Gas Relationships
Gas Laws
Gas Variables
• Temperature (T) = avg Kinetic Energy
• Kelvin = C + 273
• Always use Kelvin (K)
• Volume (V) = length x width x height
• Pressure (P) = force/Volume
• Amount of Matter (n) = number of moles
Kinetic Theory of Matter
1. All Matter is made of tiny particles (Atoms or
Molecules)
2. The Particles are in constant Motion
3. The Particles undergo elastic collisions
a. No Energy is gained or lost
4. The Space between the particles is huge
compared to the particles.
a. The volume of the particles is basically zero.
5. There is no interaction between the particles.
States of Matter Kinetic Theory
• Solids:
– Particles are held in place and can’t move they just
vibrate.
• Liquids:
– Particles have limited movement they just flow past
each other.
• Gases:
– No attractive forces, gas particles are free to move
about without restriction.
Absolute Zero
• O Kelvin or -273.2 Celsius
• The point at which all motion stops, the
volume of all particles is zero.
• The Point at which the mass of all matter is
zero.
What is…….
• Volume: The amount of space an object takes up.
• Pressure: The force of the particles colliding with
the sides of a container.
– Higher Temperature and/or Smaller container more
Pressure.
• Temperature: A measurement of the Kinetic
Energy (speed) of the particles.
– Higher Temperature = Faster Particles
– Lower Temperature = Slower Particles
Ideal Gas
• Particles have no volume
• Particles are in:
• Constant, rapid, random motion
• Always move in straight lines
• No attractive or repulsive forces
• Temperature (K) proportional to Kinetic Energy
Standard Temp and Press
(STP)
• 273 K and 1 atm
• 273 K and 101.3 kPa
• 273 K and 760 mm Hg
Gas Laws
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Boyle’s Law
Charles’ Law
Gay-Lusac Law
Avagadros Law
Dalton’s Law
Combined Law
• Ideal Law
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PiVi = PfVf
Vi/Ti = Vf/Tf
Pi/Ti = Pf/Tf
Vi/ni = Vf/nf
Pt = P1 + P2 + ….
PiVi = PfVf
niTi nfTf
• PV = nRT
Pressure Versus Volume
P1V1 = P2V2
• Pressure Increases-Volume Decreases
• Pressure Decreases-Volume Increases
Pressure and Volume
• As a general rule, as Pressure goes up, Volume must go
down.
• If the same amount of material (moles) are placed in two
different containers, the smaller container will have a
greater pressure.
Volume Versus Temperature
V1/T1 = V2/T2
• Volume Increases-Temperature Increases
• Volume Decreases-Temperature Decreases
• Temp in Kelvin
Pressure Vs Temperature
P1/T1 = P2/T2
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Pressure Increases-Temperature Increases
Pressure Decreases-Temperature Decreases
Temp in Kelvin
Kelvin = C + 273
Avogadro’s Principle
• Equal volumes of gases under the same
conditions have:
• Equal number of moles
Avagadro’s Law
• As the VOLUME of a container increases,
the amount of MATTER (moles) must
increase proportionally, If Pressure and
Temperature are constant
• As the PRESSURE of a container increases,
the amount of MATTER (moles) must
increase proportionally, If Volume and
Temperature are constant
Pressure versus Material
• If different amounts of material are placed in the
same size containers, at the same temperature, the
more material the greater the pressure.
What is the Paradox?
• In looking at these Gas Laws a Paradox
emerges:
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As Pressure goes UP, Volume Goes DOWN
As Volume goes DOWN, Temperature goes DOWN
As Temperature goes DOWN, Pressure goes DOWN
How is that possible? Pressure went UP to start with?
Combined Gas Law
P1V1/n1T1 = P2V2/n2T2
• Real World: You change one variable ALL Change
• Temp must be in Kelvin
Partial Pressures
Pt = P1 + P2 + …..
• Total Pressure = Adding up the Parts
Ideal Gas Law
• PV = nRT
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P = Pressure
V = Volume
n = Number of Moles
T = Temperature (K)
R = Universal Gas Constant
• If P in atm, then R = 0.0821
• If P in kPa, then R = 8.314
• If P in mmHg, then R = 62.4
Boyle’s Law Example
• The volume of the lungs is measured by the volume of air
inhaled or exhaled. If the volume of the lungs is 2.400 L
during exhalation and the pressure is 101.70 KPa, and the
pressure during inhalation is 101.01 KPa, what is the
volume of the lungs during inhalation?
Charles Law Example
• A gas system has initial volume and
temperature of 3390mL and 159oC If the
volume changes to 6.79L, what will the
resultant temperature be in oC?
G-L Example
• Determine the pressure change when a
constant volume of gas at 1.00 atm is heated
from 20.0 °C to 30.0 °C.
Avagadro’s Law Example
• If a 500 mL glass beaker were determined
to contain 0.25 moles of He gas, at STP,
how many moles of the He gas would have
to be in a 1500 mL glass beaker?
Combined Gas Law
• A closed gas system initially has pressure
and temperature of 1.57atm and 568K with
the volume unknown. If the same closed
system has values of 2.00 atm, 6240mL and
1165 oC, what was the initial volume in
mL?
Dalton’s Law Example
• A 1.5 Liter container of gas was determined
to consist of Nitrogen Gas, Oxygen Gas and
Carbon Dioxide Gas. The pressure of
Nitrogen gas was determined to be 95.0
kPa, and Oxygen gas was determined to be
32.0 kPa, if the Total Pressure was 132.0
kPa, what is the Pressure of Carbon
Dioxide?
Ideal Gas Law
• How many moles of an ideal gas are in a
volume of 5530mL with a temperature of
34C and a pressure of 1.41atm ?
Phase Diagrams
• A Diagram that predicts the Phase
Terms for Phase Diagrams
• Solid Phase – Normally at Low Temps and High
Pressure
• Liquid Phase – Normally at either Low Temps or
High Pressure
• Gas Phase – Normally at High Temps and Low
Pressure
• Triple Point – A highly precise point in which a
substance exists in all three phases
• Critical Point – The Point at which the compound
falls apart.
Carbon Dioxide
Water Phase Diagram