Ch 12 Gases

1. Ch 12 Gases • Three reasons for studying gases • 1. Some common elements and compounds exist as gases • 2. Our atmosphere is gaseous • 3. Gas behavior is easy to understand at the molecular level, using a mathematical model, which works for most gasses.

2. Properties of gases • Gases can be described using four quantities P, V, T (in K) and n (moles)

3. Gas Pressure A tube is filled with mercury. The tube is inverted into a dish containing mercury. The mercury assumes a level in the tube such that the pressure exerted by the mass of the column of mercury in the tube is balanced by the pressure of the atmosphere pressing down on the surface of the mercury in the dish. At seal lever, the mercury-filled barometer will rise a760 mmHg in the tube. This unit is sometimes called the torr for Torricelli inventor of the barometer

4. Gas Pressure This Galileo thermometer combines art with science. It provides an accurate reading of current weather conditions. Temperature is indicated by the lowest "floating" sphere in the top grouping. As accurate as laboratory thermometers. Predict changes in the weather by referencing fluid rise and fall in the barometric tube. The hygrometer measures humidity. How the thermometer works:The colored floating spheres are "pushed" either up or down depending on the changing density of the clear fluid inside the glass thermometer body. When the temperature goes up, the clear fluid becomes less dense and rises - forcing the spheres down one by one. When the temperature goes down, the clear fluid becomes denser - forcing the spheres upward. 

5. Gas Pressure How the barometer works:While not as accurate as modern day aneroid barometers, the principle of the early "Water Barometer" is sound. When atmospheric pressure decreases, the fluid is pulled upward toward the top of the barometer tube (low pressure). As atmospheric pressure increases, the fluid is "pushed down" (high pressure). Standard atmospheric pressure at sea level is 29.92".

6. Gas Pressure Water-based barometers This concept of "decreasing atmospheric pressure predicts stormy weather" was invented by Lucien Vidie It consists of a glass container with a sealed body, half filled with water. A narrow spout connects to the body below the water level and rises above the water level, where it is open to the atmosphere. When the air pressure is lower than it was at the time the body was sealed, the water level in the spout will rise above the water level in the body; when the air pressure is higher, the water level in the spout will drop below the water level in the body.

7. Gas Pressure An aneroid barometer uses a small, flexible metal box called an aneroid cell. This aneroid capsule(cell) is made from an alloy of beryllium and copper.[2] The evacuated capsule (or more usually capsules) is prevented from collapsing by a strong spring. Small changes in external air pressure cause the cell to expand or contract. This expansion and contraction drives mechanical levers such that the tiny movements of the capsule are amplified and displayed on the face of the aneroid barometer.

8. Gas Pressure When the pressure gauge is applied to the valve stem of a tire, the pressurized air from the tire rushes in and pushes the piston toward the right. The distance the piston travels is relative to the pressure in the tire. The pressurized air is pushing the piston to the right, and the spring is pushing back

9. Gas Pressure The calibrated rod fits inside the spring. The calibrated rod rides on top of the piston, but the rod and the piston are not connected and there is a fairly tight fit between the rod and the stop. When the piston moves to the right, it pushes the calibrated rod. When the pressure is released, the piston moves back to the left but the rod stays in its maximum position to allow you to read the pressure.

10. Units of Gas Pressure 1 standard atmosphere = 1 atm 1 atm = 760 mm Hg The SI unit of Pressure is the pascal (Pa) Pressure = force / area 1 Pa = 1 newton / meter2 a Pa is small so kPa is used 1 atm = 760 mmHg = 101.3 kPa = 1.013 bar

11. Units of Gas Pressure Convert 635 mm Hg into atm and kPa Rank the following in decreasing order 75 kPa, 250 mm Hg, 0.83 bar, 0.63 atm.

12. Gas Pressure and Volume Boyle dbhs.wvusd.k12.ca.us/webdocs/GasLaw/Gas-Boyle.html Volume is inversely proportional to Pressure when n and T are constant P V = constant when n and T are constant P1V1 = P2V2 www.onr.navy.mil/Focus/blowballast/sub/work4.htm

13. Gas Temperature and Volume Charles Law www.chm.davidson.edu/ChemistryApplets/GasLaws/CharlesLaw.html

14. Gas Temperature and Volume Charles Law allows the calculation of absolute 0 or 0 K

15. Combined Gas Las • Combination of Charles and Boyle’s Law • The ratio between the pressure-volume constant and the temperature of a system remains constant.

