Download Chapter 5 Gases

Chapter 5
Gases
Air Pressure & Shallow Wells

Gases
•Are mostly empty space
• Occupy containers uniformly and
completely
• The densities of gases are much
smaller than those of liquids and
solid and highly variable depending
on temperature and pressure
• Expand infinitely
• Diffuse and mix rapidly
2
Gases Pushing



gas molecules are constantly in motion
as they move and strike a surface, they
push on that surface
◦ push = force
if we could measure the total amount
of force exerted by gas molecules
hitting the entire surface at any one
instant, we would know the pressure
the gas is exerting
◦ pressure = force per unit area
Pressure:
Force
Unit area
3
Atmospheric Pressure Effects
differences in air pressure result in
weather and wind patterns
 the higher up in the atmosphere you
climb, the lower the atmospheric
pressure is around you
◦ at the surface the atmospheric
pressure is 14.7 psi, but at 10,000
ft it is only 10.0 psi
 rapid changes in atmospheric
pressure may cause your ears to
“pop” due to an imbalance in
pressure on either side of your ear
drum

4
The Pressure of a Gas
result of the constant movement of the
gas molecules and their collisions with
the surfaces around them
 the pressure of a gas depends on several
factors
◦ number of gas particles in a given
volume
◦ volume of the container
◦ average speed of the gas particles

5
Measuring Air Pressure
Units
Pa (SI unit)
torr
mm Hg
atm
bar
Conversions
1 atm = 760 mm Hg
(exact)
1 torr = 1 mm Hg
1 bar = 1 x 105 Pa
(exact)
1 atm = 101 325 Pa
1 atm = 14.7 psi
(exact)
Barometer
Gases and Gas Pressure
The Gas Laws
Ideal Gas: A gas whose behavior follows the gas laws exactly.
The physical properties of a gas can be defined by four variables:
P
T
V
n
pressure (atm)
temperature (calculation must be in Kelvin)
volume (L)
number of moles
The Ideal Gas Law, PV = nRT,
- models the behavior of ideal gases. Other gas laws can be derived from the
Ideal Gas Law for either one set of conditions or for two sets of conditions
(initial and final conditions).
To derive gas laws for two sets of conditions, solve the Ideal Gas Law for R
PV
L atm
R = 0.08206
---- = R
K mol
nT
Boyle’s law
o pressure of a gas is inversely
proportional to its volume
o constant T and amount of gas
o as P increases, V decreases by the
same factor
1
V a
P
(constant n
and T)
Two sets of conditions
P1 x V1 = P2 x V2
Boyles’ Law and Breathing
During an inhalation,
• the lungs expand.
• the pressure in the lungs
decreases.
• air flows towards the
lower pressure in the
lungs.
Examples

A cylinder with a movable piston has a volume of 7.25 L at 4.52 atm.
What is the volume at 1.21 atm?

A balloon is put in a bell jar and the pressure is reduced from 782 torr to
0.500 atm. If the volume of the balloon is now 2780 mL, what was it
originally?
Charles’s Law
In Charles’s Law,
• the Kelvin temperature of a gas is
directly related to the volume.
• P and n are constant.
• when the temperature of a gas
increases, its volume increases.
Charles' Law & Absolute Zero
• For two conditions, Charles’s law is
written
T1
Volume (L) of 1 g O2 @ 1500 torr
Volume (L) of 1 g O2 @ 2500 torr
0.5
= V2 (P and n constant)
T2
Charles’s Law can be used to
approximate absolute zero. At a
temperature of absolute
zero (0K), theoretically an ideal gas has
no volume.
Volume (L) of 0.5 g O2 @ 1500 torr
Volume (L) of 0.5 g SO2 @ 1500 torr
0.4
Volume, L
• V1
0.6
0.3
0.2
0.1
0
-300
-200
-100
0
Temperature, °C
100
200
Charles’ Law – A Molecular View


the pressure of gas inside and
outside the balloon are the same
at low temperatures, the gas
molecules are not moving as fast,
so they don’t hit the sides of the
balloon as hard – therefore the
volume is small
• the pressure of gas inside and
outside the balloon are the
same
• at high temperatures, the gas
molecules are moving faster,
so they hit the sides of the
balloon harder – causing the
volume to become larger
Examples

A gas has a volume of 2.57 L at 0.00°C. What was the temperature at 2.80
L?

The temperature inside a balloon is raised from 25.0°C to 250.0°C. If the
volume of cold air was 10.0 L, what is the volume of hot air?
Avogadro’s Law
Va n
(constant T and P)
V
n
Vinitial
ninitial
=k
=
Vfinal
nfinal
Examples

A 0.225 mol sample of He has a volume of 4.65 L. How many
moles must be added to give 6.48 L?

