1 Ch 10: Gases Brown, LeMay AP Chemistry

2 10.1: Characteristics of Gases 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.)

3 10.2: Pressure (P) A force that acts on a given area 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

4 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 Measuring pressure (using Hg) Evangelista Torricelli ( )

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

6 Difference in Hg levels (h) shows P of gas in container compared to P atm 2. Open-end:

7 10.3: The Gas Laws Amadeo Avogadro ( ) Robert Boyle ( ) Jacques Charles ( ) John Dalton ( ) Joseph Louis Gay-Lussac ( ) Thomas Graham ( )

8 10.3: The Gas Laws Boyle’s law: the volume (V) of a fixed quantity (n) of a gas is inversely proportional to the pressure at constant temperature (T). 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

9 V of a fixed quantity of a gas is directly proportional to its absolute T at constant P. T V Animation: Charles’ law 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?

10 * Questionably named, 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. T P “Gay-Lussac’s law”

11 Equal volumes of gases at the same T & P contain equal numbers of molecules n V Avogadro’s hypothesis

12 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? Combined gas law V 2 =120 L

13 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? 10.4: The ideal gas law n = 3.0 x mol

14 What is the V of mol of an ideal gas at standard temperature and pressure (STP, 0.00°C and atm) 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 

: More of the ideal gas law Gas density (d): Molar mass ( M ):

: Gas Mixtures & Partial Pressures 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 + …)

Ex: What are the partial pressures of a mixture of 0.60 mol H 2 and 1.50 mol He in a 5.0 L container at 20ºC, and what is the total P? = 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 +

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

19 Collecting Gases “over Water” 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 See Appendix B for vapor pressures of water at different temperatures.

: Kinetic-Molecular Theory * 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. Daniel Bernoulli ( )

: Kinetic-Molecular Theory 4.Two gases at the same T have the same kinetic energy KE is proportional to absolute T 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 ( )

22 Maxwell-Boltzmann distribution graph James Clerk Maxwell ( )

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

: Molecular Effusion & Diffusion 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. m = mass (kg) M = molar mass (kg/mol) R = ideal gas law constant, 8.31 J/mol·K

25 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

26 Graham’s law The effusion rate of a gas is inversely proportional to the square root of its molar mass r = u = rate (speed) of effusion t = time of effusion

: Deviations from Ideal Behavior 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) 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 ( )

: Deviations from Ideal Behavior 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.