 1 mm Hg)
Less commonly used:
pounds per square inch (psi)
millibars (mb)
Conversion Factors and STP
Conversion Factors and STP
1 atm = 760 mm Hg = 760 torr = 101.3 kPa
= 29.921 in Hg = 1013.25 mb = 14.969 psi
STP –
Standard Temperature (0ºC) and Pressure (1 atm)
Pressure
BAROMETER (developed
by Torricelli in 1643)
Use:
Measures pressure of air
Image from Dr. Walt Volland, all rights reserved 1998-2005
Barometric Pressure
Column height measures the
pressure of the atmosphere

1 standard atm
= 760 mm Hg
= 29.921 inches Hg
= about 34 feet of water
Manometers

Use:
Measures the pressure
of a gas in a closed
system.
Open Manometer: Two Cases
Sample Manometer Problem
An open manometer is filled with Hg and connected to a container
of hydrogen. The mercury level is 40.0 mm lower in the arm of the
tube connected to the air. Air pressure is 1.00 atm. What is the
pressure of the hydrogen gas in mm of Hg?
Boyle’s Law
RELATIONSHIP
BETWEEN PRESSURE
AND VOLUME
Boyle’s Law in Real Life
 Popping a balloon
 As
you squeeze the balloon, what happens to the
pressure and volume inside the balloon?
P
 Are
V
pressure and volume directly proportional or
inversely proportional?
Boyle’s Law in Real Life
 Operating a syringe
 As
you pull back on the plunger, are you
increasing or decreasing the volume? How does
the pressure change?
P
 Are
V
P and V directly or inversely proportional?
Boyle’s Law in Real Life
 Marshmallow/balloon in a vacuum
 As
we evacuate the chamber, what do you think
will happen to the pressure? What do you think
will happen to the volume of the marshmallow?
P
 Are
V
P and V directly or inversely proportional?
400 Marshmallows in a Vacuum
Boyle’s Law
 When temperature is held constant, pressure and
volume increase and decrease as opposites
 If pressure increases, volume decreases
 If pressure decreases, volume increases
P1V1 = P2V2
Practice with Boyle’s Law
 A balloon contains 30.0 L of helium gas at 103 kPa.
What is the volume of the helium when the balloon
rises to an altitude where the pressure is only
25.0 kPa? (Assume temperature is held constant)
P1V1 = P2V2
P1 =
V1 =
P2 =
V2 =
Practice with Boyle’s Law
 At room temperature, 10.01 L of a gas is found to
exert 97.0 kPa. What pressure (in atm) would be
required to change the volume to 5.00 L?
P1V1 = P2V2
P1 =
V1 =
P2 =
V2 =
1 atm = 101.3 kPa
Practice with Boyle’s Law
 Nitrous oxide (N2O) is used as an anesthetic. The
pressure on 2.50 L of N2O changes from 105 kPa to
40.5 kPa. If the temperature does not change, what
will the new volume be?
P1V1 = P2V2
P1 =
V1 =
P2 =
V2 =
CHARLES’ LAW:
Relating Volume and Temperature
Charles’ Law in Real Life

Balloons popping when kept outdoors
 As
the balloons sits outside, what happens to the
temperature of the gas inside the balloon? What
happens to the volume of the balloon?
V

T
Are volume and temperature directly proportional
or inversely proportional?
Charles’ Law in Real Life

A ball outside on a cold day
 You
pump the ball up indoors. After going outside
where it’s colder, what happens to the volume of the
ball?
V

T
Are volume and temperature directly or
inversely proportional?
Charles’ Law in Real Life

Liquid Nitrogen demo video
 When
the balloon is placed in the liquid nitrogen,
what happened to the temperature of the gas inside
the balloon? What happened to the volume?

V
T
Are volume and temperature directly or
inversely proportional?
Charles’ Law

If pressure is held constant (doesn’t change), volume
and temperature increase or decrease together
 If volume increases, so does the temperature
 If temperature decreases, so does the volume
V1 V2

T1 T2
***T must
be in
Kelvin!!!
Practice with Charles’ Law

A balloon inflated in a room at 24 ºC has a volume
of 4.00 L. The balloon is then heated to a
temperature of 58 ºC. What is the new volume if
the pressure remains constant?
V1 =
T1 =
V2 =
T2 =
V1 V2

T1 T2
Practice with Charles’ Law

Exactly 5.00 L of air at -50 ºC is warmed to some
temperature so that the volume was 8.36 L. What
temperature was the system warmed to?
V1 =
T1 =
V2 =
T2 =
V1 V2

