TOPIC 2. Topic 2. States of Matter (I) - Gases. 1

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1 Chemistry TOPIC 2 States of Matter (I) - Gases Topic 2. States of Matter (I) - Gases. 1

2 Contents 1. Introduction 2. Pressure measurement 3. The Ideal Gas equation 4. Efusion and Diffusion 5. Kinetic Molecular Theory 6. Dalton s Law of Partial Pressure 7. Real Gases: van der Waals equation Topic 2. States of Matter (I) - Gases. 2

3 1. Introduction States of Matter Distances Interactions Movement Solid Short Very strong Highly restricted Liquids Short Strong Restricted Gases Long Weak Almost Free : Principles and Moderns Applications R.H. Petrucci Topic 2. States of Matter (I) - Gases. 3

4 1. Introduction Where do we find gases? _exhaust_gas.jpg Topic 2. States of Matter (I) - Gases. 4

5 2. Pressure Measurement Barometer UNIVERSIDAD CARLOS III DE MADRID Vaccum Column of mercury P = d g h d = density g = gravity h = height 760 mmhg for standard atmosphere Atmospheric pressure 1 atm = 760 mmhg atmospheric pressure at sea level 1 Torr = 1 mmhg Pa = N/m 2 <> 1/ Torr Standard Atmospheric Pressure 1.00 atm 760 mm Hg, 760 Torr kpa bar mbar Topic 2. States of Matter (I) - Gases. 5

6 2. Pressure Measurement UNIVERSIDAD CARLOS III DE MADRID Manometer P atm Open end Closed end P h = ρ (Hg) g h P gas P gas ρ (Hg) = density of mercury 13.6 g cm 3. g = 9.8 m s -2. h = distance B-N (in m). (a) (b) P gas = P h P gas = P atm + P h Topic 2. States of Matter (I) - Gases. 6

7 3. Gases Laws Boyle s Law P 1/V when T & n are constant P V = k P 1 V 1 = P 2 V 2 = P 3 V 3 = For a fixed amount of an ideal gas at a constant temperature, pressure and volume are inversely proportional. Topic 2. States of Matter (I) - Gases. 7

8 3. Gases Laws Charles and Gay-Lussac s Law UNIVERSIDAD CARLOS III DE MADRID V T V 1 /T 1 =V 2 /T 2 =k (P & n constant) V = a(t + 273) where: - V=volume - t=temperature in Celsius - a= slope of the straight line. T = t T= Absolute temperature (K) Image from: For a fixed amount of an ideal gas at a constant pressure, the volume is directly proportional to the temperature. V = c T Topic 2. States of Matter (I) - Gases. 8

9 3. Gases Laws The Ideal Gas equation UNIVERSIDAD CARLOS III DE MADRID Boyle s law V 1/P Charles s law V T Avogadro s law V n The Gas Constant V nt P PV = nrt At STP (0 ºC and 1atm) 1 mol gas = 22.4 L gas R pv 1atm*22.4L = = = 0. nt 1mol *273.15K 082 atml Kmol R = 8, atmlmol -1 K -1 <> Jmol -1 K -1 <> 1,987 calmol -1 K -1 Topic 2. States of Matter (I) - Gases. 9

10 4. Diffusion and Efusion UNIVERSIDAD CARLOS III DE MADRID Diffusion Graham s Law Graham's law states that the rate of diffusion of a certain gas is inversely proportional to the square root of its molecular weight. R 1 ρ R 1 M Topic 2. States of Matter (I) - Gases. 10

11 4. Diffusion and Efusion Why do tyres deflate? Efusion rate rate of of effusion of effusion of A B R R A B = = Graham s Law B M M A Topic 2. States of Matter (I) - Gases. 11

12 5. Kinetic Molecular Theory Why do tyres deflate? Particles are point masses (with no volume) in constant, random and straight line motion. Particles are separated by great distances, almost infinite. Collisions are elastic. There are no intermolecular forces between the particles. The total energy of the system remains constant. N Probabilit y V Nmu 3V N Concentration = V 2 Energy per collision = mu p = 2 No. Molecules (%) u m u av u rms u m is the modal speed u av is the simple average u 2 rms = u Degrees of liberty = Speed (m/s) Topic 2. States of Matter (I) - Gases. 12

13 5. Kinetic Molecular Theory Let s consider 1 mol of gas: PV = 1 3 N A mu If PV = RT (for n= 1 mol): 3RT = N 3RT = Mu mu Considering that N A m = M: A Relative number of Mole ecules (%) u rms = Oxygen at 273 K Oxygen at 1000 K Hydrogen at 273 K 3RT M u rms = 3RT M Speed (m/s) Topic 2. States of Matter (I) - Gases. 13

14 6. Dalton s Law of Partial Pressure The total pressure of a mixture of gases is the sum of the pressures that each gas would exert if it were present alone. p T = p A + nrt i pi = V p B + p C N + = p i= 1 i p χ i = ipt where : V, T constant χi = mole fraction p = total pressure T Example: Calculate the total pressure of a mixture of H 2 and O 2 whose partial pressures are P H2 = 2.9 atm and P O2 = 7.2 atm respectively P 1 = 3.1 atm P 2 = 6.4 atm P total = P 1 + P 2 = 9.5 atm Topic 2. States of Matter (I) - Gases. 14

15 7. Real Gases For exactly one mole of an ideal gas: UNIVERSIDAD CARLOS III DE MADRID The factor Z = PV/NRT is known as COMPRESSIBILITY FACTOR and should be one for an ideal gas. For exactly one mole of a real gas: a) Effect of the nature of the gas b) Effect of the temperature 3 2 PV RT =1.0 1 NH3 CH4 H2 Ideal Gas PV RT = K 500 K 200 K Ideal Gas P(atm) Topic 2. States of Matter (I) - Gases P(atm)

16 7. Real Gases UNIVERSIDAD CARLOS III DE MADRID P V = n R T The Ideal Gas Equation P + an 2 (V nb) = nrt ( ) V 2 The van der Waals Equation (a real gas equation) Pressure Correction Volume Correction a: Effect of intermolecular forces (i.e. nature of the gas) b: Effect of molecular volume Particles are NOT point masses (with no volume as states the kinetic molecular theory). Topic 2. States of Matter (I) - Gases. 16

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