Chap. 5 GASES & KINETIC- MOLECULAR THEORY

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1 Chap. 5 GASES & KINETIC- OLECULAR THEORY Use the ideal gas law to describe the behavi of gases. Understand how kinetic-molecular they provides the basis f understanding gas behavi Be able to describe effusion and diffusion of gases. Explain what properties of gases give rise to deviations from ideal behavi. 5.1 The Physical States of atter PROPEY DENSITY SHAPE COPRESSIBILITY as ƒ(pressure) THERAL EXPANSION as ƒ(temperature) SOLID LIQUID GAS high (N g/cm 3 ) definite moderate to high (N g/ml) indefinite (fluid) low (N g/l) indefinite (fluid) small small large very small small moderate 5.2 Gas Pressure SOLIDS LIQUIDS GASES Particles vibrate around fixed positions Strong cohesive fces Particles in constant, random motion Cohesive fces dominate, particles see each other Particles in constant, random motion Weak cohesive fces, particles move independently of each other Gas molecules exert PRESSURE on any container by colliding with its walls Pressure = fce per unit area P = F/A SI unit: Pascal (Pa) = 1 N/m 2 Standard Atmosphere Atmospheric pressure as measured by a barometer at sea level: New Yk Denver 1 atm in Hg 760 mm Hg = 1 atm 760 tr 14.7 psi 1.01 bar kpa Pressure, atm ount Everest La Paz Altitude, km Boiling Point, C Page 5-1

2 5.3 The Gas Laws BOYLE S LAW The volume of of a gas is is inversely proptional to to its its pressure at at constant temperature 1 P P = constant P 1 1 = P 2 2 Increase the pressure, decrease the volume 1 atm 20 L 2 atm 10 L CHARLES LAW The volume of of a gas is is directly proptional to to its its temperature (K) at at constant pressure / T = constant 1 T 1 = 2 T 2 = 0 at T = 0 K Increase the temperature, increase the volume 10 L 15 L T = 1 C 274 K T = 138 C 411K Combined Gas Law This covers both Boyle s and Charles Laws: AOGADRO S LAW Equal volumes of of gas at at the same temperature and pressure contain equal numbers of of molecules P 1 1 P 2 2 = T 1 T 2 EX: When the temperature is constant (T 1 = T 2 ), the Combined Law becomes P 1 1 P 2 2 = P 1 1 = P 2 2 (Boyle s Law) T 1 T 1 / n = constant no. of moles 1 n 1 = 2 n 2 Increase the number of moles, increase the volume: P = 1 atm T = 25 C 1 L 2 L Combined Gas Law, Redux This covers Boyle s, Charles, and Avogadro s Laws: P 1 1 P 2 2 = n 1 T 1 n 2 T 2 This allows you to describe the changes in a sample of gas as it goes from one state (set of physical conditions) to another. This also leads to The Ideal Gas Law Combining Boyle s, Charles and Avogadro s Laws: P N T R P = n = pressure (atm, tr) = volume (L) = mol = temperature (K) = L atm / K mol gas constant J / K mol Page 5-2

3 Standard Temperature and Pressure Standard temperature = 0.00 C Standard pressure = atm The volume occupied by 1 mol of gas at STP is = n / p (1 mol L atm / K mol K) = atm = L 5.4 Further Applications DENSITY OF A GAS: m P =, where m = mass, = mol wgt so P d = Density is directly proptional to mol wgt Density is inversely proptional to T Partial Pressure: Gas ixtures OLAR ASS (W) OF A GAS: m P = so m = P olar mass is directly proptional to the weight of a specific volume of gas DALTON S LAW The total pressure of of a mixture of of gases is is the sum of of the pressures (partial pressures) that each would exert if if it it were present alone n T = n + n + n n T n n n P T = + + P T = = (n + n + n ) P T = P + P + P 5.6 Kinetic olecular They P T = ΣP j P i n i / n i n i = = = χ i OLE FRACTION P T n T / n T Σn j P i = i χ i PT i PT = χ = 0.10, χ = 0.20, χ = Explains gas behavi in terms of particle (molecular) motion A gas consists of particles that Have no significant volume (point masses) Are constant, rapid motion = KINETIC ENERGY (E k ) considerations imptant Experience no interparticle fces POTENTIAL ENERGY considerations not imptant Collide with no net loss of energy (E k constant) Have kinetic energy proptional to the temperature Describes pressure and temperature on the molecular level P = ƒ(n,t) Page 5-3

4 olecular speeds at 25 C: 0 C In terms of molar mass: χ u 0 u C χ O u rms = 3 avier molecules have lower average speeds E k = ½mu 2 rms where u rms is the rms speed , m / s , m / s Temperature is ƒ(e k ), not ƒ(e T ): E k = 3 2 N A olecular Effusion and Diffusion At a given temperature, the average kinetic energy of any gas has a specific value This means that u rms speed varies inversely with the molar mass (): 3 u rms = As a result, two physical phenomena, effusion and diffusion, can be described in terms of their mass dependence Effusion Escape of a gas through a narrow (D << d) opening: d D Graham s Law: r 1 r 2 = 2 1 Diffusion Spreading dispersion of a gas through space through another substance. Follows Graham s law. Because of frequent encounters with other gas particles, the path of any molecule actually consists of sht segments linking collisions. As a result, diffusion rates << u rms Rate DIFF << DIFF << Rate EFF EFF 5.7 Real Gases: Deviations from Ideal Behavi Real molecules have finite volumes The free volume of a container varies with the gas pressure As pressure increases, free volume decreases Real molecules attract one another Interparticle collisions are inelastic Interparticle attractions decrease the fce of wall impacts Real pressure is less than ideal pressure As temperature decreases, E k decreases but interparticle attractions are unchanged; E p becomes imptant Page 5-4

5 P / GAS molar, L DEIATION, % CH 4 Ar C NH P, atm The van der Waals Equation K 500 K P + n 2 a ( - nb) = n 2 P 1000 K crection f interparticle attraction crection f finite volume 1.0 GAS DE., % a b P, atm Ar C NH Real Ideal Inelastic collisions lower the actual gas pressure Imptant at higher P, lower T Interparticle fces, loss of free volume become imptant as d interparticle decreases n P + 2 a ( - nb) = n 2 At low P and high T, the /n term is relatively large, so (n/) 2 is very small >> nb van der Waals equation collapses to Ideal Gas Law Imptant at high P Page 5-5