1 Chapter 5 The Gas Laws

2 n Gas molecules fill container n Molecules move around and hit sides. n Collisions are force. n Container has area. n Measured with a barometer.

3 First Barometer Invented by Torricelli n The pressure of the atmosphere at sea level will hold a column of mercury 760 mm Hg. n 1 atm = 760 mm Hg 1 atm Pressure 760 mm Hg Vacuum

4 Manometer Gas h n Greater Atmospheric Pressure P gas = P atm - h Gas Pressure Less Than Atmospheric Pressure

5 Manometer n Higher Gas Pressure P gas = P atm + h h Gas Gas Pressure Greater Than Atmospheric Pressure

6 Units of pressure n 1 atmosphere = 760 mm Hg = 760 torr = 101,325 Pascals = kPa n Can make conversion factors from these.

7 n What is 724 mm Hg in kPa? n in torr? n in atm?

8 The Boyle’s Gas Laws n Pressure and volume are inversely related at constant temperature. n PV= k n As one goes up, the other goes down. n P 1 V 1 = P 2 V 2 n Ideal Gas is one that strictly obeys Boyle’s Law n What does it look like graphically?

9 Volume Pressure Pressure vs. Constant Temperature

10 Volume 1/Pressure Slope = k 1/Pressure vs. Constant Temperature

11 Pressure x Volume Pressure CO 2 O2O L atm Ne Ideal Gas PV vs. P For Several Gases Below 1 Atm

12Examples 20.5 L of nitrogen at 25ºC and 742 torr is compressed to 9.8 atm at constant Temperature. What is the new volume? What is the new volume? Need to be in same units Your turn #33 p. 219

13 Charle’s Law n Volume of a gas varies directly with the absolute temperature at constant pressure. n V = kT T must be in Kelvin n Graphically

14 V (L) T (ºC) He H2OH2O CH 4 H2H ºC Volume vs. Constant Pressure

15 Examples n What would the final volume be if 247 mL of gas at 22ºC is heated to 98ºC, if the pressure is held constant? Change o C to K V 2 = 3.10 x 10 2 mL Your Turn - #34 p. 219

16 Avogadro's Law n n At constant temperature and pressure, the volume of gas is directly related to the number of moles. n n (n = number of moles) n n Try #35 p. 220

17 Gay- Lussac Law n At constant volume, pressure and absolute temperature are directly related. n What would be the final pressure of a gas at 243 kPa and 355K if it was heated 15K more?

18 Combined Gas Law n If the moles of gas remains constant, use this formula and cancel out the other things that don’t change.

19 Ideal Gas Law n PV = nRT »V in L, »P in atm, »T in K n R is the universal gas constant, there are 4 different numbers depending on units. n Watch the units when setting up Ideal Gas Law – they all must match

20 Ideal Gas Law n An equation of state. n Where the state of the gas is its condition at the given time described by pressure, volume, temperature and number of moles. n Given 3 values in equation, you can determine the fourth. n An Ideal Gas is an hypothetical gas whose behavior is described by the equation

21 Ideal Gas Law n Think of it as a limit. n Gases only approach ideal behavior at: » low pressure (< 1 atm) & »high temperature n Use the laws anyway, unless told to do otherwise. n They give good estimates.

22 Practice Using Formula p n n Ideal Gas Law I – Calc. # mol Ex. 5.6 p.187 n n Solve for n n n Be careful, make sure all units match n n Ideal Gas Law II – Calc. final press. Ex.5.7 p. 188 n n Through algebraic manipulation, the problem becomes a simple Boyles problem.

23 Practice Using Formula p  Ideal Gas Law III – Calc. new vol. Ex. 5.8 p. 188  Through algebraic manipulation, the problem becomes a simple Charles Law problem.  Ideal Gas Law IV – Calc. vol. Ex. 5.9 p.189  Through algebraic manipulation, the problem becomes a simple Combined Gas Law problem. Try a couple: p.220 #44, & 46

24 Gases Stoichiometry n Reactions happen in moles n At Standard Temperature and Pressure (STP, 0ºC and 1 atm) 1 mole of gas occuppies L. n If not at STP, use the ideal gas law to calculate moles of reactant or volume of product. What is the volume of an ideal gas at STP? Show complete setup.

