Gas Laws Solid -- Liquid -- Gas

Gases: low densities easily compressed larger expansion & contraction when T changed

THEORY

1. Gases move randomly, no attractive forces, mix quickly together

2. Gases occupy less vol. than the vol. a gas occupies; more vol. between gases than gases themselves

3. K.E. of gas is proportional to K temp.; higher temp results in more K.E. results increase velocity

4. Total K.E. of particles is constant; more forceful collisions results in higher pressure

Pressure:atm: atmospheresmm Hg or torr

Temperature: K Volume: L1 mol of gas = 22.4 L

LABELS

1 atm =760 mm Hg1 mm Hg = 1 torr STP:

standard pressure & temp.273.15 K (0oC) -- 1 atm (760 mm Hg)

P1; V1; T1; n1 P2; V2; T2; n2

initial, starting, values

final, ending, values

BOYLE’S LAW

P V: V inversely proportional to P

P1V1 = P2V2

changes in P & V @ constant T

V

P

CHARLE’S LAW

T V : V directly proportional to T

2

2

1

1

T

V

T

V

VT

changes in V & T @ constant P

GAY-LUSSAC

T P : P directly proportional to T

2

2

1

1

T

P

T

P

PT

changes in T & P @ constant V

COMBINE GAS LAW

2

22

1

11

T

VP

T

VP

changes in T, P, & V nothing held constant

IDEAL GAS LAW

PV = nRT

n: amt, # of moles of gasR: gas constant

Kmol

atmL 0.0821

Kmol

Hg mmL 62.4

Vol: LTemp: K

AVOGADRO’S LAW -- VOL & MOLAR AMTS

vol. directly proportional to moles (molar amt)

Vmoles

2 diff. gases @ same T & P (STP)

2

2

1

1

n

V

n

V

DALTON’S LAW -- PARTIAL PRESSURE

Ptotal = P1 + P2 +P3 + Pnsum of all partial pressures contributed from eachdiff. gas is equal to the Total Pressure

Each partial pressure: % gas * P = partial pressure

PROBLEMS

BOYLE’S The volume of a balloon is 3.50 L at 1.00 atm.What is the pressure if the balloon is compressed to 2.00 L?

P1V1 = P2V2P1 = P2 =V1 = V2 =

1 atm X3.50 L 2.00 L

atm 1.75 L 00.2

L) atm)(3.50 (1

V

VP P

2

112

CHARLE’S A balloon has a volume of 43.0 L at 20 oC.What is its volume at -5 oC?

2

2

1

1

T

V

T

V V1 = V2 =

T1 = T2 =

43.0 L X20 + 273.15 -5 + 273.15293.15 268.15

L 39.3 K 293.15

K) L)(268.15 (43.0

T

TV V

1

212

GAY-LUSSAC An aerosol can has an internal pressure of 3.75 atm at 25 oC.What temperature is required to raise the pressure to 16.6 atm?

2

2

1

1

T

P

T

P P1 = P2 =

T1 = T2 =

3.75 atm 16.6 atm25 + 273.15 X298.15

K 1320 atm 3.75

atm) K)(16.6 (298.15

P

PT T

1

212

COMBINE GAS LAW Scuba divers carry compressed-air tank which hold 8.00 Lat a pressure of 140 atm at 20 oC. What is the volume of air in the tank at 0 oC and 1.00 atm?STP conditions

2

22

1

11

T

VP

T

VP

P1 = P2 =V1 = V2 =T1 = T2 =

140 atm 1.00 atm8.00 L X20 + 273.15 0 + 273.15293.15 273.15

L 1040 K) 5atm)(293.1 (1.00

K) L)(273.15 atm)(8.00 (140

TP

TVP V

12

2112

IDEAL GAS LAW

PV = nRT

How many moles of gas will occupy a volumeof 0.55 L at 347 K and 2.50 atm?

P = n =V = T= R =

2.50 atm X0.55 L 347 K

Kmol

atmL 0.0821

mol 0.048 K) )(347

KmolatmL 0.0821

(

L) atm)(0.55 (2.50

RT

PV n

AVOGADRO’S LAW How many moles of methane gas, CH4, are in a tank thatholds 1.00*105 L at STP? How many grams of CH4?

2

2

1

1

n

V

n

V

V1 = V2 = n1 = n2 =

22.4 L 1*105 L 1 mol X

mols 4464 L 22.4

L) 10*mol)(1 (1

V

Vn n

5

1

212

1 mol CH4 = 16.0 g

44 CH g 10*7.14

mol 1

g 16.0

1

mols 4464

DALTON’S PARTIAL PRESSURE

Ptotal = P1 + P2 + P3

A closed system contain 3 diff gases (15% CH4, 45% CO2, H2). The totalpressure is 6.42 atm. What is the partial pressure each gas is contributing?

CH4 = .15 * 6.42 =CO2 = .45 * 6.42 = H2 =

H2 = 100% - 15% - 45% = 40%

.40 * 6.42 =

0.963 atm2.89 atm2.57 atm

Convert total pressure to mm Hg or torr

1 atm = 760 mm Hg

Hg mm 4879 atm 1

Hg mm 760

1

atm 42.6

INTERMOLECULAR FORCES

Forces that act between diff. molecules

Gases: <<< forces, act independently of each other

Liquids/Solids: >>>> Forces

KEY PTS.

Stronger the Force -------- more difficult to separate atoms/molecules

---- higher melting/boiling pts of subst.

3 MAJOR FORCES

Dipole-DipoleDipole-Dipole London DispersionLondon Dispersion

Polar Cov. Bonds “net polarity”

Weak Force

+/- ends of molecules align together

Dipole-Dipole London Dispersion Hydrogen Bonding

All molecules; behavior due to e- movement w/i subst.

Nonpolar molecules form temporary Polarity

Weak Force; as mole.wt.

Surface Area: > S.A. ---- > Force stronger the molecule held together

Hydrogen BondingHydrogen Bonding

Strong bond Force

H bonded to an O, N, or F of one molecule; that H will be attracted to unsharede- pair of O, N, or F of another molecule

O

H H

....O

HH

.. ..N

F....

..

..

Cl.. ....H

H F.. ....

LIQUIDLIQUID

Energetic molecules of liquid in motion, near surface molecules escape to become vapor (gas?)

Closed System: these molecules create vapor pressure according to Dalton’s Law

V.P.: depends on Temp & subst. of liquid

pt boiling P. atm

SOLIDSSOLIDS

Crystalline: ordered arrangement of particles in solid

Amphorous: random arrangement

IONIC: composed of ions BaCl2 (s) --- Ba+2 (s) + 2 Cl-1 (s)

MOLECULAR: held together by intermolecular Forces

COVALENT NETWORKING: linked by covalent bonds

METALLIC: metal ions linked by surrounding “e- field”

CHANGE OF STATE solid – liquid - gas

Heat of Fusion: E required to complete the melting of a subst.

Heat of Vaporization: E required to complete liquid to vapor (gas) phase

PHASE CHANGE ????