Transcript The Nature of Gases

Solids, Liquids, & Gases
Chapter 7
The Nature of Gases
• Indefinite shape and
indefinite volume
•expand to fill their containers
•compressible
•Fluid – they flow
•Low density
•1/1000 the density of
the equivalent liquid or
solid
•Undergo effusion and
diffusion
Diffusion
• Diffusion:
describes the
mixing of gases.
The rate of
diffusion is the
rate of gas
mixing.
Effusion
• Effusion:
describes the
passage of
gas into an
evacuated
chamber
Pressure
 Is caused by the collisions of
molecules with the walls of a
container
 Is equal to force/unit area
 P=F/A
 SI units = Newton/meter2 =
1 Pascal (Pa)
 101,325 Pa = 1 standard
atmosphere (1atm)
 1 atm = 760mmHg = 760 torr
Measuring Pressure
 The first device for
measuring atmospheric
pressure was developed
by Evangelista Torricelli
during the 17th century.
 The device was called a
“barometer”
 Baro = weight
 Meter = measure
An Early Barometer
• The normal
pressure due to the
atmosphere at sea
level can support a
column of mercury
that is 760 mm
high.
The Aneroid Barometer
The Digital Barometer
GAS LAWS
Boyle’s Law
Charles’ Law
Gay-Lussac’s Law
BOYLE’S LAW
The Relationship Between Pressure and Volume
Robert Boyle
(1627-1691)
 Boyle was born into an
aristocratic Irish family
 Became interested in
medicine and the new
science of Galileo and
studied chemistry.
 A founder and an
influential fellow of the
Royal Society of
London
 Wrote prolifically on
science, philosophy,
and theology.
Boyle’s Law
• Boyle’s Law: The volume of a gas is inversely
proportional to the pressure applied to the gas
when the temperature is kept constant.
• Decrease in volume = Increase in pressure.
• Increase in volume = Decrease the pressure
Boyle’s Equation:
• P 1 V1 = P 2 V 2
• Therefore:
• V1=(P2V2)/P1
• V2= (P1V1)/P2
• P1=(P2V2)/V1
• P2=(P1V1)/V2
Problems
1) You have a 2L cylinder of gas that is
under 100 kPa of pressure. If you
compress the gas to 1L, what will the
new pressure be?
2) You have a 10.0L container of gas under
505 torr of pressure. If you increase the
pressure to 1155 torr, what will the new
volume be?
The Relationship Between Temperature and Volume
Jaques Charles (1746-1823)
Charles studied the
compressibility of
gases nearly a
century after Boyle
French Physicist
Conducted the first
scientific balloon flight
in 1783
Charles’ Law
• At a fixed pressure, the volume of a gas is
proportional to the temperature of the gas.
• As the temperature increases, the volume
increases.
• As the temperature decreases, the volume
decreases.
How Did He
Figure It Out?
A cylinder with a piston and
a gas is immersed in a water
bath.
A mass is placed on top of
the piston which results in a
pressure on the gas. This
mass is held constant, which
means that the pressure on
the gas is constant.
 The gas volume is
measured as the
temperature is increased and
V vs. T data point plotted.
This is continued over a large
range of temperatures.
Charles’ Equation
• Rearrange the equation to solve for V1, T1,
V2, or T2
•
•
•
•
V1=(V2T1)/T2
T1=(V1T2)/V2
V2=(V1T2)/T1
T2=(V2T1)/V1
• All temperatures must be in KELVIN!!!
Problems
1) A cylinder contains 5.00L of gas at 225K. If the
temperature is increased to 345K, what will the
new volume be?
2) A tire contains 2.00L of air at 300.0K, if the
volume in the tire decreased to 1.50L, what
must the new temperature be?
3) A ball contains 3.0L of air at 32ºF, if the
volume increases to 5L, what must the
temperature have changed to?
Gay-Lussac’s Law
The Relationship Between
Pressure and Temperature
Joseph Louis Gay-Lussac
1778 - 1850
 French
chemist and
physicist
 Known for his studies
on the physical properties
of gases.
