WEBVTT chemistry/general-chemistry/ow 00:00:00.000 --> 00:00:02.300 Hi, welcome back to Educator.com. 00:00:02.300 --> 00:00:08.900 Today's lecture from general chemistry is on gases. 00:00:08.900 --> 00:00:14.500 Going to start off with a brief introduction followed by the following series of topics. 00:00:14.500 --> 00:00:17.700 The first is what we call the kinetic molecular theory of gases 00:00:17.700 --> 00:00:24.300 which is basically a bunch of postulates that describe gas behavior. 00:00:24.300 --> 00:00:35.100 We are then going to go over the parameters that are used to characterize gases--namely pressure, volume, temperature, and moles. 00:00:35.100 --> 00:00:42.100 When we combine those, we are going to get a series of gas laws which relates all four of those parameters. 00:00:42.100 --> 00:00:48.000 All of these simple gas laws are then going to culminate into what we call the ideal gas law. 00:00:48.000 --> 00:00:53.700 After we study the ideal gas law, we are then going to go over some applications of the ideal gas law 00:00:53.700 --> 00:01:01.100 because we can come up with several additional parameters straight from that law. 00:01:01.100 --> 00:01:06.800 A unique topic then is going to be gas mixtures and what we call partial pressures. 00:01:06.800 --> 00:01:17.500 Finally the last topic is going to be stoichiometry and applying it to reactions that involve a gas. 00:01:17.500 --> 00:01:25.500 Then of course as always, we will finish off with a summary followed by some sample problems. 00:01:25.500 --> 00:01:32.500 Basically there are five postulates to the kinetic molecular theory of gases. 00:01:32.500 --> 00:01:34.800 The first one is the following. 00:01:34.800 --> 00:01:46.000 It deals with gas motion and basically tells us that gases travel in straight lines obeying Newton's laws. 00:01:46.000 --> 00:01:49.700 They have straight trajectories; they are in constant motion. 00:01:49.700 --> 00:01:54.100 Number two, the molecules in the gas occupy no volume. 00:01:54.100 --> 00:01:58.800 That is we treat them as individual points. 00:01:58.800 --> 00:02:04.300 In other words, if you look at a gas sample, most of it is actually empty air. 00:02:04.300 --> 00:02:11.100 Number three, when gas molecules collide, we say that they follow elastic collisions. 00:02:11.100 --> 00:02:15.700 That is upon collision, there is no loss of energy. 00:02:15.700 --> 00:02:17.800 There is no transfer of energy. 00:02:17.800 --> 00:02:23.400 You can imagine a bunch of billiard balls colliding with each other. 00:02:23.400 --> 00:02:27.000 After they collide, they bounce off each other and go their separate ways. 00:02:27.000 --> 00:02:33.600 Imagine that but pretty much going on infinitely with no loss of energy. 00:02:33.600 --> 00:02:39.500 Number four, there are no attractive or repulsive forces between gas molecules 00:02:39.500 --> 00:02:46.100 which explains why gases are so diffuse if you will. 00:02:46.100 --> 00:02:51.200 Finally when we talk about the kinetic energy of a gas, 00:02:51.200 --> 00:02:58.400 the kinetic energy of a molecule is really related to its kelvin temperature. 00:02:58.400 --> 00:03:10.600 Any gas that follows these five postulates of the kinetic molecular theory, we call that gas an ideal gas. 00:03:10.600 --> 00:03:14.900 In reality, there is no such thing as an ideal gas. 00:03:14.900 --> 00:03:20.200 But by applying this model, it allows us to make a lot of simplifications and 00:03:20.200 --> 00:03:26.100 a lot of assumptions which allows us to further study the gases and 00:03:26.100 --> 00:03:34.800 use models which help us to describe gas behavior pretty well actually. 00:03:34.800 --> 00:03:38.900 That is the kinetic molecular theory of gases. 00:03:38.900 --> 00:03:43.700 We now next turn to the parameters that are used to characterize gases. 00:03:43.700 --> 00:03:51.100 The parameters are basically pressure, volume, temperature, and moles. 00:03:51.100 --> 00:03:57.600 From physics, pressure is formally defined as the amount of force per unit area. 00:03:57.600 --> 00:04:06.000 Pressure is equal to force per unit area. 00:04:06.000 --> 00:04:12.000 If we had for example a flat surface and we put a box on it, 00:04:12.000 --> 00:04:15.700 that box is applying a downward force on the surface. 