Gas RelationshipsGas 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

• Boyle’s Law

• Charles’ Law

• Gay-Lusac Law

• Avagadros Law

• Dalton’s Law

• Combined Law

• Ideal Law

• 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

• 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:

• 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 LawP1V1/n1T1 = P2V2/n2T2

• Real World: You change one variable - ALL Change

• Temp must be in Kelvin

Partial PressuresPt = P1 + P2 + …..

• Total Pressure = Adding up the Parts

Ideal Gas Law

• PV = nRT– 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