gas laws nm standards students know how to apply the gas laws to relations between the pressure,...
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Gas LawsGas Laws
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NM StandardsNM Standards
Students know how to apply the gas laws to relations between the pressure, temperature, and volume of any amount of an ideal gas or any mixture of ideal gases.
Students know how to apply the gas laws to relations between the pressure, temperature, and volume of any amount of an ideal gas or any mixture of ideal gases.
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Ideal Ideal GasesGasesIdeal gases are imaginary gases that perfectly fit all of the assumptions of the kinetic molecular theory.
Gases consist of tiny particles that are far apart relative to their size.
Collisions between gas particles and between particles and the walls of the container are elastic collisions
No kinetic energy is lost in elastic collisions
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Ideal Gases Ideal Gases (continued)
Gas particles are in constant, rapid motion. They therefore possess kinetic energy, the energy of motion
There are no forces of attraction between gas particles
The average kinetic energy of gas particles depends on temperature, not on the identity of the particle.
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Real Gases Do Not Behave Real Gases Do Not Behave IdeallyIdeally
Real gases DO experience inter-molecular attractions
Real gases DO have volume
Real gases DO NOT have elastic collisions
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Deviations from Ideal Deviations from Ideal BehaviorBehavior
Likely to behave Likely to behave nearly ideallynearly ideally
Gases at high temperature and
low pressure
Small non-polar gas molecules
Likely not to Likely not to behave ideallybehave ideally
Gases at low temperature and
high pressure
Large, polar gas molecules
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Boyle’s LawBoyle’s Law
Pressure is inversely proportional to volume when temperature is held constant.
2211 VPVP
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A Graph of Boyle’s A Graph of Boyle’s LawLaw
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Charles’s LawCharles’s LawThe volume of a gas is directly proportional to temperature, and extrapolates to zero at zero Kelvin.
(P = constant)
Temperature MUST be in KELVINS!
2
2
1
1
T
V
T
V
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A Graph of Charles’ A Graph of Charles’ LawLaw
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Gay Lussac’s LawGay Lussac’s LawThe pressure and temperature of a gas aredirectly related, provided that the volume remains constant.
Temperature MUST be in KELVINS!
2
2
1
1
T
P
T
P
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Gay - Lussacs
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A Graph of Gay-Lussac’s A Graph of Gay-Lussac’s LawLaw
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The Combined Gas LawThe Combined Gas LawThe combined gas law expresses the relationship between pressure, volume and temperature of a fixed amount of gas.
2
22
1
11
T
VP
T
VP
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Combined Gas Law
• The good news is that you don’t have to remember all three gas laws! Since they are all related to each other, we can combine them into a single equation. BE SURE YOU KNOW THIS EQUATION!
P1 V1 P2 V2
= T1 T2
No, it’s not related to R2D2
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Combined Gas Law
If you should only need one of the other gas laws, you can cover up the item that is constant and you will get that gas law!
=
P1 V1
T1
P2 V2
T2
Boyle’s Law
Charles’ Law
Gay-Lussac’s Law
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Combined Gas Law Problem
A sample of helium gas has a volume of 0.180 L, a pressure of 0.800 atm and a temperature of 29°C. What is the new temperature(°C) of the gas at a volume of 90.0 mL and a pressure of 3.20 atm?
Set up Data Table
P1 = 0.800 atm V1 = 180 mL T1 = 302 K
P2 = 3.20 atm V2= 90 mL T2 = ??
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CalculationP1 = 0.800 atm V1 = 180 mL T1 =
302 KP2 = 3.20 atm V2= 90 mL T2 = ??
P1 V1 P2 V2
= P1 V1 T2 = P2 V2 T1
T1 T2
T2 = P2 V2 T1
P1 V1T2 = 3.20 atm x 90.0 mL x 302 K
0.800 atm x 180.0 mL
T2 = 604 K - 273 = 331 °C
= 604 K
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Learning Check
A gas has a volume of 675 mL at 35°C and 0.850 atm pressure. What is the temperature in °C when the gas has a volume of 0.315 L and a pressure of 802 mm Hg?
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Solution
T1 = 308 K T2 = ?
V1 = 675 mL V2 = 0.315 L = 315
mL
P1 = 0.850 atm P2 = 802 mm Hg = 646 mm Hg
T2 = 308 K x 802 mm Hg x 315 mL
646 mm Hg 675 mL= 178 K - 273 = - 95°C
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One More Practice Problem
A balloon has a volume of 785 mL on a fall day when the temperature is 21°C. In the winter, the gas cools to 0°C. What is the new volume of the balloon?
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SolutionComplete the following setup:Initial conditions Final conditionsV1 = 785 mL V2 = ?
T1 = 21°C = 294 K T2 = 0°C = 273 K
Since P is constant, P cancels out of the equation. V1 V2 V1 T2 = V1T2 = T1V2 = V2 T1 T2 T1
= 728 mLCheck your answer: If temperature decreases,
V should decrease.
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And now, we pause for this commercial message from STP
OK, so it’s really not THIS kind of STP…
STP in chemistry stands for Standard Temperature and PressureStandard Pressure =
1 atm (or an equivalent) Sea Level
Standard Temperature = 0 deg C (273 K) freezing temp of water
STP allows us to compare amounts of gases between different pressures and temperatures
STP allows us to compare amounts of gases between different pressures and temperatures
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Try This One
A sample of neon gas used in a neon sign has a volume of 15 L at STP. What is the volume (L) of the neon gas at 2.0 atm and –25°C?
P1 = 1.0 atm V1 = 15 L T1 = 273 K
P2 = 2.0 atm V2 = ?? T2 = 248 K
V2 = 15 L x 1.0 atm x 248 K = 6.8 L
2.0 atm 273 K
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Avogadro’s Avogadro’s HypothesisHypothesis
Equal volumes of gases at the Equal volumes of gases at the same T and P have the same same T and P have the same number of molecules.number of molecules.
V = n (RT/P) = knV = n (RT/P) = kn
V and n are directly related.V and n are directly related.
twice as many twice as many moleculesmolecules
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Avogadro’s Hypothesis Avogadro’s Hypothesis and Kinetic Molecular and Kinetic Molecular
TheoryTheory
Avogadro’s Hypothesis Avogadro’s Hypothesis and Kinetic Molecular and Kinetic Molecular
TheoryTheory
P proportional to nP proportional to n
The gases in this The gases in this experiment are all experiment are all measured at the measured at the same T and V.same T and V.
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STP and Volume
• AT STP one mole of gas has a volume of 22.4 Liters
• Standard temperature: 0°C = 273.15 K
• Standard pressure = 1 atmosphere = 760 mmHg = 101.3 kPa
• Standard volume of 1 mole of an ideal gas at STP: 22.4 liters
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Dalton’s Law of Partial Dalton’s Law of Partial PressuresPressures
For a mixture of gases in a container,
PPTotalTotal = = PP11 + + PP22 + + PP33 + . . . + . . .
This is particularly useful in calculating the pressure of gases collected over water.
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• Practice
• http://www.chm.davidson.edu/vce/gaslaws/GasConstant.html
• http://www.chm.davidson.edu/vce/gaslaws/GasConstant.html