16. Combined Gas Las • Weather balloons • http://www.ultimatechase.com/chase_accounts/Weather_Balloon_Launch.htm • You have a 22 L cylinder of He at a pressure of 150 atm and at 31 oC. How many balloons can you fill, each with a volume of 5.o L, on a day when the atmospheric pressure is 755 mmHg and the temperature is 22 oC?

17. Avogadro’s Hypothesis Equal volumes of gases under the same conditions of temperature and pressure have equal numbers of molecules. Four interrelated quantities can be used to describe a gas: P, V, T, and n. These 4 quantities can be made into a mathematical equation by introducing a proportionality constant now labeled R R = .082 l.atm mol. K

18. Ideal Gas Law • http://intro.chem.okstate.edu/1314F00/laboratory/GLP.htm

19. Ideal Gas Law • R has a different value for each different unit of pressure and the other quantities used. Some values are... • R = 8.314472 m3·Pa·K-1·mol-1 • R = 0.08205784 L·atm·K-1·mol-1 • R = 62.3637 L·mmHg·K-1·mol-

20. Ideal Gas Law • The state of an amount of gas is determined by its pressure, volume, and temperature according to the equation:

21. Ideal Gas Law • A balloon with 1300 mol of H2 is at a temperature of 23oC and a pressure of 750 mmHg, what is the volume of the balloon?

22. Ideal Gas Law • As the amount of substance could be given in mass instead of moles, sometimes an alternative form of the ideal gas law is useful. • The number of moles (n ) is equal to the mass m() divided by the molar mass (M): • Then, replacing gives:

23. Density of a Gas • Given that D = m/V rearrange the equation to solve for the D of a gas Divide by V P = m R T Then get only m on one side V M V So D = m = PM V RT

24. Density of a Gas • Calculate the density of CO2 gas. Is it more or less dense than air.

25. Calculating Molar Mass • Calculate the molar mass (M) of a compound when a 0.100 g sample exerts a pressure of 70.5 mm Hg in a 250 mL container at 22.3 oC. The empirical formula is CHF2. Calculate the molecular formula.

26. Gas Laws and Chemical Reactions

27. Gas Laws and Chemical Reactions Use the following reaction to prepare D2. 2 Li(s) + 2 D2O(l) -> 2 LiOD(aq) + D2(g) Place 0.125 g of Li metal in 15 mL of D2O (d = 1.11 g / mL) . What amount od D2 (in moles) can be prepared? If dry D2 gas is captured in a 1450 mL flask at 22.o oC, what is the pressure of the gas in mm Hg?. D has an atomic mass of 2.0147 g/ mol)

28. Gas Laws and Chemical Reactions Write the reaction for the synthesis of ammonia from its elements. Assume that 355 L of H2 gas at 25oC and 542 mm Hg is combined with excess N2gas. What amount (mol) of NH3 gas can be produced? If this amount of NH3 gas is stored in a 125 -L tank at 25 oC, what is the pressure of the gas?

29. Gas and Partial Pressures Dalton’s Law of Partial Pressure the pressure of each gas in a mixture is called its partial pressure P the pressure of a mixture of gases is the sum of the partial pressures of the different gases Ptotal = P1 + P2 + P3….. http://www.chm.davidson.edu/ChemistryApplets/GasLaws/DaltonsLaw.html

30. Dalton’s Law of Partial Pressures

31. Dalton’s Law of Partial Pressures Dalton's Law of Partial Pressures states that for a mixture of gases in a container, the total pressure is equal to the sum of the pressures of each gas. The gas that a diver breathes must be maintained at a partial pressure of 0.20 atm of oxygen. More oxygen could poison the diver, and less would lead to suffocation. The total pressure, however, must be equal to the external pressure to avoid collapsing the lungs. So, a special valve is used to equalize the pressure inside the divers lungs with the external pressure by adding helium gas. The valve also maintains oxygen levels by using Dalton's Law.