T1 T2
Practice with Charles’ Law

A 50.0 mL sample of a gas is cooled from 119 ºC
to 353 K. If the pressure remains constant, what is
the final volume of the gas?
V1 =
T1 =
V2 =
T2 =
V1 V2

T1 T2
Avogadro’s Hypothesis
Equal volumes of gases at the same T and P have the
same number of molecules.
V = kn
V and n are directly related.
twice as many
molecules
Avogadro’s Hypothesis & Molar Volume
Image from
library.thinkquest.org/12
596/avogadro.html
1 mol gas @ STP = 22.4 L
(a new conversion factor for moles!!)
Sample Problem
Example 5.3
What is the mass of propane gas, C3H8, that can be
held in a 5.0 L container at STP?
Combined Gas Law
Combining all four
variables:
P1V1 = P2V2
n1T1
n2T2
If any one of these variables does not change in the
problem, you can eliminate it from the equation
before starting!
Imploding Can Demo

What happened to the volume of the
can?

What happened to the temperature of
the gas inside the can?

How did pressure play a role in the can
imploding?
IDEAL GAS LAW
P V = n R T
P = pressure
V = volume
n = # of moles
R = Ideal gas constant
T = temperature (in Kelvin)
Gas Law Constant (R)
R: Universal or ideal gas constant
Can be in different units, depending
on units used in the equation!
0.082058
L atm/mol K
62.364 L torr/mol K
8.3145 J/mol K
Sample Problem
Example 5.4 If a fixed amount of gas occupies 2.53
m3 at -15°C and 191 Torr, what will the volume of the
same gas be at 25°C and 1142 Torr?
Sample Problem
Example 5.5 A gas cylinder is filled with 100 g of
CO2 at 25oC and a pressure of 1000 mmHg. If 50
more grams of CO2 are added and the cylinder is
stored at a temperature of 50oC, calculate the new
pressure inside the cylinder.
Using PV = nRT
How much N2 is required to fill a small room with a volume of
960 cubic feet (27,000 L) to a pressure of 745 mm Hg at
25°C?
Sample Problem
Example 5.7 If 0.623 g of ethane, C2H6, is introduced
into an evacuated 2.00 liter container at 23°C, what is
the pressure, in atmospheres, in the container?
Sample Problem
Example 5.8 How much gas can be placed in a gas
cylinder with a volume of 10.0 L and which is designed
to store gas at a maximum pressure of 75.0 atm and at
a maximum of 50°C?
Gas Density and Molar Mass
PV = nRT
n
P
=
V
RT
m
P
=
M• V
RT
where M = molar mass
and density (d) = m/V
m
PM
d =
=
V
RT
d and M proportional
Sample Problem
Example 5.9 A sample of phosgene (a highly toxic
gas) is collected in a flask with a volume of 247 mL at a
pressure of 751 mmHg and a temperature of 21°C. If
the mass of the gas is 1.00 g, what is the molar mass of
phosgene?
Sample Problem
Example 5.10 What is the density of methane, CH4,
at 0.940 atm and 23°C?
Gases in Reaction Stoichiometry
Review of steps in Stoichiometry Problems:
1.
Balance equation & convert to moles for known.
2.
Convert moles of known to moles of unknown
quantity using coefficient ratio.
3.
Convert moles of unknown to required unit (g,
L)
Short-cut when dealing with all gases
in an equation
1.
2.
If have all gases in an equation, can go directly
from V of the given to V of the asked for quantity
using the coefficients.
ONLY works for equations with all gases!
Sample Problem
Write the balanced equation for the synthesis of
gaseous water from gaseous hydrogen and oxygen. If
we start with 5.4 L of oxygen, how much water in Liters
is produced?
Sample Problem
What is the mass, in grams, of potassium chlorate that
must be used to produce 1.50 L of oxygen gas
measured at 18°C and 0.950 atm?
Sample Problem
How many liters of oxygen, measured at 725 mmHg
and 21°C are required to burn 1.00 g of butane gas,
C4H10, to produce water and carbon dioxide?
GRAHAM’S LAW &
DALTON’S LAW
Racing Gases Demo:
If concentrated HCl is at one end of
the tube and concentrated NH3 is at
the other end, which gas do you
think will move farthest and fastest
down the tube?
HCl (g)
NH3 (g)
Racing Gases Demo
RACING GASES DEMO
The
gases will diffuse down the tube
 Diffusion – tendency of molecules to
move from areas of higher
concentration towards areas of lower
concentration
Example: spraying perfume and
smelling it across the room
DIFFUSION
Originally
Over Time
RACING GASES DEMO
 The
gases diffused at different rates
 If the white ring forms closer to the HCl end
of the tube, which gas moved farthest and
fastest?