A chemical reaction occurring in a cylinder equipped with a
moveable piston produces 0.621 mol of a gaseous product. If the
cylinder contianed 0.120 mol of gas before the reaction and had an
initial volume of 2.18L, what was its volume after reaction?
The Ideal Gas Law
Ideal Gas Law:
PV = nRT
R is the gas constant and is the same for all gases . R is independent of the
particular gas studied
L atm
R = 0.082058
K mol
since the volume of a gas varies with pressure and temperature, chemists
have agreed on a set of conditions to report our measurements so that
comparison is easy – we call these standard conditions
Standard Temperature and Pressure
(STP) for Gases
T = 0 °C (273.15 K)
P = 1 atm
Examples

A 0.250 mol sample of argon gas has a volume of 9.00L at a
pressure of 875 mmHg. What is the temperature (in oC) of the
gas?

What volume is occupied by 25.7 g of carbon dioxide gas at 25.0oC
and 371 torr?
Molar Volume


solving the ideal gas equation for the volume of 1 mol of gas at STP
gives 22.4 L
◦ 6.022 x 1023 molecules of gas
we call the volume of 1 mole of gas at STP the molar volume
◦ it is important to recognize that one mole of different gases have
different masses, even though they have the same volume
19
Concept problem

What is the volume occupied by 2.75 moles of N2 gas at STP?

Assuming ideal behavior, which of the following gas samples will
have the greatest volume at STP?
a. 1 g H2
b. 1 g O2
c. 1 g Ar
Gas Density and Molar Mass
The density of a gas is proportional to its molar mass. As the molar mass of a
gas increases, so does the density of the gas. Matter often separates according to
its density, with less dense matter floating on matter of higher density
PV  nRT
m
PV  RT
M
Rearrange
m
P

M
V RT
m
P
d
M
V
RT
21
Examples

Calculate the density of gaseous hydrogen at a pressure of 1.32 atm
and a temperature of -45.0oC.

A sample of gas has a mass of 0.827g. Its volume is 0.270L at a
temperature of 88.0oC and a pressure of 975 mmHg. Find its molar
mass
Partial Pressure
when gases are mixed together, their molecules
behave independent of each other
 the pressure of a single gas in a mixture of gases is
called its partial pressure
 we can calculate the partial pressure of a gas if
 the sum of the partial pressures of all the gases in
the mixture equals the total pressure

◦ Dalton’s Law of Partial Pressures
PT = P1 + P2 + P3 +....
23
The partial pressure of each gas in a mixture can be
calculated using the ideal gas law
for two gases, A and B, mixed together
nA x R x T
nB x R x T
PA 
PB 
V
V
the temperatu re and volume of everything
in the mixture are the same
n total  n A  n B
n total x R x T
Ptotal  PA  PB 
V
24
Example
 PHe=341 mmHg, PNe=112 mmHg, Ptot = 662
mmHg, V = 1.00 L, T=298 K
Find the partial pressure of neon in a mixture with
total pressure 3.9 atm, volume 8.7 L, temperature 598
K, and 0.17 moles Xe.
Mole Fraction
the fraction of the total pressure that a
single gas contributes is equal to the
fraction of the total number of moles
that a single gas contributes
the ratio of the moles of a single
component to the total number of
moles in the mixture is called the mole
fraction, c
the partial pressure of a gas is equal to
the mole fraction of that gas times the
total pressure
PA
nA

Ptotal n total
nA
cA 
n total
PA  c A  Ptotal
26
Deep Sea Divers & Partial Pressure
its also possible to have too much O2, a condition called oxygen
toxicity
 PO2 > 1.4 atm
 oxygen toxicity can lead to muscle spasms, tunnel vision, and
convulsions
 its also possible to have too much N2, a condition called nitrogen
narcosis
 also known as Rapture of the Deep
 when diving deep, the pressure of the air divers breathe increases –
so the partial pressure of the oxygen increases
 at a depth of 55 m the partial pressure of O2 is 1.4 atm
 divers that go below 50 m use a mixture of He and O2 called
heliox that contains a lower percentage of O2 than air

27
Mountain Climbing & Partial Pressure
our bodies are adapted to
breathe O2 at a partial pressure
of 0.21 atm
 partial pressures of O2 lower
than 0.1 atm will lead to
hypoxia

◦ unconsciousness or death

climbers of Mt Everest carry O2
in cylinders to prevent hypoxia
◦ on top of Mt Everest, Pair = 0.311
atm, so PO2 = 0.065 atm
28
Example

Find the mole fractions and partial pressures in a 12.5 L tank
with 24.2 g He and 4.32 g O2 at 298 K

A diver breathes a heliox mixture with an oxygen mole
fraction of 0.050. What must the total pressure be for the
partial pressure of oxygen to be 0.21 atm?
Collecting Gases



gases are often collected by
having them displace water
from a container
the problem is that since
water evaporates, there is also
water vapor in the collected
gas
the partial pressure of the
water vapor, called the vapor
pressure, depends only on
the temperature
30
Vapor Pressure of Water
Tro, Chemistry: A Molecular
31
Examples

1.02 L of O2 collected over water at 293 K with a total
pressure of 755.2 mmHg. Find mass O2.

0.12 moles of H2 is collected over water in a 10.0 L container
at 323 K. Find the total pressure.