00:04:15.700 --> 00:04:19.700 In other words, the box is applying a certain pressure on the surface. 00:04:19.700 --> 00:04:25.900 If we take the same box but we stand it upright this time, same box, 00:04:25.900 --> 00:04:33.400 my area of contact is now a lot smaller than in the first picture. 00:04:33.400 --> 00:04:44.000 In this case, because the area is smaller, the pressure is going to be larger. 00:04:44.000 --> 00:04:49.800 That is our formal definition of pressure as defined from physics. 00:04:49.800 --> 00:04:57.600 But in terms of gases, we are going to describe pressure from a particulate level diagram. 00:04:57.600 --> 00:05:00.800 Imagine a container. 00:05:00.800 --> 00:05:07.300 Basically we have gas particles that are moving in random directions once again following 00:05:07.300 --> 00:05:13.900 the kinetic molecular theory of gases and moving in straight lines, constant motion. 00:05:13.900 --> 00:05:19.300 Not only do the gas particles collide with each other but the gas particles 00:05:19.300 --> 00:05:30.700 also collide with the container wall; collision with container wall. 00:05:30.700 --> 00:05:34.300 When that collision occurs with the wall of the container, that itself 00:05:34.300 --> 00:05:38.900 generates a force just like billiard balls colliding with each other. 00:05:38.900 --> 00:05:48.200 It is this force of impact that we tend to relate to gas pressure. 00:05:48.200 --> 00:06:02.000 Force of impact is proportional to gas pressure. 00:06:02.000 --> 00:06:10.100 For chemistry, for gases, this is our interpretation of pressure. 00:06:10.100 --> 00:06:12.700 Now that we have defined pressure, let's go ahead and talk about 00:06:12.700 --> 00:06:19.700 the common units of pressure that are used to make measurements. 00:06:19.700 --> 00:06:28.400 From physics, the typical units of pressure are going to be ψ which is pounds per square inch and pascal. 00:06:28.400 --> 00:06:40.000 All of us see ψ in tires; we also see ψ for water pressure too. 00:06:40.000 --> 00:06:41.900 We are not going to use ψ and pascal too much. 00:06:41.900 --> 00:06:47.400 Really in chemistry, we are going to use these three--millimeters of mercury, atm, and torr. 00:06:47.400 --> 00:06:54.100 Millimeters of mercury is what we see on a barometer for the weather report. 00:06:54.100 --> 00:06:58.700 We also see that whenever you take your blood pressure reading. 00:06:58.700 --> 00:07:10.600 Atm stands for atmospheres or one atmosphere of pressure. 00:07:10.600 --> 00:07:20.600 Basically one atmosphere of pressure is going to be the pressure roughly at sea level. 00:07:20.600 --> 00:07:25.200 Once again at sea level, we are at roughly one atm of pressure. 00:07:25.200 --> 00:07:42.100 Finally torr, torr is named after Torricelli who invented the barometer. 00:07:42.100 --> 00:07:46.900 Given at the bottom, we have the relationships for each of these units. 00:07:46.900 --> 00:07:55.000 One atm is equal to 14.7 pounds per square inch which is equal to 760 millimeters of mercury 00:07:55.000 --> 00:08:01.000 which is equal to 760 Torr which is equal to 101.325 kilopascals. 00:08:01.000 --> 00:08:03.600 Of course, you see all of these equivalent statements. 00:08:03.600 --> 00:08:10.000 From equivalent statements, we can then use them as conversion factors. 00:08:10.000 --> 00:08:14.600 Now that we have talked about pressure, let's continue on. 00:08:14.600 --> 00:08:20.400 From the kinetic molecular theory, we are told that gases travel in straight paths. 00:08:20.400 --> 00:08:22.300 This implies the following. 00:08:22.300 --> 00:08:25.300 That gases are going to travel in straight paths until they collide with something, 00:08:25.300 --> 00:08:28.100 either with each other or the wall of the container. 00:08:28.100 --> 00:08:34.100 What that says is that gases are going to expand to fill their entire container. 00:08:34.100 --> 00:08:42.000 Hence the volume of a gas is strictly determined by the container that it is placed into. 00:08:42.000 --> 00:08:46.600 The reason why we can do this is because gases are compressible. 