1 Gases Key Points States or Phases of Matter –Gas Compressible, variable volume and pressure Expands into available space Rapid mixing No collective structure … except the container Subject to condensation into liquid –Liquid Incompressible Flows under pressure Conforms to container Slow mixing (relative to gases) Cohesive collective structure subject to evaporation into gas

Overview More States of Matter –Solid Retains shape, not container confined Subject to cleavage, breakage, bending More structure, higher degree of order –Crystalline shapes are common –“Lattice Energy” holds things together No (or slow) mixing, diffusion limited –Plasma … the “4 th state of matter” Not part of everyday experience Ionized gases, charged particles, subatomic species –Interior of the Sun, “Solar Wind” –Florescent or Neon gas electrical discharge –Arc Welding, “sputtering” of metals in vacuum –Plasma metal cutters, 30K degrees

4 Gases in the minority of elements Less than 10% of 116 elements are gases –Six of these are non-reactive “noble gases” He, Ne, Ar, Kr, Xe, Rn –Five remaining gases H 2, N 2, O 2, Cl 2, F 2 All are diatomic, yielding octets of 8 electrons All are reactive, N 2 and O 2 in atmosphere All have some biologic role

The Gaseous Elements 5

6 Atmospheric Gases –Atmosphere is homogeneous mixture of gases Nitrogen 76% - “inert” for most uses, but reactive –Numerous oxides “NO X “ components of “smog” –Anesthetics, nitrate fertilizer, nitrite preservatives Oxygen 21% - essential for animal life –Product of photosynthesis –Oxidizes food for chemical energy, kinetic energy, and heat Argon 0.93% - most abundant “noble” or inert gas –Used in light bulbs to prevent darkening by evaporating W –Used in gas discharge lamps (blue), lasers, protective package Carbon Dioxide 0.037% - breathing, fermentation, combustion –Required by plants to provide cellulose, sugars, and Oxygen –Basis of carbonated drinks … soda, beer, champagne –Most life on earth involves both CO 2 and O 2 Methane % - natural gas, animal waste –Very common natural product »“swamp gas”, land fill decomposition, animal flatulation –Lighter than air, very little stays near the surface

Gas Behavior Gases –Intertwined relationships Compressibility relates volume & pressure Amount of material controls volume of that material Volume changes with Temperature –Basis of “heat engines” Subject to phase changes –Water vapor into liquid water or ice –“Liquid Air”, sublimation of “dry ice” –Models needed to explain & predict behavior Started with simple “2 at a time” relationships –P & V, moles & V, V & Temp, etc Evolved to “Ideal Gas Law”, PV=nRT –Includes all the variables in one equation –Reduces to named gas laws with omitted variables

9 Gases & Gas Laws Gas laws with 2 variables –Boyle’s law, Charles’ law, Avagadro’s Law Combined gas law with 3 variables –PV/T=constant Ideal Gas Law with all 4 variables –PV=nRT Applications –Density and Lift –Air Bags, etc.

Gas Pressure Pressure Units of Measure –Air pressure is familiar concept High altitude, auto tires, skin diving, sailboats Pressure defined as force per unit area –Originally 1 Atmosphere = 760 mm Hg (sea level) –1 Atmosphere = 14.4 psi (Imperial system) –1 atmosphere ≡ 101,325 Pascal (mks) –MKS units often inconvenient, leading to new units 100,000 Pa = 1 Bar (not tied to atmosphere) 1mm Hg = 1 Torr (1/760 = 0.13% of atmospheric pressure)

Units of Pressure

Mercury Barometer Vacuum at top of glass –Zero pressure at glass top Mercury rises in tube –Air pressure pushes Hg up –Mercury height = pressure –760mm Hg ≡ 1 atmosphere –32 feet H 2 O ≈ 1 atmosphere Blowing versus Sucking –Which is stronger? –Establishes pump designs

14 Two Variable Gas Laws Boyle’s Law –Pressure and Volume are inversely related –Pressure * Volume = constant assumes constant amount of material & temp If pressure goes up, volume goes down.. & vice versa Charles’ Law –Adds temperature as a new variable –Volume proportion al to temperature –Volume = constant * Temperature (or V/T=constant) Assumes constant amount of material and pressure If temperature goes up, so does volume Avagadro’s Law –Adds amount of material as a new variable –Volume of gas depends on moles Volume = constant * Moles (or V/M=constant) If moles goes up, so does volume Each mole of gas occupies approx 22.4 liters

Boyle’s Law Pressure and Volume inversely related see NASA animation related to this image

