Gases Edward Wen, PhD
Properties of Gases expand to completely fill their container take the shape of their container low density much less than solid or liquid state compressible when pressure is changed. mixtures of gases are always homogeneous (common air) fluid 2
Properties of Gas: Indefinite Shape & Volume Gas molecules: have enough kinetic energy and little attractions keep moving around and spreading out fill the container of whatever shape 3
Comparison: Gas, Liquid, Solid State Shape Volume Compress Flow Solid Fixed Fixed No No Liquid Indef. Fixed No Yes Gas Indef. Indef. Yes Yes 4
Kinetic Molecular Theory 5
Pressure: Gases Pushing What are Gas molecules doing? constantly in motion as they move and strike a surface, they push on that surface push = force Pressure of gas: total amount of force exerted by gas molecules hitting the entire surface at any one instant pressure = force per unit area 6
Measuring Air Pressure use a barometer: column of mercury supported by air pressure Force of the air on the surface of the mercury Gravity on the column of mercury gravity 7
Common Units of Pressure Unit Average Air Pressure at Sea Level pascal (Pa) 101,325 kilopascal (kpa) 101.325 atmosphere (atm) millimeters of mercury (mmhg) torr (torr) 1 (exactly) 760 (exactly) 760 (exactly) pounds per square inch (psi, lbs./in 2 ) 14.7 8
Practice: Convert Pressure between units 735.0 mmhg =? atm 35. psi =? torr Ans: 0.9671 atm Ans: 1.8 10 3 torr 9
Pressure of a Gas, P Cause: constant movement of the gas molecules and their collisions with the surfaces around them Pressure depends on: number of gas particles in a given volume volume of the container average speed of the gas particles 10
The Effect of Gas Pressure whenever there is a Pressure difference, a gas will flow from area of High pressure area of Low pressure the bigger the difference in pressure, the stronger the flow of the gas if there is something in the gas path, the gas will try to push it along as the gas flows 11
Gas Pressure in Soda Straws Straw at idle: Pressure of the air inside the straw = Pressure of the air outside the straw liquid levels is the same on both sides Suction of the straw: Pressure of the air inside the straw is < Pressure of the air outside the straw liquid is pushed up the straw by the outside air 12
Atmospheric Pressure & Altitude Altitude Atmospheric pressure At the surface, P = 14.7 psi, At 10,000 ft altitude, P = 10.0 psi Rapid changes in atmospheric pressure may cause your ears to pop an imbalance in pressure on either side of your ear drum (driving or flying) Demo: Can you make a piece of paper uphold a bottle of water? 13
Boyle s Law For the gas contained Pressure of a gas is inversely proportional to its volume: P 1/V constant T and amount of gas P x V = constant P 1 x V 1 = P 2 x V 2 Q: How does the size of an air bubble change along the way it rises from the deep water to the surface? 14
Soda bottle Submarine P inside Pressure surge when bottle being squeezed Volume of the air inside the dropper decreases Water filling up the dropper Increased density of dropper (Mass dropper /Volume ) Dropper sinking! 15
Boyle s Experiment added Hg to a J- tube with air trapped inside Plotting Volume of air vs. Air pressure 140 120 100 Inverse Volume vs Pressure of Air, Boyle's Expt. Pressure, inhg 80 60 40 20 0 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 Inv. Volume, in -3 16
When you double the pressure on a gas, the volume reduces to one half, (as long as the temperature and amount of gas do not change) 17
Example: Boyle s Law
Example: A cylinder equipped with a moveable piston has an applied pressure of 4.0 atm and a volume of 6.0 L. What is the volume if the applied pressure is decreased to 1.0 atm? 19
Example: A cylinder equipped with a moveable piston has an applied pressure of 4.0 atm and a volume of 6.0 L. What is the volume if the applied pressure is decreased to 1.0 atm? Information Given: P 1 = 4.0 atm P 2 = 1.0 atm Find: V 2 =? L V 1 = 6.0 L Answer: 24 L 20
We re losing altitude. Quick Professor, give your lecture on Charles Law! 21
Charles Law For the gas contained and at constant Pressure: Volume is directly proportional to temperature V T constant P and amount of gas graph of V vs T is straight line as T increases, V also increases Kelvin K = C + 273 V = constant x T if T measured in Kelvin V 1 = T 1 V T 2 2 22
Charles Law in Action The density of common air depends on the temperature. Higher T, lower Density Why the air vents for the air conditioning system are located at the ceiling? When measuring the weight of an object, why the high temperature of the object can affect the measurement? 23
Example: Charles Law
Example: A sample of gas has a volume of 2.80 L at an unknown temperature. When the sample is submerged in ice water at 0 C, its volume decreases to 2.57 L. What was the initial temperature in kelvin and in celsius? (assume constant pressure) 25
Example: A gas has a volume of 2.80 L at an unknown temperature. When the sample is at 0 C, its volume decreases to 2.57 L. What was the initial temperature in kelvin and in celsius? Information Given: V 1 = 2.80 L V 2 = 2.57 L T 2 = 0 C Find: temp 1 in K and C T 1 = 297 K = 24 C 26