 In 1804 he made balloon
ascensions to study
magnetic forces and to
observe the composition
and temperature of the air
at different altitudes
Gay-Lussac’s Law
• The pressure of a fixed amount of gas at
fixed volume is directly proportional to its
temperature in Kelvin.
• As the temperature increases, the
pressure also increases
• As the temperature decreases, the
pressure also decreases
Gay-Lussac’s Law
Expressed Mathematically as:
 Rearranging this equation to solve for
the variables gives us:
P1=(P2T1)/T2
P2=(P1T2)/T1
T1=(P1T2)/P2
T2=(P2T1)/P1
Problems
1) Jim-Bob has revved his engine enough so that
the internal temperature and pressure of his
engine are 700.0K and 200.0kPa. If the
temperature outside was 295K before Jim-Bob
got into his car, what was the internal pressure
in his engine?
2) Today, the barometer reads 750mmHg and the
thermometer says that it is 65ºF. At 6am, the
barometer read 700mmHg, what was the
temperature at that time?
The Combined Gas Law
The Relationship Between
Pressure, Volume, and
Temperature
The Combined Gas Law
• A combination of Boyle’s,
Charles’, and GayLussac’s laws.
• Written mathematically as:
• Temperature must be in
KELVIN.
• Rearranged to solve for each variable:
P1=(P2V2T1)/(V1T2)
V1=(P2V2T1)/(P1T2)
T1=(P1V1T2)/(P2V2)
P2=(P1V1T2)/(V2T1)
V2=(P1V1T2)/(P2T1)
T2=(P2V2T1)/(P1V1)
Problems
1) Rhonda’s helium balloon has a volume of
2.00L at 2.00atm and 395K. If the temperature
is raised to 500.K and the gas is compressed
to 1.00L, what is the new pressure?
2) Ryan ate at Taco Smell last night. He now has
gas which takes up 1.29L of bowel space
under 2.35atm of pressure at 310K (body
temp). What will be the volume of Jeremy’s
gas after he expels it if the atmospheric
temperature and pressure are 75ºF and
1.00atm respectively?
Avogadro’s Law
The Relationship Between Pressure,
Temperature, Volume and Moles
Amedeo Avogadro
(1776-1856)
• Italian physicist and
mathematician
• Born in a noble ancient
family of Piedmont
• “Avogadro’s Number”
is named after him
• 6.022 x 1023
• The number of things in
a mole
Avogadro’s Law
• One mole of any gas occupies
exactly 22.4 liters (dm3) at
STP.
– STP = Standard
Temperature and Pressure
– Temp = 0ºC = 273K
– Pressure = 1atm = 760
mmHg = 760 torr etc.
• This is often referred to as the
“molar volume” of a gas.
• Equal volumes of gases, at the same
temperature and pressure, contain the
same number of particles, or molecules.
• Thus, the number of molecules in a
specific volume of gas is independent of
the size or mass of the gas molecules.
• Therefore, IT DOESN’T MATTER WHICH
GAS YOU ARE TALKING ABOUT.
Problems
1) Luis has 3.5 mol of H2 gas at STP. What
volume will this gas occupy?
2) Joann has a can of CO2 gas that
contains 0.180 mol CO2 at 1atm and
273K. If Joann let half of the gas out,
what would the new volume be?
Avogadro’s Law
• Written
mathematically:
• Where “n” is the
number of moles of
gas present
• Mini Version:
More Problems
1) Joe’s balloon contains 1.0 mole of Helium at
STP. If Joe blows another mole of Helium into
the balloon, heats it to 350K, and decreases
the volume to 0.75 L, what will the new
pressure be inside the balloon?
2) A 1.0L cylinder contains 2.0 moles of gas at
250K and 1.0atm. If the temperature and
pressure are increased to 350K and 3.5atm
and the new volume of gas is 0.50L, how much
gas was added/removed?