Gas Law Animations NASA site for gas law animations 12/airplane/Animation/gaslab/gastil.html –“stop” prior animation, lower left red box in the animation itself –Select “New Case”, left-hand column –Freeze 2 of 4 variables –Select one of 2 cases to animate

Alternative Boyle’s Formulas P 1 V 1 = P 2 V 2 = constant –Generally used relationship, most often quoted V 2 = V 1 *(P 1 /P 2 ) solving for Volume –This rearrangement has Volumes directly related V = V*(ratio) –Note that Pressure dimensions cancel (psi, pascal, etc.) –Note that volumes must have same dimensions (liter, quart, mL) –Assumes NO CHANGE in temperature or amount of material P 2 = P 1 *(V 1 */V 2 ) solving for Pressure –Same idea as for volume, cancellation of units –Can use arbitrary units of measure, but must be consistent 17

18 Boyle’s Law Calculation Example Bag of potato chips San Jose  Tahoe –What is the volume at Tahoe pressure? P 1 = 1.0 atmosphere (14.7psi) in San Jose V 1 = 1.0 liter air volume in San Jose P 2 = 0.75 atmosphere at Lake Tahoe (6225 feet) V 2 = ? P 1 V 1 = P 2 V 2, or V 2 = V 1 *(P 1 /P 2 ) –V 2 = 1 Liter * (1 atmos / 0.75 atmos) –V2 = 1/0.75 = 1.3 liters volume at Tahoe Note that pressure units vanish, anything consistent is OK (atm, psi, pascals, etc.). Same for volume

19 Pressure vs Altitude 6225 ft at Lake Tahoe, ≈ 0.75 atmosphere

20 Temperature Change, Charles’ Law Charles’ Law: V 1 / T 1 = V 2 / T 2 –Adds temperature as a variable –Volume proportional to temperature –Volume / Temperature = constant Assumes constant amount of material & pressure If temperature goes up, so does volume –NASA graphic shows 4 liters at 300 degrees Also shows 3 liters at 225 degrees 4 / 300 = / 225 = Both divisions yield same value = a constant

Charles’ Law Volume of gas proportional to absolute temperature See NASA animation of slide below

What Temperature Scale to use? Cannot use arbitrary scales –2 o F is NOT “twice as hot” as 1 o F, equally cold –0 o C =melting ice, not absence of temperature –We use ratios in gas law calculations Temp. Ratio 1 o C/0 o C = ∞ … not very useful What’s needed –A scale with truly proportional temperatures Where 100 o is actually “Twice as Hot” as 50 o –A scale which goes to true (absolute) zero No negative temperatures

Traditional Temperature Scales

Proportional P vs T with scale through zero Proportional scale defined using “Kelvin” degrees

Kelvin Scale is simple idea Absolute zero is absence of all motion –Cannot go any lower than 0 o K –Close to zero is boiling point of helium at 4 o K Kelvin degree “size” same as Centigrade –Zero Kelvin becomes -273 o C –Conversion is o K = o C+273 –Going the other way o K-273 = o C Some die-hards like Fahrenheit degrees –Conversion is “Rankine” scale o R = o F+492 –Could be handy if you have lots of Fahrenheit data

27 Charles’ Law Calculation Example Balloon from ski area into heated lodge V/T = constant V 1 /T 1 = V 2 /T 2 = constant –V 1 = 1 liter –T 1 = -10 o C at ski lift ( =263 o K) –T 2 = 25 o C in lodge ( = 298 o K) –V 2 = V 1 *(T 2 /T 1 ) = 1 Liter* (298/263) –V 2 = 1.13 Liters (constant pressure)

28 Gay-Lussac Law Same as Charles’ law, substitute Pressure P = k*T P & T proportional, k=constant P 1 /T 1 = P 2 /T 2 assumes constant volume P 2 /P 1 = T 2 /T 1 P’s and T’s together –Useful because easy to see that units cancel P 1 *T 2 = P 2 *T 1 avoids division in formula

An example What is pressure inside a tennis ball going from warm room to winter tennis court P 1 /T 1 = P 2 /T 2, P 2 =P 1 *(T 2 /T 1 ) –P 1 = 2 atmospheres inside ball (assumed) –no change to tennis ball volume –T 1 = 298 o K (25 o C), T 2 = 263 o K (-10 o C) P 2 =P 1 *(T 2 /T 1 ) –P 2 = 2atm*(263/298) = 2*0.88 atm –P 2 = 1.76 atmospheres (less bounce) 29