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Gay-Lussac s Law For the gas contained at constant Volume: Pressure is directly proportional to temperature P T constant V and amount of gas graph of P vs T is straight line as T increases, P also increases Kelvin K = C + 273 P = constant x T if T measured in Kelvin P T P 1 2 = T 1 2 28
Gay-Lussac s Law in Action The pressure of gas in a sealed container depends on the temperature. Higher T, higher Pressure Keep the propane container in a cool place, avoid from direct sunlight. 29
Example: Gay-Lussac s Law
Example: The tire on a bicycle stored in a cool garage at 18 C had a pressure of 30. psi. What is the pressure inside the tire after riding the bike at 35 C? Assume the volume of the tire remains constant. 31
The tire on a bicycle stored in a cool garage at 18 C had a pressure of 30. psi. What is the pressure inside the tire after riding the bike at 35 C? Assume the volume of the tire remains constant. Information Given: T 1 = 18 C, P 1 = 30. psi T 2 = 35 C Find: P 2 in psi. T 1 = 291 K, T 2 = 308 K, P 2 = 32 psi 32
P VT Keep P Keep T P, V, T Keep V P V T P V T
Avogadro s Law Volume directly proportional to the number of gas molecules V = constant x n constant P and T more gas molecules = larger volume count number of gas molecules by moles Equal Volumes of gases contain Equal numbers of molecules the gas doesn t matter V 1 = n 1 V n 2 2 34
Avogadro s Law 35
Example: Avogadro s Law
Example: A 4.8 L sample of helium gas contains 0.22 mol helium. How many additional moles of helium must be added to obtain a volume of 6.4 L? (assume constant pressure and temperature) 37
Example: A 4.8 L sample of helium gas contains 0.22 mol helium. How many additional moles of helium must be added to obtain a volume of 6.4 L? Information Given: V 1 = 4.8 L, n 1 =0.22 mol V 2 = 6.4 L Find: n 2, mol and added mol 0.07 mole 38
Combined Gas Law Boyle s Law : Pressure and Volume at constant temperature Charles Law : Volume and absolute Temperature at constant pressure P 1 V1 = P2 V2 V 1 = T 1 V T 2 2 Volume of a sample of gas when both the Pressure and Temperature change ( P ) ( ) 1 V1 ( T ) 1 = ( P ) ( ) 2 V2 ( T ) 2 39
Example: The Combined Gas Law
Example: A sample of gas has a volume of 158 ml at a pressure of 755 mmhg and a temperature of 34 C. The gas is compressed to a volume of 108 ml and heated to 85 C, what is the final pressure in mmhg? Information Given: V 1 = 158 ml, P 1 = 755 mmhg, t 1 = 34 C V 2 = 108 ml, t 2 = 85 C Find: P 2, mmhg 3 P 2 = 1.25 10 mmhg 41
Ideal Gas Law Combined Gas Law + Avgadro s Law Ideal Gas Law ( P) ( V) ( n) ( T) = or PV nrt R is called the Gas Constant the value of R depends on the units of P and V R = 0.0821 atm/k mol convert P to atm and V to L Application of Ideal Gas law: when T, P, V of a gas all changes R = 42
Example: The Ideal Gas Law Requiring Unit Conversion
Example: Calculate the number of moles of gas in a basketball inflated to a total pressure of 24.2 psi with a volume of 3.2 L at 25 C 44
Example: Calculate the number of moles of gas in a basketball inflated to a total pressure of 24.2 psi with a volume of 3.2 L at 25 C Information Given: V = 3.2 L, P = 24.2 psi, t = 25 C Find: n, mol n = 0.22 mol 45
Air: Mixtures of Gases Air is a mixture (N 2, O 2 ) Each gas in the mixture behaves independently of the other gases though all gases in the mixture have the same volume and temperature all gases completely occupy the container, so all gases in the mixture have the volume of the container Gas % in Air, by volume Gas % in Air, by volume nitrogen, N 2 78 argon, Ar 0.9 oxygen, O 2 21 carbon dioxide, CO 2 0.03 46
Dalton s Law: Partial Pressure 47
Collecting gas over water Zn metal reacts with HCl(aq) to produce H 2 (g). The gas flows through the tube and bubbles into the jar, where it displaces the water in the jar. P gas = P H 2O + P H 2 Because water evaporates, some water vapor gets mixed in with the H 2. 48
Standard Conditions (STP) Common reference points for comparing Standard Temperature & Pressure Standard Pressure = 1.00 atm Standard Temperature = 0 C = 273 K 49
Molar Volume of a Gas at STP Definition: The volume of 1 (exact) mole gas at STP Use the Ideal Gas Law: PV = nrt L atm 1mole 0.0821 273K n R T V = = mole K = P 1.00 atm 1 mole of any gas at STP will occupy 22.4 L ==> Molar volume can be used as a conversion factor as long as you work at STP 1 mol 22.4 L 22.4L 50
Molar Volume So much empty space between molecules in the gas state, the volume of the gas is not effected by the size of the molecules, (under ideal conditions). 51
Density of Gas at STP Since every exactly one mole of any gas has a volume of 22.4 L, whereas the mass of such gas would be as the molar mass in grams Density of Gas = Molar mass / Molar Volume Example: Density of Oxygen gas at STP = 32.00 g/mol / 22.4 L/mol = 1.43 g/l 52
Density of Common Gases At STP, the density of common gases (in g/l) as: H 2 0.0900 He 0.179 CH 4 0.716 N 2 1.25 Air 1.29 O 2 1.43 CO 2 1.96 Cl 2 3.17 Which one, hydrogen gas or helium gas, is better in blimps in providing lift? Why carbon dioxide is used in putting out fire? What if its density is less than the air? 53
Real Gases Ideal gas laws assume 1) No Attractions between gas molecules 2) No Volume: gas molecules do not take up space based on the Kinetic-Molecular Theory Real gases: often do not behave like Ideal gases at High pressure ( Squeezed ) or Low temperature ( Frozen ) 54
Ideal vs. Real 55