The Ideal Gas Law
• The Ideal Gas Law is most often written
as: PV=nRT
• Rearranging the equation gives us:
P = (nRT)/V
V = (nRT)/P
n = (PV)/(RT)
T = (PV)/(nR)
• R is the Universal Gas Constant
R = 0.082 L x atm x K-1 x mol-1
R = 62.36 L x torr x K-1 x mol-1
R = 62.36 L x mmHg x K-1 x mol-1
R = 8.315 L x kPa x K-1 x mol-1
Problems
1)
2)
3)
Rosy has a 5.0L tank of H2 gas. If the pressure inside
the tank is 800.0torr and the temperature is 300.0K,
how many moles of hydrogen does her tank contain?
Chris’ favorite meal is a bean and cheese burrito from
Del Taco. Unfortunately, this means that his intestines
were filled with 1.50 moles of CH4 gas under 2atm of
pressure. What is the volume of gas that occupies his
bowels? *Make an assumption about Temp*
Jose wants to cook up some steaks for Super Bowl
Sunday. He looks at his BBQ and notices that his
Propane (C3H8) tank contains 10.0L of the gas under
3.0atm at room temperature. How many grams of
propane does Jose own?
Dalton’s Law
The Law of Partial Pressures
John Dalton
(1766-1844)
• English Chemist
and Physicist
• Did much research
on color blindness
– He was colorblind
• Famous for his
atomic theory
• Worked with gases
• Dalton’s Law: The total pressure exerted
by a mixture of gases is the sum of the
individual pressures of each gas in the
mixture
• Dalton’s Equation:
Problems
1) The air in this room contains the gases
shown below at their respective partial
pressures in kPa. What is the pressure
your body feels from the air in this room?
2) What is the pressure
in problem 1 if you
convert it to atm?
Torr? mmHg?
3) Scuba Divers use gas
mixtures of O2 and
He. If the diver to
your right breathes
in a mixture that has
a total pressure of
6.5 atm and a partial
pressure from O2 of
1.2 atm, what is the
partial pressure of
He?
Liquids
• Particles close, but far
apart enough to allow
for movement
– Slide passed each other
– Fluid
•
•
•
•
•
Definite volume
No definite shape
High density
Low compressibility
Low thermal expansion
Solids
•
•
•
•
•
Atoms very close
Definite shape
Definite volume
High Density
Very small thermal
expansion
Intermolecular Forces
1) Ionic bonds
•
Occur between ions
•
•
•
Usually a metal and a non-metal
Hold ions close together
Require large amounts of energy to break
•
Example: M.P. of NaCl = 801°C
2) Dipole-Dipole Attractions
•
•
Attraction between two polar molecules
Positive end of one molecule is attracted to
the negative end of another molecule
Chloroform (l)
3) Hydrogen bonds
• Special dipole-dipole
attraction
• Occurs between the H
that is bonded to a very
electronegative atom (O,
N, F) on one molecule
and the lone pair(s) on a
very electronegative
atom on another
molecule
• Surface tension
4) Dispersion forces/London forces/Van Der
Waals forces
• Caused by momentary dipoles in otherwise
non-polar molecules
• Effect is often seen in very large molecules
Interaction
Ionic
Relative
Strength
1000
Hydrogen Bond
100
Dipole-Dipole
10
Dispersion
1
Problems
Identify the major interaction expected for
the following molecules
• Cl2
• NH3
• C10H22
• KI
• HBr
Identify the major interaction expected between
the following molecules
• Water and ammonia (NH3)
• Formaldehyde (CH2O) and methane (CH4)
Change of State
a.k.a. freezing
Melting Point (Freezing Point)
• The temp at which the solid form of a
substance begins to melt and the liquid
form of that substance begins to solidify
• Most often referred to as M.P.
• F.P. understood
• Both solid and liquid exists at this temp
• Example: Water’s M.P. is 0°C
Boiling Point (Condensation Point)
• Temp at which the liquid form of a
substance begins to vaporize and the
gaseous form of that same substance
begins to liquify
• Usually referred to as B.P.
• C.P. understood
• Both liquid and gas occur at this temp
Substance M.P. (°C)
B.P. (°C)
H2O
0
100
Au
1064
2856
CH4
-182.5
-161.6
NaCl
801
1465
Why is CO2 not listed?