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

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…

Thermal EquilibriumZeroth Law

•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

alpha= coefficient of linear expansionLo = Original Length

To= Initial temp

L= Length after heating/coolingT= final temp

ΔT= T-To ; if temp is negative this means length shortens

ΔL = alpha Lo ΔT L = Lo (1+ alpha

ΔT) ΔT = ΔL/ alpha Lo

Loat To

ΔL

at T

L

Volume Expansion

*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

ΔV = β Vo ΔT

Anomaly of Water

13-5Pg. 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.

V (alpha) 1/P P is absolute pressure- not gauge

If pressure is doubled, Volume is halved

On a graph

…P

V

PV= Constant

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…

-273 0° T °C

V V

T KelvinThe Kelvin Scale also

comes from here0 K = -273.15 °C

0°C= 273.15K

100°C= 373.15K

Any °C + 273.15 = 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) TThis 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…

• 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

PV (alpha) mT

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 = 20g1 mol of CO2 = 44g

12 + (16x2)

Number of moles = n = mass(grams)/ molecular mass (g/mol)

Example:

•n in 132g of CO2 is…

n132g

44g/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 STPV = 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

10m3 of O2 corresponds to…10m3

22.4 m3/mol

n =

= 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

=3.01 x105 Pa(313K)

283K=

= 333kPa

absolute pressure

…• Gauge Pressure= 232 kPa

– Still a 15% increase• This is why we check air

pressure on “cold” tires

HW: 28, 30, HW: 28, 30, 34, 36, 38, 40

34, 36, 38, 40

HW: 28, 30, HW: 28, 30, 34, 36, 38, 40

34, 36, 38, 40

Ideal Gas Law

• 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

-In terms of number of molecules

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 = N/NA (RT)PV = nRT

PV = NkTWhen K is Boltzman constant…

k = R/ NA

K=1.38x10-23 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 moleculesPractice on pg. 414 - #’s 42, 43, 44

Kinetic Theory

4 Postulates Brief Overview2 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 velocityVrms =

√v2

= √3kT/m

Temperature related to KE of molecules

KE = 1/2mv2 = 3/2kTThe 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…

Vp Vrms

Speed, V

Rela

tive

nu

mb

er

of

mole

cu

les

Vp = most probable speed

Vrms = √v2

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

Liquid Liquid

Vacuum

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?

• 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

Pg. 415 #’s 57, 58, 60-62

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 atmospheresubstances into and out of cells

Review Problems

pg. 411 5

pg. 412 9, 22, 26, 27

pg. 414 32, 42, 47

pg. 415 58

Review Problems

pg. 411 5

pg. 412 9, 22, 26, 27

pg. 414 32, 42, 47

pg. 415 58