25 #53 p. 221 Try #54

26 Gas Density and Molar Mass Substitute above into ideal gas equations gives: Because: we can substitute D for m/V giving new equation OR Now if know density of gas, you can find molar mass

27 Think Through #61 p. 221 Know the formula Know the density = 3.164g/L Know R = Know STP: Temperature = 273K, Pressure = 1 atm It’s a “Plug and Chug” The gas is diatomic so 7.098x10 -1 / 2 = g which is the atomic mass of Cl so the gas is Cl 2

28 Dalton’s Law n The total pressure in a container is the sum of the pressure each gas would exert if it were alone in the container. n P Total = P 1 + P 2 + P 3 + P 4 + P 5... n For each P = nRT/V

29 Dalton's Law n P Total = n 1 RT + n 2 RT + n 3 RT +... V V V n In the same container R, T and V are the same.

30 The mole fraction n Ratio of moles of the substance to the total moles. n Read the derivation of the mole fraction on p. 195 symbol is Greek letter chi  symbol is Greek letter chi 

31 Examples 3.50 L O L N atm n When these valves are opened, what is each partial pressure and the total pressure? 4.00 L CH atm atm

32 Vapor Pressure n Water evaporates! n When that water evaporates, the vapor has a pressure. n Gases are often collected over water so the vapor pressure of water must be subtracted from the total pressure. n It must be given. n See #71-73 p. 222

33 Kinetic Molecular Theory n Explains why ideal gases behave the way they do. n Postulates simplify the theory, but don’t work in real gases.  The particles are so small we can ignore their volume.  The particles are in constant motion and their collisions cause pressure.

34 Kinetic Molecular Theory  The particles do not exert force on each other, neither attracting or repelling.  The average kinetic energy is proportional to the Kelvin temperature. n Appendix 2 p. A13 shows the derivation of the ideal gas law. n Kelvin temperature is the result of random motions of particles.

35Effusion n Passage of gas through a small hole, into a vacuum. n The effusion rate measures how fast this happens. n Graham’s Law the rate of effusion is inversely proportional to the square root of the mass of its particles.

36 Diffusion n The spreading of a gas through a room. n Slow considering molecules move at 100’s of meters per second. n Collisions with other molecules slow down diffusions.

37 Real Gases n Real molecules do take up space and do interact with each other (especially polar molecules). n Need to add correction factors to the ideal gas law to account for these.

38 Pressure correction n Because the molecules are attracted to each other, the pressure on the container will be less than ideal n depends on the number of molecules per liter. n since two molecules interact, the effect must be squared.

39 Deriving the Ideal Gas Law AKA Physicists Having Fun P = Pressure n = moles N A = Avogadro’s number m = mass of particle u 2 = average velocity V = Volume of container

40 Volume Correction n The actual volume free to move is less because of particle size. n More molecules will have more effect. n Corrected volume V’ = V - nb n b is a constant that differs for each gas. n P’ = nRT (V-nb)

41 Pressure correction n Because the molecules are attracted to each other, the pressure on the container will be less than ideal n depends on the number of molecules per liter. n since two molecules interact, the effect must be squared. P observed = P’ - a 2 () V n

42 Altogether n P obs = nRT - a n 2 V-nb V n Called the Van der Wall’s equation if rearranged n Corrected Corrected Pressure Volume ()

43 Where does it come from n a and b are determined by experiment. n Different for each gas. n Bigger molecules have larger b. n a depends on both size and polarity. n once given, plug and chug.

44 Example n Calculate the pressure exerted by mol Cl 2 in a L container at 25.0ºC n Using the ideal gas law. n Van der Waal’s equation –a = 6.49 atm L 2 /mol 2 –b = L/mol