Download Chapter 12 Notes, part I

Chapter 14 Notes Part I
Boyle’s, Charles’ and Gay-Lussac’s Laws
Combined Gas Laws
Gas
Review
• In chapter 13 gases were
said to be mostly empty
space.
• This gives rise to a
property called
compressibility.
• The particles in a gas can
be forced closer
Kinetic Theory
• Kinetic Energy—Energy that an
object has due to motion.
• The Kinetic Theory states that
tiny particles form all matter,
and they are constantly in
motion.
Gases
A gas is composed of particles
that are small, hard spheres
with almost no volume or
particle interaction.
Gases
Particles in a gas are in
constant motion—they travel
straight paths unless they
collide with another particle or
their container.
Gases
All collisions are considered
elastic—no energy is lost
Temperature
When a substance is
heated, the particles
speed up, causing faster
movement and more
collisions.
This is a rise in
temperature.
Obj. 1…Ideal vs. real gases
•
behavior of ‘ideal gases’ (from kinetic theory)…
inverse relationship b/n P and V.
~ ______
direct relationship b/n T and V.
~ ______
direct relationship b/n T and P.
~ ______
•
however, there are no ‘ideal’ gases in existence.
•
two properties keep ‘real’ gases from being ‘ideal’…
~ real gas particles have distinct volumes …there comes a
point where V can not get smaller, no matter how much P is applied
~ real gas particles are slightly attracted to each other…
intermolecular attraction of gas molecules causes gases to occupy
less space than assumed by the KT.
Obj. 2-3…STP
•
STP = standard temperature and pressure
•
standard temp =
~ 0°C
~ 273 K **
•
standard pressure =
~ 1 atm
~ 101.3 kPa
~ 760 mmHg
• There are three
relationships between the
conditions a gas is in that
will be affected by this
property.
• Pressure and volume
• Volume and temperature
• Pressure and temperature
• Boyles Law states that as the volume of a gas
is decreased, the amount of pressure is
increased at constant temperature.
• (P#V$ or P$V#)
• Mathematically,
P1V1=P2V2
Obj. 4-6…Boyle’s Law
•
relationship b/n P and V is expressed in the Boyle’s Law
equation.
~ inverse relationship
~ only works if T remains constant!
p1v1 = p2v2
Ex…
V1
P1
• The pressure on 2.5 L of a gas decreases from 105 kPa to
40.5 kPa. What is the new volume of the gas?
•
P2
V2
105(2.5) = 40.5(x)
262.5 = 40.5(x)
40.5
40.5
6.5 liters
Why?
• With less volume, there is
greater frequency of the
same amount of particles
hitting the surface of the
container.
• Charles Law states that as the temperature of a gas
is increased, the volume is also increased at constant
pressure.
• (V#T# or V$T$)
• Mathematically:
V1 = V2
T1 T2
Obj. 7-9…Charles’s Law
•
relationship b/n T and V is expressed in the Charles’ Law
equation.
~ direct relationship
~ only works if P remains constant!
~ temp. MUST be in Kelvin!!! (°C + 273)
v1 = v2
T1
T2
Ex…
V1
T1 = 398 K
• If a sample of gas occupies 6.8 L at 125°C, what will its
volume be at 38°C if pressure remains constant?
•
V2
T2 = 311 K
6.8
=
398
x
311
6.8 (311)
x=
398
5.3 liters
Why?
• As the temperature increases,
the average kinetic energy of
the particles increases.
• This increases the amount of
volume needed to maintain the
same frequency of collision with
the surface of the container.
Meanwhile...
• Jaques Charles also noticed that
no matter what gas he
experimented with, when he
extrapolated the volume down
on a graph, the temperature was
the same: -273oC!
Kelvin
• William Thomson (a.k.a. Lord Kelvin) recognized
this as the theoretical point at which the average
kinetic energy of all substances would be zero.
• Thus, the concept of absolute zero and the
Kelvin scale were born!
o
K= C+273
When comparing temperatures during this
chapter, they must be in Kelvin, because Celsius
is a degreed scale and Kelvin is an absolute
scale!
• Gay-Lussac’s Law states that as you increase
temperature of an amount of gas, its pressure will
increase if at a constant volume.
• (P#T# or P$T$)
• Mathematically:
P1 = P2
T1 T2
Obj. 10-12…Gay-Lussac’s Law
•
relationship b/n T and P is expressed in the Gay-Lussac’s
Law equation.
~ direct relationship
~ only works if V remains constant!
~ temp. MUST be in Kelvin!!! (°C + 273)
P1 = P2
T1
T2
Ex…
P1
T1
• A sample of gas has a pressure of 6.58 kPa at 339 K. What
will the temperature be at 4.21 kPa?
•
P2
T2
6.58
=
339
4.21
x
339 (4.21)
x=
6.58
217 K
Why?
• As the temperature increases, the
average kinetic energy of the
particles increases, thus they
move faster.
• This increases the frequency of
collisions, as well as the amount of
force in each collision.
But wait a minute...
Are you saying that I have to keep ALL these
equations straight in my head?
NO! There’s a handy, dandy equation that will show
you ALL these equations in one!
Combined Gas Laws
P1V1 P2V2
=
T1
T2
When one variable is constant, you can just
cross it out, and the equation works for all
three laws, as well as for combined problems!
Practice Problem #1
• The pressure on 2.5L of
anesthetic gas changes from
105 kPa to 40.5 kPa. What will
the new volume be if the
temperature is constant?
Practice Problem #2
• A balloon has a volume of 6.7L
at 20oC. What will its volume
be at 350oC if it is at constant
pressure?
Practice Problem #3
• The pressure in an automobile
tire that has a constant volume
is 198 kPa at 27oC. On a hot
sunny day the pressure has risen
to 225 kPa. What is the
temperature?
Practice Problem #4
• A gas at 155 kPa and 25oC
occupies a container with an
initial volume of 1.00L. By
changing the volume the pressure
of the gas increases to 605 kPa
as the temperature is raised to
125oC. What is the new volume?