the gas laws -_________ ________ provides a ______ that explains the properties of ________,...
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The Gas Laws
-_________ ________ provides a ______ that explains the properties of ________, _________, and ______ in terms of __________ that are always in ________ and the ________ that exist between them
kinetic theory modelsolids liquids
I. Kinetic Theory
gases particlesmotion forces
-actual gases don’t always obey, but ___________ the ____________made by the _________ ________
approximateassumptions kinetic
theory
A. Gas particles do not attract or repel eachother
B. Gas particles are much smaller than the distances between them
C. Gas particles are in constant, random motion
D. No energy is lost in the collisions of gas particles
E. All gases have same average kinetic energy at same temperature
The Gas Laws
II. Boyle’s Law -the _______ of a gas _________ _________ with the _________, providing the ___________ is held ________
Robert Boyle (1627-1691)
volume varies inverselypressure temperatureconstant
P1V1 = P2V2 orP1
P2
___=
V2
V1
___
If a sample of Argon gas occupies a volume of 10.0 liters at a pressure of200 kilopascals, at what pressure would the same sample of gas occupy5.0 liters, if the temperature remains constant?
P1
P2
___=
V2
V1
___
200 kPa
P2
______ =5.0 L
10.0 L____
P2 = 400 kPa
The Gas Laws
II. Boyle’s Law
Boyle’s Vacuum Chamber,Designed by Robert Hooke
If a sample of Carbon dioxide gas occupies a volume of 35.0 liters at apressure of 1.10 atmospheres, what volume would the same sampleof gas occupy at 1.25 atmospheres, if the temperature remains constant?
P1
P2
___=
V2
V1
___
1.10 atm
1.25 atm_______ =
V2
35.0 L_____
V2 = 30.8 L
The Gas Laws
III. Charles’s Law -the _______ of a gas _________ _________ with the ___________, providing the _________ is held ________
Jacques Charles (1746-1823)
volume varies directlytemperature pressureconstant
V1T2 = V2T1 orV1
V2
___=
T1
T2
___
If a sample of Chlorine gas occupies a volume of 250 milliliters at atemperature of 22°C, what volume would the same sample of gas occupy at -22°C, if the pressure remains constant?
V1
V2
___=
T1
T2
___
250 mL
V2
______ =22°C
-22°C____
V2 = -250 mL?A negative volume?
We need a temperature scale with no zero, and nonegative values!
K = °C + 273250 mL
V2
______ =295 K
251 K_____
V2 = 213 mL
The Gas Laws
III. Charles’s Law -_________ _____ is the _______ possible theoretical temperature, equal to _________, and is the ___________ at which the ________ of a sample of gas is _____, and all ________, __________ movement of particles ________
absolute zero lowest-273.15°Cvolumetemperature
zero randomBrownian ceases
-the coldest _______ temperature is _______, or _________, the temperature of ______ _______
actual 4.22 K-268.78°C liquid Helium
William Thomson (Lord Kelvin)(1824-1907)
The Gas Laws
III. Charles’s Law
If a sample of methane gas occupies a volume of 14.75 liters at atemperature of 68°F, at what temperature, in °F, would the same sample of gas occupy 16.00 liters, if the pressure remains constant?
V1
V2
___=
T1
T2
___
14.75 L
16.00 L______ =
293 K
T2
_____
T2 = 318 K
°F +9/5
Charles’s Hydrogen-filledballoon over Paris, 1783
K = °C + 273
= °C 32
T2 = 113°F
The Gas Laws
IV. Gay-Lussac’s Law -the _______ of a gas _________ _________ with the ___________, providing the _________ is held ________
Joseph Gay-Lussac (1778-1850)
pressure varies directlytemperature
volume constant
P1T2 = P2T1 orP1
P2
___=
T1
T2
___
If the pressure in a propane tank is 965 mm Hg at a temperature of 25°C, what would the pressure in the tank be at 50°C, if the volume remains constant?
P1
P2
___=
T1
T2
___
K = °C + 273
965 mm Hg
P2
_________ =298 K
323 K_____
P2 = 1040 mm Hg
The Gas Laws
IV. Gay-Lussac’s Law
If the air pressure in an autoclave is 833 torr at a temperature of 212°F, at what temperature, in °F, would the air pressure be 900 torr, if the volume remains constant?
P1
P2
___=
T1
T2
___
833 torr
900 torr______ =
373 K
T2
_____
T2 = 403 K
°F +9/5
Gay-Lussac and Jean-BaptisteBiot in Hydrogen balloon, 1804
K = °C + 273
= °C 32
T2 = 266°F
The Gas Laws
V. Combined Gas Law -the _______ of a gas is _________ proportional to ________ and directly proportional to ___________, and ________ is __________ proportional to ____________
pressure inverselyvolume
directlytemperature
volume
P1V1 =P2V2_____
T1 T2
_____
If the volume of a sample of Hydrogen sulfide gas is 2.00 liters at a pressure of 110 kilopascals and a temperature of 30.0°C, what is the volume of the same sample of Hydrogen sulfide, in liters, at a temperature of 80.0°C and a pressure of 440 kilopascals?
K = °C + 273
(2.00 L)303.0 K
_____________ =353.0 K
(440 kPa)__________
V2 = 0.582 L
temperature
P1V1 =P2V2_____
T1 T2
_____ (110 kPa) V2
The Gas Laws
V. Combined Gas Law
If a Helium-filled balloon at sea level has a volume of 2.1 liters at a pressure of 0.998 atmospheres and a temperature of 36°C, and it is released and rises to an elevation at which the temperature is 28°C and the pressure is 0.900 atmospheres, what will be the new volume of the balloon?
K = °C + 273
(2.1 L)
309 K_____________ =
301 K
(0.900 atm)__________
V2 = 2.3 L
P1V1 =P2V2_____
T1 T2
_____ (0.998 atm) V2
The Gas Laws
VI. Avogadro’s Principle -______ ________ of gases at the same ____________ and _________ contain ______ numbers of ________
equal volumestemperature
particlespressure
equal
mole-one ______ of gas contains __________ particles and occupies _______ at _________ temperature and pressure, which is ______ and ________
6.02 x 1023
22.4 Lstandard
0.00°C 1.00 atm
Amadeo Avogadro (1776-1856)
How many molecules in 3.73 liters of ozone at STP?
3.73 L O3 x 1 mole O3___________22.4 L O3
= 1.00 x 1023 molecules O3
conversion factor
x 6.02 x 1023 molecules O3_________________1 mole O3
The Gas Laws
VI. Avogadro’s Principle
What is the volume, in liters, of 0.881 moles of Fluorine gas at STP?
0.881 mole F2 x 22.4 L F2________1 mole F2
= 19.7 L F2
How many moles of Nitrogen gas are in 2.00 liters at STP?
2.00 L N2 x 1 mole N2________22.4 L N2
= 0.0893 moles N2
What is the volume, in liters, of 5.0 kilograms of methane at STP?
5.0 kg CH4 x 1000 grams CH4____________1 kg CH4
= 7.0 x 103 L CH4
conversion factor
x 1 mole CH4______________16.043 grams CH4
x 22.4 L CH4_________1 mole CH4
What mass, in grams, of Nitrogen dioxide occupies 15.50 liters at STP?
15.50 L NO2 x 1 mole NO2__________22.4 L NO2
= 31.8 g NO2x 46.005 grams NO2______________1 mole NO2