Behavior of Gases 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 All Matter is made of tiny particles (Atoms or Molecules) The Particles are in constant Motion The Particles undergo elastic collisions No Energy is gained or lost

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 (or torr)

Gas Laws Boyle’s Law Charles’ Law Gay-Lussac 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 + …. 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 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 Dalton’s Law

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?

Gay-Lassac 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 ?

The Gas Laws

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 Phase diagram

Water Phase Diagram