Atomic Theory of Matter
• Idea of an atom
• indivisible
• Atomic Mass or Molecular Mass
• Also called unified Atomic Mass
(u)
• it is basically the mass of a
proton or neutron
12C has 6 protons, 6 neutrons ; 12 atomic
units
• Electrons are there, they
are just so small we don’t
consider them. It takes
almost 2000 e’ to have a
mass of one proton.
1u = 1.66 x 10-27 kg
Brownian Movement
• Robert Brown 1827
• Water & Pollen Grains
• Albert Einstein took this
observation and calculated the
diameter of an atom. (10-10m)
On a microscopic level, we understand
SOLIDS, LIQUIDS and GASES
• SOLIDS: e’ shells repel. e’ shells are
attracted to other nuclei, yet atoms stay
in fixed positions. “Crystal Lattice”
atoms are in motion- they vibrate
• LIQUIDS: atoms or molecules move
more rapidly atoms roll over one
another
• GASES: forces between atoms are weak.
atoms move at high speeds. they don’t
stay close to one another.
Temperatures and
Thermometers
• Temperature: a measure of how hot
or cold something is
• Most things expand when heated
and contract when cooled.
• Thermometers: instruments to
measure temperature. Most use
idea that expansion/ contraction
occurs when there is a temperature
change.
Galileo had 1st idea for
thermometer…
• Fluid in glass
• Bimetallic Strip
• Scales: Celsius, Fahrenheit, Kelvin
– Conversions : Pg. 386
Thermal Equilibrium
- occurs when 2 substances
have the same temperature
- Occurs when NO energy
flows between 2 objects
Thermal Equilibrium
Zeroth Law
Can you know if 2 systems are in thermal
equilibrium if they are NOT in contact
with one another?
• 2 systems (A & B) are NOT touching. However, both
are touching system C.
• If A is in equilibrium with C and B is in equilibrium
with C- is A in equilibrium with B?
• The answer isn't completely obvious but
experimentally we find that it is… We
have a name for it…
• Physics already named 1st & 2nd
laws…what’s less than 1 & 2?
ZERO!
• The main idea behind the Zeroth
law is that temperature is a valid
variable
Thermal Expansion
• Different materials expand
with different results.
• The change in length (ΔL) of
most solids is (for the most
part) directly proportional to
the change in temperature
(ΔT)
Thermal Expansion
Formula
ΔL = alpha Lo ΔT
L = Lo (1+ alpha ΔT)
ΔT = ΔL/ alpha Lo
alpha= coefficient of linear expansion
Lo = Original Length
To= Initial temp
L= Length after heating/cooling
T= final temp
ΔT= T-To ; if temp is negative this means length
shortens
at To
Lo
Δ
L
at T
L
Volume Expansion
ΔV = β Vo ΔT
*Think length changing in 3 directions:
length, width and height*
ΔV = β Vo ΔT
• ΔV = Change in Volume
• β = Coefficient of
Volume expansion (3 alpha)
• Vo= initial volume
• ΔT= temp (T-To)
*Linear expansion has no meaning to fluids
Anomaly of Water
13-5
Pg. 390
The Gas Laws
We will consider only
equilibrium states- that means
the variables TEMPERATURE,
VOLUME and PRESSURE are
the same and NOT changing in
time.
Boyle’s Law
• The volume of a gas is inversely
proportional to the pressure applied to
it when the temperature is kept
constant.
P is absolute pressureV (alpha) 1/P
not gauge
If pressure is doubled, Volume is halved
On a
graph…
PV=
Constant
P
V
Charles Law
• The volume of a given amount of gas is
directly proportional to the absolute
temperature when the pressure is kept
constant.
V (alpha) T
It is from this that we get
absolute zero
Consider the graph…
V
-273
V
0°
T °C
The Kelvin Scale also comes
from here
0 K = -273.15 °C
0°C= 273.15K
100°C= 373.15K
Any °C + 273.15 = Kelvin
T Kelvin
If you double the temperature of
10o C. How cold would it be?
Gay- Lussac’s Law
• At constant volume, the pressure of a
gas is directly proportional to the
absolute temperature
P (alpha) T
This is why aerosol cans blow up when
thrown into a fire- PLEASE don’t go home
and try this!
Conceptual Questions 13-9 Pg. 394
The Ideal Gas Law
• By combining the 3 gas laws we get PV
(alpha) T. However, the mass of a gas
present is also a factor. Therefore…
PV (alpha) mT
• This proportion can be made into an
equation by inserting a constant of
proportionality. This constant would
have a different value for every gas.
However, if we use a mole(mol) instead
of mass, we get a constant that can be
applied to all gasses
Mole…
• 1 mole = the number of grams of a
substance numerically equal to the
molecular mass of the substances
1 mol of H2 = 2g
1 mol of Ne = 20g
1 mol of CO2 = 44g 12 + (16x2)
Number of moles = n = mass(grams)/ molecular mass (g/mol)
Example:
• n in 132g of CO2 is…
n=
132g
g
44 /
=
mol
3 mol
The Ideal Gas Law is…
PV = nRT
• R is chemical gas constant
• R = 8.315 j/mol•k
• R = .0821 L •atm/ mol•k
• R = 1.99 calories/ mol•k
STP= standard temperature and pressure
T = 273K = 0°C
P = 1atm = 1.013 x 105 N/m2 = 101.3 kPa
Example…
Find the volume of 1mol of any gas
at STP
V = nRT/P
V= 1mol(8.315 j/mol•k)(273K)
1.013 x 105 n/m2
= 22.4 x 10-3 m3
1 Liter = 1000cm3 = 1 x 10-3 m3
1 mol of any gas = 22.4 Liters at STP
think of a cube 28cm per side (about 1ft3)
Example…
A flexible container of Oxygen (O2
molecular mass= 32ų) at STP has a
volume of 10m3. What is the mass of
gas enclosed?