What if it was closer to the NH3 end?
RACING GASES DEMO
What
happened in the tube?
Was
the reaction closer to the HCl or
NH3 end of the tube?
Calculate
the molar mass of NH3(g) and
HCl(g). Did the lighter or heavier gas
move faster?
GRAHAM’S LAW OF
EFFUSION
The
demo is related to Graham’s Law of
Effusion – gases of lower molar masses
effuse faster than gases with higher molar
masses
 Effusion – when a gas escapes through a
tiny hole in its container
Example: Helium balloons shrinking
compared to normal balloons
GRAHAM’S LAW
 Graham’s
Law can also be applied to the
diffusion of a gas
 Gases with lower molar masses (lighter
gases) diffuse faster than gases with higher
molar masses (heavier gases)

The lighter the gas, the faster it moves
GRAHAM’S LAW
Which
gas would both diffuse and
effuse faster…
 Methane (CH4) or carbon dioxide (CO2)?
 Chlorine (Cl2) or oxygen (O2)?
 Hydrogen sulfide (H2S) or carbon
monoxide (CO)?
GAS DIFFUSION AND
EFFUSION
Graham’s law calculates:
rate of effusion and
diffusion of gas molecules.
Rate (Gas 1)
M of 2
Rate(Gas 2)
M of 1
Rate of effusion is
inversely proportional
to its molar mass.
Thomas Graham, 1805-1869.
Professor in Glasgow and London.
Sample Problem
If they are compared under the same conditions, how
much faster than helium does hydrogen effuse through a
tiny hole?
Sample
Problem
The rate of a volume of an unknown gas to effuse through
a pinhole was 4.00 moles/sec. The rate calculated for the
same volume at the same temperature and pressure of
oxygen was 2.00 moles/sec. Calculate the molar mass of
the unknown gas.
REVIEW - PRESSURE OF A GAS
If
the gas molecules in a sample
collide more with the walls of the
container, will the pressure increase
or decrease?
If
the number of gas molecules
increases, what will happen to the
pressure?
DALTON’S LAW
DALTON’S LAW
 Partial
pressure – the contribution of each
gas in a mixture to the total pressure
 Dalton’s
Law of Partial Pressures – for a
mixture of gases, the total pressure is the sum
of the partial pressure of each gas in the
mixture
Ptotal = P1 + P2 + P3 + …
(at constant volume and temperature)
PRACTICE – DALTON’S LAW
Determine the total pressure of a gas mixture
that contains oxygen, nitrogen, and helium. The
partial pressures are:
PO2= 20.0 kPa, PN2=46.7 kPa, and PHe=26.7 kPa.
Ptotal = P1 + P2 + P3 + …
PRACTICE – DALTON’S LAW
Air contains O2, N2, CO2, and trace amount of
other gases. What is the partial pressure of
oxygen (PO2) if the total pressure of the system is
101.3 kPa and the partial pressures of N2, CO2,
and the other gases are 79.10 kPa, 0.040 kPa, and
0.94 kPa, respectively?
Ptotal = P1 + P2 + P3 + …
Vapor Pressure of Water
If the total pressure
is 788 mm Hg at
25oC, what is the
partial pressure of
hydrogen collected
over water?
Ptotal = P(gas) + P(H2O) = 788 mm Hg
Deviations from Ideal Gas Law occur because
of two main factors:
1. Real molecules have volume.
2. There are forces between molecules.
 Otherwise a gas could not become
a liquid.
These factors are important at
HIGH pressures and LOW
temperatures.
Deviations from Ideal Gas Law occur
because of two main factors:
1. Real molecules have volume.
2. There are forces between molecules.
 Otherwise a gas could not become
a liquid.
In general, the closer a gas is to the
LIQUID state, the more it will deviate
from the Ideal Gas Law.
Deviations from Ideal Gas Law
Account for volume of molecules and
intermolecular forces with VAN DER
WAALS’s EQUATION.
Measured V = V(ideal)
Measured P
(
2
P
n a
+ ----2
V
)
V
-
nb
vol. correction
intermol. forces
nRT
J. van der Waals,
1837-1923,
Professor of
Physics,
Amsterdam.
Nobel Prize 1910.
Deviations from Ideal Gas Law
Cl2 gas has a = 6.49, b = 0.0562
For 8.0 mol Cl2 in a 4.0 L tank at 27 oC.
P (ideal) = nRT/V = 49.3 atm
P (van der Waals) = 29.5 atm