Gases: Macroscopic Observation Gases fill the container into which they are placed Gases are compressible Gases mix completely and evenly when confined to the same container Gases have much lower densities than solids or liquids (g/L)
Gases: Molecular View Fill space evenly and completely: randomly, fast moving particles Low density and compressibility: large distances between particles Idealized assumptions –Gas particles have no volume –Gas particles have no interaction, so identity of gas particle is inconsequential
Gases: Historical View Molecular basis –Kinetic energy of molecules much greater than intermolecular forces Historical studies precede the atom –First we will look at non-molecular properties
Torricelli ( ) 1 atm = 760 torr
Pressure Velocity = distance / time (m/s) Acceleration = change in velocity / time (m/s 2 ) Force = mass x acceleration (kg m/s 2 = N) Pressure is the force of the gas pressing on a given area P = F/A (N/m 2 = Pa) –Ability to cut with a knife doesn’t depend simply on amount of force
Test the concept
Pressure Pressure = Force/Area Force = mass acceleration –Acceleration = g = pull of gravity –mass = V = h A where =density of Hg, h= height of Hg, A = cross-sectional area of column Force = h A g Pressure=( h A g)/A = h g P height and density If the density of mercury is 13.6g/ml, what is the height of a column of water under vacuum at atmospheric pressure? (76 cm =2.5 ft)
Experimenting with Gases As P (h) increases V decreases Robert Boyle ( )
Plot of Pressure vs Volume
Boyle’s Law V =k/P
Boyle’s Law P 1/V, when one sample is kept at constant temperature Acts as an “Ideal Gas”
Ideal Gas Pressure is inversely proportional to volume at a range of constant temperatures and sample sizes –k changes value at different temperatures, but is constant…well, almost constant Also notice that identity of gas matters little, and all approach same ideal (all data from 1 mol samples at 0 o C)
Ideal Gas Molecular perspective Assumptions –Molecules occupy no space –Molecules do not interact with each other Good assumptions?
Test your Understanding When you blow up your tire, you increase the pressure and volume simultaneously. According to Boyle, pressure and volume are inversely proportional. What gives?
Charles’s Law Jacque Charles ( ) Solo balloon flight At constant pressure, volume increases linearly with temperature Write Law
Charles’s Law (1783) V T –T in Kelvin –K = o C Absolute zero
Pressure and Temperature Draw Pressure as a function of Temperature at constant volume
Avagadro’s Law (1811) In light of Dalton’s Atomic Theory (1808) Based on Gay-Lussac –Law of combining volumes
Avogadro’s Law At constant P and T, the volume of a gas is proportional to the amount of gas molar volume V m = V/n V n Little known historical fact: Junior High nickname happened to be “The Mole”
Combined Ideal Gas Law
Problem Types If three variables known, calculate fourth Some conditions change—how does it affect others? Stoichiometry Determine a molar mass
Molar Volume Molar Volume = V m –Defined as the volume taken up per mole of gas V m at STP = L/mol Standard Pressure is 1 atm What is standard temperature in Celcius?
A flask that can withstand an internal pressure of 2500 torr, but no more, is filled with a gas at 21.0 o C and 758 torr and heated. At what temperature will it burst? Strategy/Sketch: Answer: 7.0 x 10 2 o C
Change in State of Ideal Gas If the stopcock is opened, the total pressure is atm. What was the original pressure of the red bulb? Strategy: Logic Check: 2.00L Ar at 360 torr 1.00 L Ar unknown pressure Assumption Check: According to ideal gas, would the total pressure change if the right bulb were filled with 1 L of carbon dioxide? Answer: 1.50 x 10 3 torr
Dalton’s Law of Partial Pressures An example of early utility of Dalton’s atomic theory
Collecting a Gas Over Water Gases collected by water displacement are a mixture of the gas and water vapor. All liquids have a certain amount in the gas phase. This is known as the Vapor Pressure of the liquid. It is temperature dependent. P T = P gas + P H 2 O
Experimental Determination of R NameMass Mg (g)Moles MgMoles H 2 T (Celsius)T (Kelvin)P T (mm Hg)P H2O (mm Hg)P H2 (mm Hg)P H2 (atm)V H2 (mL)V H2 (L)R (L-atm/mol-K) Joe Dirk Joe Dirk Joe Dirk Anne Marie, Emily Anthony Nick Jon Josh mike jeremy mike jeremy mike jeremy Marissa, Natalie, Katie Kim, Dave Marshall, Brian Alysha, Ashley Ryan, Valerie Toni, Bryson
Kinetic Molecular Theory Describes gases at the molecular level 1. Gases consist of small particles separated by large distances (assume no volume.) 2. Constant, random motion. Collisions with wall cause pressure 3. Gas particles have no interaction with one another (no intermolecular forces.) Collisions occur continuously and are elastic (no gain/loss of KE). 4. KE T, average kinetic energy only changes when temperature changes.
Ideal Gas Law from Theory: Qualitative
Is KMT consistent with Observation? Compressibility Boyle – P and V Charles – V and T, P and T Avogadro – V and n Dalton’s Partial Pressures
Ideal Gas Law from Theory: Quantitative
Derivation of KMT See handout
The meaning of Temperature
Velocity of particles in Gas
Maxwell-Boltzmann Distribution How does this function form the shape of the distribution? How does high mass shift curve? How does high T shift curve?
“Typical” Velocities at 298 K in m/s These gases are at the same temperature, so they have the same __________ but they have different average velocities because they have different _________________.
Three ways to describe a “typical velocity” Most probable Average RMS
Determination of RMS velocity
Root Mean Square Speed
Test your understanding
Diffusion Effusion Gas Motion on a Molecular Level
Diffusion and Effusion Diffusion – mixing due to motion Effusion – passage of a gas through a small hole into an evacuated space Ratio of effusion or diffusion rates depends on relative velocities of gases
Real Gases At 200K Nitrogen gas
Real Gases: Check Assumptions 1. Gases consist of small particles separated by large distances (assume no volume.) 2. Constant, random motion. Collisions with wall cause pressure 3. Gas particles have no interaction with one another (no intermolecular forces.) Collisions occur continuously and are elastic (no gain/loss of KE). 4. KE T, average kinetic energy only changes when temperature changes.
Assumptions that Fail Gases have no contribution to volume. Is this assumption equally valid at all states?
Assumptions that Fail Gases velocity is unaffected by attraction to other particles.
When Is a Gas Most Ideal?
Make a “Real Gas” Law Points to consider –Volume: must factor in _________and __________ of particles –Pressure: must factor in ___________ and ___________ of interaction
Van der Waals equation nonideal gas P + (V – nb) = nRT an 2 V2V2 () } corrected pressure } corrected volume Does this experimental data match theory?