CHAPTER 12. Gases and the Kinetic-Molecular Theory

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1 CHAPTER 12 Gases and the Kinetic-Molecular Theory 1

2 Gases vs. Liquids & Solids Gases Weak interactions between molecules Molecules move rapidly Fast diffusion rates Low densities Easy to compress Liquids & Solids Strong interactions between molecules Molecules move slowly Slow diffusion rates High densities Hard to compress 2

3 Pressure Force per unit area Units of pressure: pounds per square inch (psi) mm Hg = torr atmospheres (atm) pascals (Pa) Normal atmospheric pressure the pressure of air at the sea level at 0 C (=32 F) 1 atm = 760 mm Hg = 760 torr = 101,325 Pa kpa (Evangelista Torricelli ) 3

4 Kinetic-Molecular Theory Explains the behavior of gases in terms of molecular motion The kinetic energy of gas molecules depends on their velocities: 2 mv E = 2 The gas exerts pressure due to the molecular motion: many molecules have to strike the surface to produce this macroscopic effect 4

5 Boyle s Law p V = const = k p pressure V volume (at constant temperature and amount of gas) p 1 V 1 = p 2 V 2 5

6 Boyle s Law Molecular Picture p 1 V 1 = p 2 V 2 The amount of gas (the number of gas molecules) remains constant The temperature is constant and therefore the kinetic energy of gas molecules remains about the same If the volume is decreased, then higher number of gas molecules strike a unit area, therefore the pressure increases If the volume is increased, the reverse effect takes place the pressure decreases 6

7 Boyle s Law Example A 1.00 L sample of gas at 760 mm Hg is compressed to L at constant temperature. Calculate the final pressure of the gas. 7

8 Charles Law V T or V = kt (at constant pressure and amount of gas) This equation defines a straight line Extrapolating this line to V =0 results in the absolute zero of temperature on the Kelvin temperature scale V 1 = T 1 V T 2 2 8

9 Charles Law Molecular Picture The amount of gas (the number of gas molecules) remains constant As the temperature increases, the thermal energy is converted into the kinetic energy and gas molecules move faster The gas molecules strike the surface more vigorously and, if the pressure is to be kept constant, the gas has to expand If the temperature is decreased, the volume also decreases V 1 = T 1 V T 2 2 9

10 Charles Law Example A sample of gas at 1.20 atm and 27 C is heated at constant pressure to 57 C. Its final volume is 4.75 L. What was its original volume? 10

11 Combined Gas Law For a constant amount of gas pv 1 T 1 1 = pv 2 T 2 2 Both Boyle s Law and Charles Law can be derived from the Combined Gas Law The reverse is not true! 11

12 Combined Gas Law Example A 4.00 L sample of gas at 30 C and 1.00 atm is changed to 0 C and 800 mm Hg. What is its new volume? 12

13 Ideal Gas Equation pv = nrt p pressure V volume n # of moles of the gas T temperature R universal gas constant R = J/(mol K) = (L atm)/(mol K) 13

14 Ideal Gas Equation pv = nrt Let s calculate the volume of 1 mole of some gas at 0 C and 1 atm: 14

15 Standard Molar Volume The standard molar volume of an ideal gas is equal to liters per mole at standard temperature and pressure Standard temperature and pressure (STP) T = K = 0 C = 32 F p = 760 torr = 1 atm = 101,325 Pa 1 mole of an ideal gas occupies L volume ONLY at standard temperature and pressure To find the volume of 1 mole at different conditions we have to use other gas laws 15

16 Avogadro s Law At the same temperature and pressure, equal volumes of all gases contain the same number of molecules At constant T and p, the volume V occupied by a sample of gas is directly proportional to the number of moles n V n or V = kn V 1 = n 1 V n

17 Standard Molar Volume Example What volume will be occupied by 32.0 g of oxygen at STP? How will this volume change if the pressure is increased to 3 atm and the temperature is raised to 100 C? 17

18 Ideal Gas Equation Example At 750 torr and 27 C, 0.60 g of a certain gas occupies 0.50 L. Calculate its molecular weight. 18

19 Ideal Gas Equation Example A gas is composed of 30.4% N and 69.6% O. Its density is 11.1 g/l at -20 C and 2.50 atm. What is the molecular formula of the gas? 19

20 Ideal Gas Equation Example What volume of hydrogen will be produced in the reaction of 3 g of zinc with the excess of diluted hydrochloric acid, if the reaction is carried out at room temperature (25 C) and standard atmospheric pressure (1 atm)? 20

21 Dalton s Law Mixture of gases: A, B, C, Partial pressure pressure that a gas would exert if it alone occupied all the volume occupied by the mixture of gases 21

22 Dalton s Law Example Calculate the pressure of the mixture of 0.25 mol of H 2 and 0.75 mol of N 2 if at 25 C it occupies the volume of 12 L. 22

23 Mole Fraction Mixture of gases: A, B, C, Mole fraction of gas A: n A X A = = na + nb + nc + n... n A tot 23

24 Mole Fraction Mixture of gases: A, B, C, Mole fraction of gas A: n A X A = = na + nb + nc + n... n A tot p X = A = A p + p + p + A B C p... p A tot 24

25 Dalton s Law Example Into a 5.00 L container at 18 C are placed 2.00 g H 2, 44.0 g CO 2, and 16.0 g O 2. Calculate the total pressure in the container, the partial pressure and the mole fraction of each gas. 25

26 Assignments & Reminders Read Sections 12-1 through Homework #8 is now accessible on OWL HAPPY THANKSGIVING! 26

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