1 Problem Set #8, 13, 18, 19, 24, 36, 42, 45, 58, 71, 73; Recommended #5, 16, 22, 60, 61, 83

 Particles in a gas are very far apart, and have almost no interaction. › Ex: In a sample of air, only 0.1% of the total volume actually consists of matter.  Gases expand spontaneously to fill their container (have indefinite volume and shape.)   e/gasMoleculeMotion/gasMoleculeMotion.html e/gasMoleculeMotion/gasMoleculeMotion.html 2

 A force that acts on a given area 3 Atmospheric pressure: the result of the bombardment of air molecules upon all surfaces 1 atm = 760 mm Hg = 760 torr = kPa = 14.7 PSI 100 km

Barometer: measures atmospheric P compared to a vacuum  * Invented by Torricelli in 1643  Liquid Hg is pushed up the closed glass tube by air pressure 4 Evangelista Torricelli ( )

1. Closed-end: difference in Hg levels (  h) shows P of gas in container compared to a vacuum 5 closed

 Difference in Hg levels (  h) shows P of gas in container compared to P atm 6

7 Amadeo Avogadro ( ) Robert Boyle ( ) Jacques Charles ( ) John Dalton ( ) Joseph Louis Gay-Lussac ( ) Thomas Graham ( )

 Boyle’s law: the volume (V) of a fixed quantity (n) of a gas is inversely proportional to the pressure at constant temperature (T). 8 P V 1/P V Animation: Ex: A sample of gas is sealed in a chamber with a movable piston. If the piston applies twice the pressure on the sample, the volume of the gas will be. If the volume of the sample is tripled, the pressure of the gas will be halved reduced to 1/3

 V of a fixed quantity of a gas is directly proportional to its absolute T at constant P. 9 T V Animation: Extrapolation to V = 0 is the basis for absolute zero. V = 11.5 L Ex: A 10.0 L sample of gas is sealed in a chamber with a movable piston. If the temperature of the gas increases from 50.0 ºC to ºC, what will be the new volume of the sample?

 Seen as derivative of C’s and B’s laws  P of a fixed quantity of a gas is directly proportional to its absolute T at constant V. 10 T P

 Equal volumes of gases at the same T & P contain equal numbers of molecules 11 n V

› Ex: A 10.0 L sample of gas at 100.0ºC and 2.0 atm is sealed in a chamber. If the temperature of the gas increases to 300.0ºC and the pressure decreases to 0.25 atm, what will be the new volume of the sample? 12 V 2 =120 L

 Used for calculations for an ideal (hypothetical) gas whose P, V and T behavior are completely predictable. R = Latm/molK = 8.31 J/molK › Ex: How many moles of an ideal gas have a volume of mL at 200.0ºC and 450 mm Hg? 13 n = 3.0 x mol

 What is the V of mol of an ideal gas at standard temperature and pressure (STP, 0.00°C and atm) 14 V = 22.4 L (called the molar volume) 22.4 L of an ideal gas at STP contains x particles (Avogadro’s number) )273)(0821.0)(000.1().1(KmolVatm 

 Laws/GasConstant.html Laws/GasConstant.html 15

 Gas density (d):  Molar mass ( M ): 16

 Partial pressure: P exerted by a particular component in a mixture of gases  Dalton’s law of partial pressures: the total P of a mixture of gases is the sum of the partial pressures of each gas P TOTAL = P A + P B + P C + … (also, n TOTAL = n A + n B + n C + …) 17

= P H2 =(0.60)(0.0821)(293) / 5.0 = 2.9 atm P He =(1.50)(0.0821)(293) / 5.0 = 7.2 atm P T = = 10.1 atm +

 Ratio of moles of one component to the total moles in the mixture (dimensionless, similar to a %) 19 Ex: What are the mole fractions of H 2 and He in the previous example? ∴

 When a gas is bubbled through water, the vapor pressure of the water (partial pressure of the water) must be subtracted from the pressure of the collected gas: P T = P gas + P H2O ∴ P gas = P T – P H2O 20 See Appendix B for vapor pressures of water at different temperatures.

* Formulated by Bernoulli in 1738 Assumptions: 1.Gases consist of particles (atoms or molecules) that are point masses. No volume - just a mass. 2.Gas particles travel linearly until colliding ‘elastically’ (do not stick together). 3.Gas particles do not experience intermolecular forces. 21 Daniel Bernoulli ( )

4.Two gases at the same T have the same kinetic energy › KE is proportional to absolute T 22 u rms = root-mean-square speed m = mass of gas particle (NOTE: in kg) k = Boltzmann’s constant, 1.38 x J/K Ludwig Boltzmann ( )

23 James Clerk Maxwell ( )

24 O 2 at 273K O 2 at 1000K H 2 at 273K Number at speed, u Speed, u

 Since the average KE of a gas has a specific value at a given absolute T, then a gas composed of lighter particles will have a higher u rms. 25 m = mass (kg) M = molar mass (kg/mol) R = ideal gas law constant, 8.31 J/mol·K

 Effusion: escape of gas molecules through a tiny hole into an evacuated space  Diffusion: spread of one substance throughout a space or throughout a second substance

 The effusion rate of a gas is inversely proportional to the square root of its molar mass 27 r = u = rate (speed) of effusion t = time of effusion

a = correction for dec in P from intermolecular attractions (significant at high P, low T) b = correction for available free space from V of atoms (significant at high concentrations) 28 Particles of a real gas: 1. Have measurable volumes 2. Interact with each other (experience intermolecular forces) Van der Waal’s equation: or Johannes van der Waals ( )

A gas deviates from ideal: › As the particles get larger (van der Waal’s “b”) › As the e- become more widely spread out (van der Waal’s “a”) The most nearly ideal gas is He. 29