00:08:46.600 --> 00:08:52.700 Remember that most of a gas is empty air, that they have negligible volume. 00:08:52.700 --> 00:08:56.200 I could take the same amount of gas in a ten liter bottle 00:08:56.200 --> 00:09:01.300 and compress it easily to a smaller bottle, no problem. 00:09:01.300 --> 00:09:05.100 The common units of volume are going to be liters of course and milliliters. 00:09:05.100 --> 00:09:13.200 Sometimes milliliters, you also see cc or cubic centimeters. 00:09:13.200 --> 00:09:18.700 Another postulate from the kinetic molecular theory is the kelvin temperature. 00:09:18.700 --> 00:09:23.400 We say that the kinetic energy of a gas is proportional to its kelvin temperature. 00:09:23.400 --> 00:09:29.900 In other words, temperature of a gas is directly related to how fast these particles are moving. 00:09:29.900 --> 00:09:33.000 Because it is directly related, this says the following. 00:09:33.000 --> 00:09:36.900 The faster a gas is, the hotter its kelvin temperature. 00:09:36.900 --> 00:09:43.400 We can also interpret this at the particulate level. 00:09:43.400 --> 00:09:53.000 We are saying that kinetic energy is going to be proportional to the temperature in kelvin. 00:09:53.000 --> 00:10:06.000 If you consider a gas sample, if we apply heat to this, of course that is going to result in 00:10:06.000 --> 00:10:25.600 much faster motion because the gases will get more kinetic energy; faster motion, higher kinetic energy. 00:10:25.600 --> 00:10:31.700 Finally the last parameter is the mole amount of a gas. 00:10:31.700 --> 00:10:36.900 For gases, the amount of a gas is going to be related to moles of course. 00:10:36.900 --> 00:10:44.900 Those are the four parameters--pressure, volume, temperature in kelvin, and moles. 00:10:44.900 --> 00:10:50.600 Now that we have introduced the four parameters, we now get into what is called the simple gas laws. 00:10:50.600 --> 00:10:53.000 The simple gas laws basically do the following. 00:10:53.000 --> 00:10:59.700 They are a series of equations that relate the four parameters of a gas that we just covered. 00:10:59.700 --> 00:11:02.800 There are restrictions for these gas laws to work. 00:11:02.800 --> 00:11:05.300 First we assume ideal behavior. 00:11:05.300 --> 00:11:11.500 That is the gas is going to follow all five postulates of the kinetic molecular theory. 00:11:11.500 --> 00:11:14.800 All other parameters are held constant. 00:11:14.800 --> 00:11:20.000 If I compare pressure and volume for example, that means temperature and moles are being held constant. 00:11:20.000 --> 00:11:22.400 All else is held constant. 00:11:22.400 --> 00:11:25.000 Let's go ahead and tackle each of these gas laws now. 00:11:25.000 --> 00:11:27.900 The first gas law is called Charles's law. 00:11:27.900 --> 00:11:35.900 Charles's law states that volume and temperature are directly related, holding pressure and moles constant. 00:11:35.900 --> 00:11:41.700 Volume is directly related to temperature; let's take a look at this. 00:11:41.700 --> 00:11:52.200 If I have this container and these gas particles are moving in random directions, 00:11:52.200 --> 00:11:58.900 if I heat it, the gas particles are going to have more kinetic energy. 00:11:58.900 --> 00:12:08.100 We are going to result in an expansion of the container if the container is flexible. 00:12:08.100 --> 00:12:13.600 This is going to be larger volume. 00:12:13.600 --> 00:12:19.200 That is why if you try heating a balloon up, you see the balloon expanding. 00:12:19.200 --> 00:12:26.000 It is because the temperature is going to increase the kinetic energy of the molecules. 00:12:26.000 --> 00:12:31.400 They are going to push outward on the container, on the wall of the balloon. 00:12:31.400 --> 00:12:41.800 The equation to do this, to quantify Charles's law, is V1 over T1 is equal to V2 over T2. 00:12:41.800 --> 00:12:45.600 That is if we know the initial volume and initial temperature, we can get 00:12:45.600 --> 00:12:50.900 either the final volume or the final temperature, whichever is not given. 00:12:50.900 --> 00:12:54.800 The restriction for this equation is that this must be in kelvin. 00:12:54.800 --> 00:12:57.300 Temperature must be in kelvin. 00:12:57.300 --> 00:13:06.800 Volume, it can be in any units as long as they are identical units. 00:13:06.800 --> 00:13:09.800 That is a pretty straightforward equation to use. 00:13:09.800 --> 00:13:13.800 Volume and temperature are directly proportional to each other. 00:13:13.800 --> 00:13:16.500 The next gas law is what we call Boyle's law. 00:13:16.500 --> 00:13:18.800 Boyle's law states the following. 00:13:18.800 --> 00:13:25.100 That pressure and volume of a gas are inversely related when temperature and moles are held constant. 00:13:25.100 --> 00:13:29.800 That is pressure is inversely related to volume. 00:13:29.800 --> 00:13:39.500 Let's think about this; let's say I had two gas particles in a small container. 00:13:39.500 --> 00:13:44.200 All of a sudden, let's say the size of the container has increased. 00:13:44.200 --> 00:13:47.800 I am holding everything else constant. 00:13:47.800 --> 00:14:03.800 When this happens, I am going to have a smaller rate of collision with the container wall. 00:14:03.800 --> 00:14:13.600 Because my rate of collisions with the container wall is going to be smaller, my force drops off. 00:14:13.600 --> 00:14:19.300 Therefore my pressure is going to drop off. 00:14:19.300 --> 00:14:22.200 Once again pressure is inversely related to volume. 00:14:22.200 --> 00:14:29.900 If you ever go to the higher elevation, you notice that a potato chip bag or a snack bag is always larger. 00:14:29.900 --> 00:14:35.500 It is because at the higher elevation, the outside pressure is much smaller. 00:14:35.500 --> 00:14:40.000 To compensate, the air inside the bag is going to expand. 00:14:40.000 --> 00:14:43.900 This is why balloons also tend to pop the higher they go. 00:14:43.900 --> 00:14:47.300 Because as the elevation increases, the air pressure gets lower. 00:14:47.300 --> 00:14:53.700 The air molecules inside the balloon expand against the walls of the balloon. 00:14:53.700 --> 00:15:02.500 The equation for this, for Boyle's law is P1V1 is equal to P2V2. 00:15:02.500 --> 00:15:13.200 Once again for this equation to work, P1 and P2 must be identical units. 00:15:13.200 --> 00:15:16.900 V1 and V2 also must be identical units. 00:15:16.900 --> 00:15:19.600 Once again this is a rather straightforward equation to use. 00:15:19.600 --> 00:15:26.600 We can calculate any final pressure or volume given the other three parameters. 00:15:26.600 --> 00:15:29.600 That is Boyle's law. 00:15:29.600 --> 00:15:33.300 The next gas law is what we call Gay Lussac's law. 00:15:33.300 --> 00:15:36.200 Gay Lussac's law is pressure and temperature. 00:15:36.200 --> 00:15:43.100 It tells us that pressure and temperature of a gas are directly related when volume and moles are held constant. 00:15:43.100 --> 00:15:50.400 That is pressure is directly related to temperature; that just makes sense. 00:15:50.400 --> 00:15:58.200 When we have gas particles just like this, let's say this is colder. 00:15:58.200 --> 00:15:59.800 That is going to generate some pressure. 00:15:59.800 --> 00:16:09.000 But if we take the same volume, the same box, the same amount, and I heat this sample up, that is going to 00:16:09.000 --> 00:16:22.100 result in obviously a higher rate of collision with the walls of the container; more collisions with container wall. 00:16:22.100 --> 00:16:25.500 That is going to increase my force. 00:16:25.500 --> 00:16:32.300 Because my force goes up, my pressure goes up also. 00:16:32.300 --> 00:16:42.200 On extreme temperature differences, a car tire is always going to be at a lower pressure when it is colder. 00:16:42.200 --> 00:16:48.800 Later in the day when it gets much hotter, the pressure will slightly increase because of this difference. 00:16:48.800 --> 00:16:51.300 The equation for Gay Lussac's law is the following. 00:16:51.300 --> 00:16:56.300 P1 over T1 is equal to P2 over T2. 00:16:56.300 --> 00:17:01.500 Once again the units of pressure must be identical. 00:17:01.500 --> 00:17:09.600 But remember that our temperature is always related in kelvin whenever discussing a gas. 00:17:09.600 --> 00:17:13.500 That is Gay Lussac's law. 00:17:13.500 --> 00:17:17.300 The last simple gas law is what we call Avogadro's law. 00:17:17.300 --> 00:17:19.300 Avogadro's law is the following. 00:17:19.300 --> 00:17:26.400 That the volume and moles of a gas are directly related when temperature and pressure are held constant. 00:17:26.400 --> 00:17:28.800 V is proportional to n. 00:17:28.800 --> 00:17:34.600 Just think about maybe a car tire. 00:17:34.600 --> 00:17:38.800 You put more air into it; you increase the amount of air. 00:17:38.800 --> 00:17:44.600 What happens?--the volume increases. 00:17:44.600 --> 00:17:53.000 The equation for Avogadro's law is V1 over n1 is equal to V2 over n2. 00:17:53.000 --> 00:17:59.800 Once again the volume units must be identical. 00:17:59.800 --> 00:18:04.300 n1 and n2 will always be in moles. 00:18:04.300 --> 00:18:06.200 That is Avogadro's law. 00:18:06.200 --> 00:18:10.800 If you look at the four gas laws, Charles's law, Boyle's law, Gay Lussac's law, 00:18:10.800 --> 00:18:15.700 and Avogadro's law, really Boyle's law is the only one that stands out. 00:18:15.700 --> 00:18:22.600 It is the only where we have something times something is equal to the product of something else. 00:18:22.600 --> 00:18:30.600 Every other gas law is division on the left side of the equation and on the right side of the equation. 00:18:30.600 --> 00:18:39.400 Please make a note of that, Boyle's law is definitely the one that stands out. 00:18:39.400 --> 00:18:44.400 In case your instructor ever requires you to memorize these gas laws. 00:18:44.400 --> 00:18:51.900 When we put all of these simple gas laws together, they culminate into one equation. 00:18:51.900 --> 00:18:58.100 This grand equation is what we call the ideal gas law where PV is equal to nRT. 00:18:58.100 --> 00:19:00.300 When we do this, there are a couple of restrictions. 00:19:00.300 --> 00:19:06.700 That pressure must be in atm; volume must be in liters; n is simply moles. 00:19:06.700 --> 00:19:12.200 The temperature must be in units of kelvin as we always have said. 00:19:12.200 --> 00:19:15.600 There is something we haven't introduced yet; that is what R is. 00:19:15.600 --> 00:19:18.100 R is what we call the universal gas constant. 00:19:18.100 --> 00:19:23.700 It is equal to 0.08206 liters atmosphere K mol. 00:19:23.700 --> 00:19:26.600 Once again you may or may not have to memorize this. 00:19:26.600 --> 00:19:29.200 Definitely refer to your instructor for that. 00:19:29.200 --> 00:19:31.600 That is a relatively straightforward equation to use. 00:19:31.600 --> 00:19:37.200 Pretty much for an ideal gas, I can determine the pressure, volume, moles, 00:19:37.200 --> 00:19:43.100 or kelvin temperature given any of the other three parameters. 00:19:43.100 --> 00:19:47.500 Again this is the ideal gas law. 00:19:47.500 --> 00:19:53.100 Probably something you want to be comfortable with is to solve for a single variable. 00:19:53.100 --> 00:19:57.800 Pressure here is going to be equal to nRT over V. 00:19:57.800 --> 00:20:06.100 Volume is equal to nRT over P; n is equal to PV over RT. 00:20:06.100 --> 00:20:11.400 Temperature is going to be equal to PV over nR. 00:20:11.400 --> 00:20:14.400 That is again the ideal gas law. 00:20:14.400 --> 00:20:16.800 The ideal gas law is relatively straightforward to use. 00:20:16.800 --> 00:20:26.400 But another important aspect of it is that we can derive and come to many conclusions using this law. 00:20:26.400 --> 00:20:34.700 The first relationship that we are going to get from the ideal gas law is what is called standard temperature and pressure. 00:20:34.700 --> 00:20:42.500 It becomes very difficult to compare gases because there is so many parameters--pressure, volume, temperature, and moles. 00:20:42.500 --> 00:20:46.500 A set of universal conditions has been defined. 00:20:46.500 --> 00:20:52.100 This set of universal conditions is called standard temperature and pressure or STP for short. 00:20:52.100 --> 00:20:58.300 Standard temperature is 273.15 kelvin; standard temperature is 1.0 atm. 00:20:58.300 --> 00:21:05.500 When these values are plugged into the ideal gas law, we can go ahead and solve for the ratio of volume to moles. 