Combination 3-Variable Gas Law Can combine Charles’ and Boyle’s Laws –Boyle’s Law P 1 V 1 = P 2 V 2 (constant temperature & mass) –Charle’s Law V / T = constant –Algebraic substitution & yields P*V = constant, also V/T = constant –Both are related to same variables, so P 1 V 1 / T 1 = P 2 V 2 / T 2 Can calculate any quantity if other 5 are known

Formula Variations key point that start = end metric, other ratios cancel P 1 V 1 / T 1 = P 2 V 2 / T 2 P 2 = P 1 (V 1 /V 2 )*(T 2 / T 1 ) –Pressure change given by ∆T and inverse of ∆V V 2 = V 1 (P 1 /P 2 )*(T 2 / T 1 ) –Volume change given by ∆T and inverse of ∆P T 2 = T 1 (P 2 /P 1 )*(V 2 /V 1 ) –Temperature change given by ∆P and ∆V 31

Combined Law Calculation Automobile driven to Death Valley –Temperature changed 70 o F  120 o F 70 o F  21 o C  294 o K 120 o F  49 o C  322 o K –Tire volume changed 20  21 liters –Tire pressure 30psi in S.Jose  ? In Death V. P 2 = P 1 (V 1 /V 2 )*(T 2 / T 1 ) P 2 = 30 ( 20/21)*(322 / 294) P 2 = 31.3 psi 32

33 What about mass change? Avogadro’s Law –Adds amount of material as a new variable Intuitive that volume related to material amount –Volume of gas depends on moles Volume / Moles = constant Or …. Volume = constant * moles If moles goes up, so does volume Each mole of gas occupies approx 22.4 liters

Avagadro’s Gas Law Change of mass is added variable, see animation more material  more pressure and/or more volume

35 Gas Law Summary –Four variables involved for Gases Pressure, can be “atmospheres” or Pascals –For ratios involving 2 pressures, dimensions cancel Volume, can be liters or cubic meters –For ratios involving 2 volumes, dimensions cancel Temperature, always in Kelvin, o C+273= o K –Kelvin is linear, “0” is really zero (not so for o C, o F) Mass, usually in moles –For ratios involving 2 masses, dimensions cancel

37 Gas Law Summary Why have 4 laws? –Bad News 4 different names and relationships to remember PV=c, V/T=c, V/n=constant, combo P 1 V 1 / T 1 = P 2 V 2 / T 2 Three People’s names, which one goes where? –Good News Simple formulas, only a few variables involved Dimensions tend to cancel Not forced into MKS or self-consistent unit system –Can mix any units where dimensions cancel –PSI 1 /PSI 2 = Pascal 1 /Pascals 2 = Atmosph 1 /Atmosph 2 Best to choose SIMPLEST formula to solve a problem

38 Ideal Gas Law Bringing it all together Combination of P, V, n, and T Pressure = Pascals (MKS definition, or atmos) Volume = Liters, or cubic meters n = moles of material Temperature = degrees Kelvin (Centigrade + 273) Constant = R (depends on dimensions used) –R = Joules/(mole-degree K) –R = Liter-Atmospheres/(mole-degree K) PV = nRT

39 Ideal Gas Law PV=nRT … 5 th & final Gas Law –Good News Combines all 4 variables in one relationship One formula can solve any gas problem Linear relationship, no exponents or logs –Bad News Dimensions of “R” must be consistent with inputs –R= can be (liter-atmos)/(mole- o K) commonly used –R= can be (Joule- o K)/mole MKS units Cannot mix systems of units, no ratios to cancel Need to know 3 variables to get the 4 th.

40 Ideal Gas Law PV=nRT extremely useful –Handles all 4 variables (including a constant) –Can determine 4th variable if other 3 are known Moles of methane in tank of known P, V, T Pressure on piston if V, n, and T are known Temperature of a system if P, V, and n are known Volume of gas if P, n, and T are known –Lots of examples in text and homework –These are linear relationships, no exponents

41 Ideal Gas Ideal Gas Law PV=nRT –Simplifies to Boyle’s Law when n and T are constant PV = nRT = constant “k” –Simplifies to Charles’ Law when n and P are constant V/T = nR/P = constant “k” –Simplifies to Avagadro’s Law when T and P are constant V/n = RT/P = constant “k” –PV=nRT Very useful handles many gas calculations