32. Dalton’s Law of Partial Pressures

33. Dalton’s Law of Partial Pressures For mixtures of gases, use the quantity mole fraction, X X is defined as the number of moles of a gas in a mixture divided By the total number of moles of all gasses. For a mixture of gas A and gas B and Gas C is written as follows Combining the above equation yields the important equation

34. Partial Pressure Problems Mix 15.o g of C2HBrClF2 with 23.g g of O2 The total P is 855 mm Hg Calculate the P of each gas. The mixture above is placed in a 5.00 L tank at 25oC. What is the total P? What is the P of each gas?

35. Kinetic -Molecular Theory • Gases are point masses in space. - particles small compared to the space they occupy. • Particles are in constant random motion • All gases, regardless of their molecular mass, have the same average kinetic energy at the same temperature.

36. Kinetic -Molecular Theory • http://www.bcpl.net/~kdrews/kmt/kmt.html • http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch4/kinetic4.html

37. Kinetic -Molecular Theory The kinetic energy of a single molecule of mass m is described Below where u is the speed of that molecule. Two important assumptions 1. Not all molecules have the same speed 2. As temp increases, the number of high speed molecules increases. The avg KE of a sample of gas molecules depends only on T

38. Kinetic -Molecular Theory A sample of gas molecules with avg speed u some molecules Have speed u1 other molecules have u2, therefore N is the total number of molecules (n1 + n2 …) Therefore, the avg KE of molecules is related to u2 the avg of The squares of their speeds (called mean square speed) So the avg KE is described below

39. Kinetic -Molecular Theory http://chemed.chem.purdue.edu/genchem/topicreview/ bp/ch4/kinetic4.html#kinetic http://www.chm.davidson.edu/ChemistryApplets/ KineticMolecularTheory/Maxwell.html

40. Kinetic -Molecular Theory

41. Kinetic -Molecular Theory This equation relates mass, average speed, and temperature The square root of the mean square speed, called the Root-mean-square, or rms speed. Where T is in Kelvins And related to molar mass, M, Called the Maxwell equation where R = 8.3144 J / K .Mol All gases have the same average KE at the same Temp However, smaller molecules have greater rms speed

42. Kinetic -Molecular Theory

43. Graham’s Law of Effusion • Diffusion is the mixing of molecules of two or more gases due to their molecular motions. • Effusion is the movement of gas through a tiny opening in a container into another container.

44. Graham’s Law of Diffusion A molecule of an ideal gas moves from point A to point B. The molecule ignores the other molecules present. It moves in a straight line path until it collides against the wall, bounces off, and continues to travel in a new straight-line path, again, ignoring other molecules that it passes by. It behaves like it is a billiard ball that was hit once on an empty table.Using the expression for the root mean square velocity (v = square root of (3RT/M)), at room temperature, the typical velocity should be about 100 - 1000 m/sec. One finds, however, that measured diffusion rates are much slower than the typical velocities of molecules in an ideal gas.

45. Graham’s Law of Diffusion Diffusion times are longer because the average time between collisions between molecules is very short. These collisions prevent the molecules from traveling in a straight line motion. Thus, it takes longer for one molecule to go from point A to point B.

46. Graham’s Law of Effusion

47. Graham’s Law of Effusion • Graham found experimentally that the rate of effusion of a gas is inversely proportional to the square root of the mass of its particles. Rate1 is the rate of effusion of the first gas. Rate2 is the rate of effusion for the second gas. M1 is the molar mass of gas 1 M2 is the molar mass of gas 2.

48. Nonideal Behavior: Real Gases • Real Gases:•Are affected by intermolecular forces of attraction (otherwise, a gas could not become a liquid) •Undergo non-elastic collisions •Do occupy space These differences between how a real gas and and ideal gas act are negligible except at high pressures and low temperature.Real Gases •In the real world, the behavior of gases only conforms to the ideal-gas equation at relatively high temperature and low pressure.

49. Nonideal Behavior: Real Gases

50. Nonideal Behavior: Real Gases Thus, for real gases, the following should be expected when the volume of the container becomes small that the molecules are forced to be closer to each other: