Packet 7

1. Packet 7 Gases

2. Gas Laws Crossword Handout Why study gases? • What is our atmosphere composed of? • Gas behavior can be described by fairly simple math formulas. • Some common elements (oxygen and nitrogen) are gases. • Many solvents – like gasoline – easily evaporate. Those vapors are gases!

3. atmosphere, atm atmospheric pressure Avogadro’s law Boyle’s law Charles’ law combined gas law dependent variable direct relationship ideal gas law independent variable inverse relationship kinetic molecular theory, KMT mmHg Molar volume pressure STP, standard temperature & pressure torr universal gas constant, R vapor pressure Concept Area I: Terminology

4. Concept Area II: Properties of Gases • You should understand and be able to explain the “basics” of KMT. • You should be able to explain common observations with gases; for instance, why hot air balloons fly, or why a smell fills a room.

5. Kinetic Molecular Theory • We’ve mentioned in chapter 2 that thermal energy is the kinetic energy of molecules. • Molecules, atoms, and ions are always in motion unless they are at _______________. • Of course, they are too small to see. So, we use Kinetic Molecular Theory to explain what is happening at the submicroscopic level using the macroscopic properties that we can see. • First, what determines if our submicroscopic particles will be a gas, liquid or solid?

6. Reviewing The Three States of Matter zipping • The gas particles are around like crazy. • The liquid particles are around a bit. • The solid particles are a little. • The gas particles are very far apart. • The liquid particles are spaced out a little. • The solid particles are tightly packed. moving jiggling • Above, a flask of nitrogen liquid is allowed to evaporate into gas.

7. CHE 170 Packet 5 - 7 Kinetic Molecular Theory • A gas contains a large number of individual particles that are so small as compared with the container size that even though the particles have mass, they have essentially no volume. • Average kinetic energy of a particle is proportional to its temperature in Kelvin. • The gas particles constantly move in random straight line until they collide with each other or container walls. These collisions are completely elastic – no energy is lost.

8. Implications of Kinetic Molecular Theory • How are speed, kinetic energy and temperature related? • What causes pressure according to this theory? • How can we increase the pressure of a gas?

9. 1. How are speed, kinetic energy and temperature related? The ________ the speed of particles, the ________ kinetic energy they possess, and the _________ the temperature of the sample!

10. 2. What causes pressure according to this theory? left image: Timberlake page 261

11. 3. How can we increase the pressure of a gas? Increase number of collisions by

12. Why does heating a sealed container of gas increase the pressure? • We are increasing the temperature of the gas particles, so what is happening to the speed of the particles? _________________ • This will also __________ the number of collisions with the container walls which in turn will __________ the pressure!

13. Why is there less pressure at higher altitudes? • Because there are ________ gas particles above items at higher altitudes. • Yes, that’s right. At any given time we have an enormous amount of pressure from all the gases in the atmosphere pushing down on us! • Why aren’t we crushed? Timberlake page 262 & 264

14. Why does a hot air balloon rise? • Like with the sealed container, we are still increasing the temperature of the gas particles, however, this time the container size is not fixed. • Thus, the gas particles are allowed to the volume they take up. Once they do, the . in the balloon becomes less, and it rises!

15. According to the Maxwell-Boltzmann distribution, . Notice at 273 K, the most probably speed for N2 is about 500 m/s. At 1000 K, it increases to about 900 m/s. It increases to about 1100 m/s at 2000 K. At all these temperatures, however, there are particles moving at many other speeds – faster & slower. Great! Then, are all particles in a container moving at the same speed?

16. Another question: What if the particles aren’t all the same? Would helium gas and oxygen gas have the same most probable speed? • No, they don’t. Oxygen would move slower than the other gases shown below. Why is that? Tro page 190

17. Another question: If we have the same amount of oxygen and helium in in separate containers of equal volume at the same temperature, which container would have the higher pressure, if either? Why? representing He representing O2 Tro page 190

18. One last question: • Which of the following samples of an ideal gas, all at the same temperature, will have the greatest pressure? • Why? Tro page 190

19. Concept Area III: Calculations with Gases • You need to know what STP conditions are. • You need to know how to convert between millimeters of mercury, torr and atmospheres. • You should be able to explain and use the following laws: Boyle’s Law, Charles’ Law, Combined Gas Law, and the Ideal Gas Law. • You should be able to combine gas calculations with stoichiometry problems. • You are not responsible for Dalton’s Law of partial pressures.

