נושא 6 גזים 1 Prof. Zvi C. Koren
Torricelli Charles Avogadro Graham Dalton Boyle Gay-Lussac Kelvin Maxwell Boltzmann 2 Prof. Zvi C. Koren
Gas Laws: A Practical Application - Air Bags Example: An automobile air bag is rapidly inflated by the explosion of sodium azide (NaN 3 ), which releases nitrogen gas when detonated: 2NaN 3 (s) 2Na(s) + 3N 2 (g) How much sodium azide is required to inflate an air bag with a volume of 50.0 L? Does the amount of sodium azide required depend on the temperature of the gas produced? Does altitude affect an air bag's performance? You will be able to answer these questions at the end of this chapter. 3 Prof. Zvi C. Koren
Gas-Generator Reaction Initial Reaction Triggered by Sensor. Second Reaction. Final Reaction. Air-Bag Chemistry The signal from the deceleration sensor ignites the gas-generator mixture by an electrical impulse, creating the high-temperature condition necessary for NaN 3 to decompose. Air-Bag Chemistry Reactants (Substances in red are initially in the air-bag) NaN 3 (s) Na KNO 3 (s) K 2 O Na 2 O SiO 2 (s) Na(s) N 2 (g) K 2 O(s) Na 2 O(s) N 2 Alkaline silicate (glass) Products Write balanced chemical reactions for each of these steps. extremely reactive inert reactive reactive inert inert 4 Prof. Zvi C. Koren
Properties of Gases: Gas Pressures, P The Mercury Barometer: Measuring Atmospheric Pressure Evangelista Torricelli (1608 1647, Italy): We live submerged at the bottom of an ocean of air. Aristotle (4 th century BCE): Nature abhors a vacuum. 5 Prof. Zvi C. Koren
The Mercury Barometer: Measuring Atmospheric Pressure Evangelista Torricelli meniscus vacuum The atmospheric pressure (or barometric) pressure can be described in terms of mm Hg 1 standard atmosphere is supported by a mercury column that is 760 mm Hg in height: P atm P Hg 1 atm 760 mm Hg 1 torr 1 mm Hg 760 mm Hg 600 mm Hg 6 Prof. Zvi C. Koren
Pressure Units P = pressure f = force A = area w = weight m = mass g = acceleration due to gravity = 9.80665 m/s 2 h = height of column d = density = m/v P f A w A mg A h h mgh V SI (and other) Units Energy: 1 J = 1 kg m 2 /s 2 Force: 1 N = 1 kg m/s 2 ( kms ) Pressure: 1 Pa = 1 N/m 2 = 1 kg/m s 2 1 bar = 10 5 Pa 1 torr = 1 mm Hg J = Joule, N = Newton, Pa = Pascal dgh P = d g h For the mercury barometer (at 0 o C): d Hg = 13.5951 g/cm 3 = 0.0135951 kg/cm 3 x (10 2 cm / 1 m) 3 = 1.35951 x 10 4 kg/m 3 h = 760 mm Hg = 76 cm Hg = 0.76 m Hg P = d g h 1 atm = (1.35951x10 4 kg/m 3 ) (9.80665 m/s 2 ) (0.76 m) = 1.01325x10 5 kg/m s 2 = 1.01325 x 10 5 Pa = 101.325 kpa = 1.01325 bar = 14.6960 lb/in 2 ( PSI, Pounds per Square Inch) 7 760 (exactly) mm Hg Prof. Zvi C. Koren
The Mercury Manometer: Measuring Gas Pressure CLOSED Manometer OPEN Manometer vacuum P atm P gas P H g P gas P H g gas gas P gas = P Hg P gas = P atm + P Hg 8 Prof. Zvi C. Koren
Gas Laws Changes in gas properties have been mathematically modeled for many years. These mathematical models are collectively called gas laws. They define the relationships between pairs of gas properties and experiments confirm these gas laws. Chemists use four basic measurements when working with gases: 1. The quantity of the gas, n (in moles) 2. The temperature of the gas, T (in kelvins) 3. The volume of gas, V (in liters) 4. The pressure of the gas, P (in atmospheres) 9 Prof. Zvi C. Koren
Boyle s Law Robert Boyle (1627 1691) England P V -1, [n,t] P V = k or P = k V 1, [n,t] P 1 V 1 = P 2 V 2, [n,t] 20 18 16 hyperbola piston 14 12 P 10 8 gas 6 4 2 0 0 5 10 15 20 25 10 Prof. Zvi C. Koren V
Charles s and Gay-Lussac s Law Jacques Alexandre César Charles (1746-1823) V T, [n,p] Joseph Louis Gay-Lussac (1778 1850) V = k T, [n,p] V T 1 1 V T 2 2, [n,p] V T k, [n,p] V William Thomson Lord Kelvin (1824-1907), Irish extrapolation Absolute Zero -273 o C The title Baron Kelvin was given in honor of his achievements, and named after the River Kelvin, which flowed past his university in Glasgow, Scotland. Absolute temperature scale is in kelvins: T(K) = t( 0 C) + 273.15 11 Prof. Zvi C. Koren T
Avogadro s Law Lorenzo Romano Amedeo Carlo Avogadro di Quareqa e di Carreto (1776 1854) V n, [P,T] V = k n, [P,T] V n k, [P,T] V1 V 2, [P,T] n 1 n 2 V 12 Prof. Zvi C. Koren n