42 Gas Density Ideal Gas Law P*V=n*R*T –Define “MM” = MolarMass (formula wt.)= grams/mole – n = moles = grams / MolarMass –Plug into ideal gas law … P*V= (grams/MM) R*T –MM = grams*R*T/ P*V (or MM=mRT/PV) Density definition = m/V (typically gm/ml) –From ideal law, P*V=(gram/MM)R*T, Rearrange to …. M = grams = P*V*MM/(R*T) –Density = grams/V = P*MM/(R*T) Can be a handy way to find density of a gas

43 Ideal Gas Law Standardized Conditions –Any measurement unit can be a variable –Need a “standard” set of conditions to compare –Use “STP” (not the engine additive or Hippie drug) Abbreviation for “Standard Temperature & Pressure” Reference temperature is 0 o C (usually) or 273 o Kelvin Reference pressure is 1 atmosphere (101,325 Pascals) –Pressure often cancels in calculations –Results from using pressure ratios, so dimensions cancel –Can use any consistent dimensions in those cases

44 Automobile Air Bag Reaction = 2NaN 3 + ignition  2Na + 3 N 2 Gas volume from 145 grams NaN 3 –Conditions are 1.15 atmos. Press at 30 o C Reaction ratios are always in moles –NaN 3 = 65 grams/mole, 145 gram=2.23 moles –Mole ratio for N 2 = (3/2)*2.23 = 3.35 moles –How to get to volume from moles ?

45 Automobile Air Bag Reaction = 2NaN 3 + ignition  2Na + 3 N 2 Gas volume from 145 grams NaN 3 –Conditions are 1.15 atmos. Press, 30 o C? Reaction rations are always in moles –NaN 3 = 65 grams/mole, 145 gram=2.23 moles –Mole ratio for N 2 = (3/2)*2.23 = 3.35 moles PV=nRT … or V=nRT/P –N = 3.35 mole –R = (Liter-atmosphere)/( o K-mole) –T = 30 o C+273 = 303 o K –P = 1.13 atmospheres V=nRT/P = 3.35*0.0821*303 / 1.13 = 72.4 liters

Now to our experiment We will evaluate Charles Law today –Measure gas volume at different temperatures –Compare our data to theoretical –How close do we come to Charles law?

Experiment Procedure (1) Measure air temperature in dry flask –Access path is through cork in flask –Convert hot temp. to Kelvin (add 273 o ) (2) Measure temperature of ice water –Thumb on cork until flask under water –Release thumb, shrinking air sucks in water –Convert temperature of cold bath to Kelvin –(3) Measure amount of water sucked in –(4) Measure volume of flask up to cork

Sample Calculation Temperature –Hot temperature = 70 o C+273=343 o K –Cold Temperature = 3 o C+273= 276 o K Volumes –Water sucked into flask = 30 mL –Total Flask = 145 mL –Cold air volume (total – water) = 145 – 30 = 115 mL Apply Charles Law: – Vcold = Vhot * (T2 / T1) – Vcold = 145mL * (276/343) – Calculated volume = mL –Error = Calc – Exper = = 1.7mL –Error % = [(calc-expt) / calc]*100 –Error % = [(116.7 – 115) / 116.6] *100 = 1.4%

Experiment summary Measure volume of water sucked into flask –Cold air volume = (empty flask) – (water sucked in) –Know ratios of hot/cold temperatures & volumes –Compare theoretical versus actual Repeat experiment for second trial data –Be sure to record temperatures & volumes Will share data on white board –Make sure your data makes sense before leaving Answer post-lab questions –4 items; Charles, Boyle, and combination gas laws

Charles law Experiment End of 32A lab lecture

Sample Calculation

52 Dalton's Law of Partial Pressures

53 Partial Pressures What about mixtures of gases? –Total pressure = sum of component pressures Each component gas has a “partial pressure” Partial pressure is the contribution from each gas Sum is1 atmosphere (air at sea level) –Nitrogen in air = partial atmospheres –Oxygen in air = partial atmospheres –Argon in air = partial atmospheres –Carbon Dioxide = partial atmospheres –TOTAL = 1.00 atmospheres (sum of partials)

54 Partial Pressures –Partial pressures depend on mole fractions PV = nRT, so pressure also depends on “n” Calculations will involve moles of gas Oxygen and Nitrogen = 99% of air, similar mass –O 2 at 32 gm/mole, N 2 at 28 gm/mole –Atmospheric pressure not linear with altitude Most of the air near the planet surface –Gravity keeps the air from escaping into space –Pressure vs altitude non-linear due to compression –Lake Tahoe about 0.75 Atmosphere, OK for people –Aircraft at 30,000 feet at 0.30 Atmosphere, can’t breathe