20. STP: Standard Temperature & Pressure • We have defined some standard conditions. They are: • temperature: • pressure: • Be sure to memorize these values!

21. Amount measured in ___________________ symbol/variable used: ____ Temperature – measured in measured in ___________________ symbol/variable used: ____ Volume – measured in measured in ___________________ symbol/variable used: ____ Pressure – measured in measured in ___________________ symbol/variable used: ____ What four variables will define a gas’ state?

22. Pressure, P • Where F is in newtons (N) and A is in square meters (m2). So, the SI unit for pressure is N/m2 = pascal (Pa). • For gasses, we typically compare their pressure against that of the atmosphere, so we use relative pressure instead of total pressure.

23. Pressure • At 0º C and where the force of gravity is 9.80665 m/s2, the atmosphere exerts a pressure that will cause a column of mercury in a barometer to be 760 mm tall. This is defined as one atmosphere, atm. • So, we now know that760 mm Hg = 1 atm. Timberlake page 264

24. Pressure Conversions • Okay, so we just learned that normal atmospheric pressure creates a column of mercury 760 mmHg tall, so • What about other units for pressure? • Also, just for you information • 760 mmHg = 101,325 Pa = 29.921 in Hg = 1.01325 bar • Now, how do we convert these equalities to conversion factors?

25. Gas Laws Demos Handout Gas Laws Demos

26. Volume versus PressureBoyle’s Law • At constant T, P1V1 = P2V2. • Boyle noticed that as the volume decreased on a closed container of gas, that the pressure increased. • Upon further investigation, he found their relationship: the volume of gas varies inversely with its pressure. • What demonstration corresponds with this? • Also note, gas canisters use this principle so that we can store the gas in a smaller container. Many times, the gas is under such high pressure that it is condensed into liquid! updated bottom image on Timberlake page 267

27. Why is Boyle’s Law important to scuba divers? • This very question was asked of the main character in Men of Honor. • Well, what would happen if they held their breath while going back up to the surface? Timberlake page 277

28. Temperature versus VolumeCharles’ Law • At constant P, . • Charles decided to study the effect of temperature on volume. He found their relationship to be linear: V a T. • What demonstration corresponds with this? Remember, can’t have negative volumes, so can’t use a temperature scale with negative values. Always use Kelvin! updated top right image on Timberlake page 270

29. Temperature versus PressureAmonton’s Law or Gay-Lussac’s Law • Our last relationship could be derived from the previous to give: • If we think back to KMT, we should have no problem with this relationship! • What demonstration corresponds with this? updated image Timberlake page 273

30. Moles versus VolumeAvogadro’s Law • Avogadro hypothesized that different gases if compared at the same Temperature and Pressure would have the same number of molecules in equal Volumes. • So, if we have 1 mol of He and 1 mol of CO2, Avogadro believed those two differently sized and massed molecules would take up the same volume (if T and P were constant). • This idea was finally accepted (four years after Avogadro died) in 1860. • So, at STP (Standard Temperature & Pressure) which is 0ºC and 1 atm, 1 mol of gas will have a volume of 22.4 L. Note, only three sig figs. • What demonstration corresponds with this? updated images on Timberlake pages 279 & 280

31. Graphing! • Let’s graph all these relationships on the second page of the Gas Laws Demos handout!

32. See the P vs. V graph is not linear. But, if we graph V vs. 1/P, the graph is linear! Why is that? Also, why is the volume on the x-axis on the left but on the y-axis up above?

33. Note with this V vs. T graph that we can extrapolate back to –273.15ºC. Why would that be? Even though this graph is in ºC, in calculations we must use Kelvin in calculations! This graph is just to help visualize where the concept of absolute zero came from.