Ideal Gas Law Combining all three gas laws: Boyle: P V = k, [n,t] + Charles: + Avogadro: P V T = k, [n] P V n T = k R Gas Constant At STP (Standard Temperature and Pressure), 0 o C (= 273.15 K) & 1 atm: 1 mole of an ideal gas occupies 22.414 L of volume. R P n V T (1 atm) (22.414 (1 mol ) (273.15 L) K) PV = nrt 0.082057 L atm/ mol K = 8.31 J/mol K = 1.99 cal/mol K = [energy/mol K] 13 Prof. Zvi C. Koren
mole Mole Day is celebrated on Oct. 23 rd from 6:02 am to 6:02 pm 14 Happy Mole Day to You!!! Prof. Zvi C. Koren
Summary: Moles in Chemistry # of items: Avogadro s # Mass: m/mw mole Gas: PV = nrt Solution: MV 15 Prof. Zvi C. Koren
Gas Laws and Chemical Reactions: Stoichiometry Problem: Potassium superoxide is used to purify air in a spacecraft. What mass of KO 2 is required to recycle 500.0 ml of CO 2 at 25.00 o C and 750. mmhg? 4KO 2 (s) + 2CO 2 (g) 2K 2 CO 3 (s) + 3O 2 (g) Solution: Stoichiometric Flow-Chart: mass KO 2 moles KO 2 moles CO? MW rxn 2 (V, T, P) of CO PV=nRT 2 R = 0.082057 L atm/mol K 1atm PV P = 750. mmhg = 0.98684 atm nco 2 760 mm Hg n RT 1 L CO 2 = 0.020168 V = 500.0 ml = 0.5000 L 1000 ml T = 25.00 + 273.15 = 298.15 K 4 mol KO 0.020168 mol CO 2 2 71.0971g KO 2 2 mol CO = 2.87 g KO 2 2 1mol KO 2 16 Prof. Zvi C. Koren
Gas Mixtures and Dalton s Law of Partial Pressures John Dalton (1766-1844), England 1 2 3 1 2 1 2 2 3 2 2 1 2 1 3 P i = partial pressure of gas i = n i RT/V P total = ΣP i = P 1 + P 2 + P 3 + = n 1 RT/V + n 2 RT/V + n 3 RT/V + = (n 1 + n 2 + n 3 + ) RT/V n totalrt = n total RT/V Ptotal V P nirt/v n i i Ptotal n totalrt/v n total X i mole fraction of gas i ΣX i = 1 P i = X i P total 17 Prof. Zvi C. Koren
Gas Density From: PV = nrt m MW n PV RT m V P RT MW d P RT MW d MW, [P,T] For example: do 2 @ STP (0.0821 1atm L atm/mol K)(273 K) (32.00 g / mol ) = 1.43 g/l 18 Prof. Zvi C. Koren
Determining the Molecular Weight of a Volatile Liquid Dumas Method vent Measurements: Mass of vapor = 1.2189 g (measurements of empty and filled flask) Volume of flask = 510.0 ml (measured with water) Temperature of vapor = 100.0 o C Atmospheric pressure = 745 torr MW =? 19 Prof. Zvi C. Koren
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Tenets of KMT: Kinetic Molecular Theory (KMT) of Gases 1. Gases consist of molecules whose separation is much larger than the volume of the molecules themselves. 2. The gas molecules are in continuous random and rapid motion. 3. The average kinetic energy of the gas molecules is determined by the absolute gas temperature. Notes: All gas molecules at the same T, regardless of mass, have the same average kinetic energy. Temperature is a bulk (macroscopic) property, and not one based on an individual (microscopic) molecule) 4. Gas molecules collide with each other and with the walls of the container, but they do so without loss of energy. These collisions are perfectly elastic. Ideal Gas Properties: No intermolecular forces Molecular volume is negligible 21 Prof. Zvi C. Koren
3(½ RT) = KE mole = ½Mv 2 Average Kinetic Energies, KE Kinetic Energy for one molecule KE molecule = ½mv 2, m mass of one molecule Kinetic Energy for one mole KE mole = ½Mv 2, M MW, Molecular weight Average Kinetic Energy for one mole KE mole = ½Mv 2, But also: Combine these two Average Kinetic Energy for one mole KE mole T = 3(½ RT) proof is not for this course ( 2 v ) 1/2 3RT M 1/2 R = (J/mol K) MW = (kg/mol) v rms = root-mean-square velocity (m/s) Graham s Law of Diffusion for 2 Gases at same T: v 1 /v 2 = (M 2 /M 1 ) ½ Thomas Graham (1805 1869), Scotland 22 Prof. Zvi C. Koren
Applications of KMT 1. Diffusion of NH 3 (g) vs. HCl(g) 23 Prof. Zvi C. Koren
2. Separation of Uranium Isotopes 24 Prof. Zvi C. Koren
Maxwell-Boltzmann Distribution of Molecular Speeds = f (T, MW) James Clerk Maxwell (1831 1879), Scotland Ludwig Eduard Boltzmann (1844 1906), Austria Why do molecules, all at the same T, have such a wide span of velocities? 25 Prof. Zvi C. Koren
Maxwell-Boltzmann Distribution of Molecular Velocities MW Effects: > > (continued) 26 Prof. Zvi C. Koren
Temperature Effects 1: (continued) 27 Prof. Zvi C. Koren
Temperature Effects 2: 28 Prof. Zvi C. Koren
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