1mol =22.4 x 10-3 m3
n=
10m3 of O2 corresponds to…
10m3
22.4 m3/mol
= 446mol
1 mol has a mass of .032kg (32g)
mass = 446mol x .032kg =
14.3kg
• In many cases we don’t need R or
n at all- If PTV change for a fixed
amount of gas…use this instead
P1V1
T1
=
P2V2
T2
Example…
A car tire is filled to a gauge pressure of
200kPa at 10°C. After driving a long
distance, the temperature within the tire
rises to 40°C. What is the pressure within
the tire?
Volume doesn’t change; V1 = V2
P1V1
T1
=
P2V2
T2
P2 =
P1 T2
T1
=
= 333kPa
absolute pressure
3.01 x105 Pa(313K)
283K
…
• Gauge Pressure= 232 kPa
– Still a 15% increase
• This is why we check air pressure
on “cold” tires
Ideal Gas Law
-In terms of number of molecules
• Amodeo Avogadro stated that equal volumes of
gas at the same pressure and temperature
contain equal numbers of molecules - Avogadro’s Hypothesis
• Avogadro’s Number= 6.02 x 1023 = NA
= the number of molecules in a mole
N = total number of molecules in a gas
n = number per mol
NA = Avogadro’s #
N = nNa
n = N/NA
- Further
explained on pg.
398
• Ideal Gas Law can also be
explained…
PV = nRT
PV = N/NA (RT)
PV = NkT
When K is Boltzman constant…
k = R/ NA
-23
K=1.38x10
J/K
Example…
Use NA to determine the mass of a
hydrogen atom.
•
Solution: 1mol of H (1.008ų) has a mass of
1.008g (.001008kg) and contains 6.02 x 1023
atoms. Thus one atom has < mass
m = M/NA
.001008kg
6.02 x 1023
= 1.67 x 10-27 kg
Example…
How many molecules are in one breath?
Estimate how many molecules you
breath in with < 1Liter breath of air
• Solution: one mol = Volume of 22.4L;
therefore 1L of air is 1/22.4 = .045mol
• Then 1L of air contains…
.045mol (6.02 x 1023 molecule/mol)
= 2.7 x 1023 molecules
Practice on pg. 414 - #’s 42, 43, 44
Kinetic Theory
4 Postulates Brief Overview
2 FORMULAS
1.
Kave= Average KE, the average KE of
molecules in a gas is directly proportional to
the absolute temperature
2.
Root • mean – square velocity
•
√v2
Vrms – take the square root of the mean of the
square of the velocity
Vrms = √v2
=
√3kT/m
Temperature related to KE of molecules
KE =
2
1/2mv
= 3/2kT
The average translational kinetic energy of
molecules in a gas is directly proportional to
the absolute temperature.
Example
• What is the rms speed of air
molecules (O2 & N2) at room
temperature (20°C)
m(O2) = 32(1.67 x10-27) = 5.3 x10-26 kg
m(N2) = 28 (1.67 x10-27) = 4.7 x10-26kg
rms O2 =
Vrms = √3kT/m
= √3(1.38 x 10-23)(293K)
5.3 x 10-26 kg
= 480m/s
rms N2=
√3(1.38 x 10-23)(293k)
4.7 x 10-26 kg
=510m/s
These Speeds are more than 1000mph
Distribution of Molecular
Speeds
• molecules in a gas are in random
motion, this means that many
molecules have speeds less than the
rms and others have greater speeds
• Maxwell Distribution of Speeds
– James clerk Maxwell 1859
• derived a graph showing the
distribution of gas molecular speeds…
Relative
number of
molecules
Vp = most
probable
speed
Vrms = √v2
Vp
Vrms
Speed, V
Real Gases and changes of
Phase
Vapor Pressure
• Evaporation…What is it?- in terms
of kinetic theory what is it?
• Various molecular speeds
– break away
• Does evaporation rate increase
with temperature?
– YES!
…
• This also explains evaporative
cooling
• Higher speed molecules leave- this
causes the average energy to
become less- resulting in lower
temperature
– i.e.- step out of shower, feel cold
– sweating
Condensation
• Gas to Liquid
Vacuum
Liquid
Liquid
Saturated Vapor Pressure
is the state of equilibrium
• We say the vapor is saturated
• What causes boiling?
– When saturated vapor pressure =
external pressure
• The Boiling point of a liquid
depends on external pressure
– can water boil at room temperature?
Pg. 415 #’s 57, 58, 60-62
• On Mt. Everest, water boils at 70°C
• In Mts. of Colorado, cooking times need to
be increased, pressure cookers cook at more
than 1ATM.
– are cooking timers faster?
• Relative Humidity- the part of air that is
water vapor. Expressed as a percent(%)
• Optimum humidity for people is 40-50%
– high humidity reduces evaporative cooling and
makes it tough for the body to regulate temp
– Low humidity, drying effect on skin &
membranes
Diffusion
• Diffusion is the uniform distribution of
fluids due to the random movement of
component molecules.
• Perfume, Smoke- eventually spreads
out over entire room, concentration
gets less as spreading occurs
• Normally- convection currents play a
large role in distributing molecules. But
w/ all variables controlled it still
happens- just very slowly
Diffusion in Biology
gasses in atmosphere
substances into and out of cells
Review Problems
pg. 411
5
pg. 412
9, 22, 26, 27
pg. 414
32, 42, 47
pg. 415
58