34. The Combined Gas Law • What was found to be the single mathematical expression for our four variables? (That’s the third question on our handout.) • Hopefully you have noticed that that if we combine Boyle’s Law, Charles’ Law and Avogadro’s Law we get the Combined Gas Law: • We can use this law to determine how one variable changes when the other three are held constant. Helpful problem solving hint: if problem doesn’t mention a variable, assume it remains constant! • Remember, we only care about final and initial states. The initial state is usually called “1” and the final state is usually called “2”.

35. Practice time! A happy child gets a balloon at the mall. The balloon has a maximum capacity of 5.00 L. To save on helium costs, mall policy dictates that the balloons be filled only to 4.77 L. The mall keeps the temperature at a comfortable 22.00 ºC. • Will our child still be happy upon exiting the mall if the outside temperature is 34.20 ºC, in other words, will the balloon pop? • If the balloon survives to the car, will it survive the interior temperature of the car, 37.50 ºC?

36. Another problem applying the combined gas law: If a 20.0 lb bag of pure NH4NO3 were detonated, what total volume of gases would be produced at 25.0ºC and 751 torr?2 NH4NO3(s) → 2 N2(g) + 4 H2O(g) + O2(g) Note: the notes page for this slide show this problem worked out!

37. 3.83 L 2.19 L (don’t use Celcius or get wrong answer of 2.65 L) 1.43 g 26.2 L 0.470 g C 8.73 L of Freon gas has a pressure of 735 mmHg. What will be the volume if the pressure increases to 1675 mmHg? If a gas occupies 2.15 L at 24.5ºC, how much volume will it take up at 30.2ºC? What’s the weight of 1.00L of O2 at STP? What volume does 1 mol of gas fill at 30.0ºC at 720 torr? Given the following reaction: 2C + O2→ 2 CO, how many grams of carbon are needed to react completely with 500 mL O2 gas at 30.0ºC and 740 torr? *Can also use the ideal gas law to solve this one, and probably would use it once we’ve learned. Some problems (with answers) for home practice: Note: the notes page for this slide shows these problems worked out!

38. The Ideal Gas Law • What if conditions aren’t changing and we just want to know the value of the one variable we don’t know (like in that last problem)? • Remember that single mathematical expression we found for our four variables on the worksheet? • We can combine all of our relationships into one expression: • Then, introduce a proportionality constant, R, to get an equality. R is called the gas constant and is equal to 8.314472 J/mol·K or 0.082057 L·atm/mol·K. or

39. P is pressure – in atm • V is volume – in L • n is number of moles – in mol • R is the gas constant – 0.082057 L·atm/mol·K • T is temperature – in K

40. Solving that earlier problem with PV=nRT: If a 20.0 lb bag of pure NH4NO3 were detonated, what total volume of gases would be produced at 25.0ºC and 751 torr?2NH4NO3(s) → 2 N2(g) + 4 H2O(g) + O2(g) Note: the notes page for this slide show this problem worked out!

41. A crazy example with PV=nRT! An experiment was done where the oxygen consumption was measured while male cockroaches were running on treadmills at different speeds. They found that in one hour an average cockroach running at 0.08 km/hr consumed 0.8 mL of oxygen (per gram of their weight) at 1 atm and 24 ºC. So, how many moles of oxygen would be consumed in one hour by a 5.2 g cockroach running at that speed? Note: the notes page for this slide show this problem worked out!

42. 9.17 L 30.0 kg 0.096 atm 22.0 g of CO2 at 286ºC and 2.50 atm. What is the volume of the CO2? How many kilograms of helium does a balloon have if the volume of the balloon is 1.51×105 L, the pressure is 1.20 atm and the temperature is 22 ºC? Iron reacts with hydrochloric acid to produce iron(II) chloride and hydrogen gas. The hydrogen gas from the reaction of 2.2 g of iron with excess acid is collected in a 10.0-L flask at 25 ºC. What is the pressure of the hydrogen gas in this flask?Fe(s) + 2 HCl(aq) → FeCl2(aq) + H2(g) Some problems (with answers) for home practice: Note: the notes page for this slide shows these problems worked out!

43. The End of Packet 7 Any Questions?