55 Pressure vs Altitude Lake Tahoe 6225 ft, ≈ 0.75 atmosphere

56 Partial Pressures Homework Example (textbook 8.84) –Partial Pressure of oxygen given as 160mm Hg at 1.0 atmosphere. So what is PP on top of Mt.Whitney where atm. Pressure is 440mm Hg? Assume same % oxygen. –By definition 1 atmosphere is 760 mm Hg, so air pressure on Mt Whitney is 440/760 = atmosphere –At 1 atmosphere, oxygen is 160mm Hg –Oxygen percent does not change with altitude, so same ratio applies to air on the mountain tip 160mmHg*0.579 = mmHg on Mountain –Alternatively a ratio can be used (160mmHg O 2 )/(760mmHg air) = (X mmHg O 2 )/(440mmHgair) X = mmHg O 2

2-variable Gas Laws Boyle’s Law –Pressure and Volume are inversely related –Pressure * Volume = constant assumes constant amount of material & temp If pressure goes up, volume goes down.. & vice versa Charles’ Law –Adds temperature as a new variable –Volume proportional to temperature –Volume / Temperature = constant Assumes constant amount of material and pressure If temperature goes up, so does volume

59 Gas Laws, Boyle Boyle’s Law –Pressure and Volume inversely related P 1 V 1 = P 2 V 2 Pressure * Volume = constant Pressure = constant * 1/Volume Pressure goes up, volume goes down NASA graphic shows 4 liters at 1 atmosphere Converts to 3 liters at 1.33 atmospheres –4*1 = 4, 3*1.33 = 4 –both P*V products yield same value = a constant

Gas Laws Boyle’s Law –Pressure and Volume inversely related –Pressure * Volume = constant –Pressure goes up, volume goes down NASA graphic shows 4 liters at 1 atmosphere Converts to 3 liters at 1.33 atmospheres –4*1 = 4, 3*1.33 = 4 –both P*V products yield same value = a constant –Assumes SAME amount of material present –Assumes SAME temperature both cases

Effect of Temperature Change Charles’ Law –Adds temperature as a variable –Gas volume proportional to temperature –Volume / Temperature = constant Assumes constant amount of material & pressure If temperature goes up, so does volume –NASA graphic shows 4 liters at 300 degrees Also shows 3 liters at 225 degrees 4 / 300 = / 225 = Both divisions yield same value = a constant

Examples –Boyle’s Law: PV = constant P 1 V 1 = P 2 V 2 (constant temperature & mass) Can solve for 4 th condition when other 3 are known –P 1 = P 2 V 2 / V 1 –V 1 = P 2 V 2 / P 1 –P 2 = P 1 V 1 / V 2 –V 2 = P 1 V 1 / P 2 Alternatively, can have ratios of same quantity –P 1 /P 2 = V 2 /V 1 –Important to note DIMENSIONS are UNIMPORTANT »But must be consistent to cancel

All 4 temperature scales

Gases & Gas Law Summary Avagadro’s Gas Law –Addition of mass as a variable Ideal Gas Law with all 4 variables –PV=nRT Gas Density & Volume Stoichiometry, STP Applications –Auto air Bags, dirigibles, hot-air balloons

Gas Law Summary –Boyle’s Law: PV = constant P 1 V 1 =constant=P 2 V 2 no changes in temperature or mass Only 2 variables to consider –Charles’ Law: V/T = constant Volume inversely related to absolute temperature V = constant * T (no change in pressure or mass) –says rising temperature increases volume –Assumes constant amount of material & pressure Only 2 variables involved

Gas Law Summary –Avagadro’s law: V/n = constant Volume inversely related to amount of material V = constant * moles –no changes in pressure or Temperature –More moles provides larger volume –Assumes constant Temperature and Pressure Only 2 variables involved –Combined Gas Law P 1 V 1 /T 1 = P 2 V 2 /T 2 Handles 3 variables Mass not included

Why a Gas? Gas molecules have kinetic energy –Energy proportional to Kelvin temperature Gas molecules have full octets Gas molecules have little mutual attraction Energy of collisions keeps molecules apart 67

Total of 4 Gas Law Variables –Variables involved for Gases Pressure, can be “atmospheres” or Pascals –For ratios involving 2 pressures, dimensions cancel Volume, can be liters or cubic meters –For ratios involving 2 volumes, dimensions cancel Temperature, always in Kelvin, o C+273= o K –Kelvin is linear, “0” is really zero (not so for o C, o F) Mass, usually in moles –For ratios involving 2 masses, dimensions cancel