00:21:05.500 --> 00:21:11.200 When we solve for this ratio of volume to moles, we get exactly 22.4 liters per mole. 00:21:11.200 --> 00:21:17.600 This is what we call molar volume; its significance is the following. 00:21:17.600 --> 00:21:28.100 That at STP, one mole of any ideal gas regardless of its identity occupies a volume exactly 22.4 liters. 00:21:28.100 --> 00:21:34.400 One mole equals 22.4 liters; that is an equivalence statement. 00:21:34.400 --> 00:21:38.100 From that, we can use that as a typical conversion factor. 00:21:38.100 --> 00:21:44.500 Once again molar volume at STP only, 22.4 liters per mole. 00:21:44.500 --> 00:21:52.000 Another application we can derive from the ideal gas law is gas density. 00:21:52.000 --> 00:21:55.400 Gas density is going to be measured in grams per liter. 00:21:55.400 --> 00:21:57.100 We are not going to be in its derivation. 00:21:57.100 --> 00:22:01.700 But the density of a gas in grams per liter is equal to the following. 00:22:01.700 --> 00:22:09.700 It is equal to the molar mass of the gas in grams per mole times 00:22:09.700 --> 00:22:16.700 the pressure in atm divided by the universal gas constant times the kelvin temperature. 00:22:16.700 --> 00:22:22.500 You can convince yourself that when all the units cancel, we are left with grams per liter. 00:22:22.500 --> 00:22:24.900 This equation once again is relatively straightforward to use. 00:22:24.900 --> 00:22:28.300 However there is an important thing that cannot be overlooked. 00:22:28.300 --> 00:22:33.200 We now have a relationship between density and temperature for gases. 00:22:33.200 --> 00:22:39.000 You see here that density is going to be inversely related to the kelvin temperature. 00:22:39.000 --> 00:22:40.600 That means the following. 00:22:40.600 --> 00:22:46.100 That as temperature of a gas goes up, the gas density decreases. 00:22:46.100 --> 00:22:53.100 As temperature goes up, gases tend to become lighter. 00:22:53.100 --> 00:22:58.800 Therefore they tend to rise; this explains why hot air balloons rise. 00:22:58.800 --> 00:23:05.200 As you heat the gas within the walls of the balloon, the gas becomes less dense than air. 00:23:05.200 --> 00:23:14.500 It results in a lower density and results in rising of the hot air, bringing the balloon upwards. 00:23:14.500 --> 00:23:21.100 Once again density is inversely related to the kelvin temperature of a gas. 00:23:21.100 --> 00:23:28.800 A final gas law that focuses on pressure, this is called Dalton's law of partial pressures. 00:23:28.800 --> 00:23:31.900 Dalton's law of partial pressures refers to gas mixtures. 00:23:31.900 --> 00:23:33.300 It tells us the following. 00:23:33.300 --> 00:23:39.400 Pretty much that the whole is equal to the sum of the parts. 00:23:39.400 --> 00:23:46.400 The sum of the individual pressures of each gas component is equal to the total pressure of the gas mixture. 00:23:46.400 --> 00:23:50.700 These individual pressures, the technical term is called partial pressures. 00:23:50.700 --> 00:24:03.400 Basically very simple--the total gas pressure of a mixture is equal to the partial pressure of 00:24:03.400 --> 00:24:07.900 the first gas plus the partial pressure of the second gas, etc. 00:24:07.900 --> 00:24:17.400 Once again the total pressure is equal simply to the sum of all individual pressures. 00:24:17.400 --> 00:24:23.400 We now come back to stoichiometry. 00:24:23.400 --> 00:24:27.900 Stoichiometry is something that we spend a great deal of time on. 00:24:27.900 --> 00:24:32.100 At the basis of stoichiometry was the following. 00:24:32.100 --> 00:24:35.400 We want to go from moles of A to moles of B. 00:24:35.400 --> 00:24:41.300 To do this, we use the conversion factor, the mole to mole ratio. 00:24:41.300 --> 00:24:49.500 From moles of B, you can go to grams using molar mass. 00:24:49.500 --> 00:25:00.900 You can go to atoms and molecules using Avogadro. 00:25:00.900 --> 00:25:06.700 You can go to liters if it is a solution using molarity. 00:25:06.700 --> 00:25:12.500 The same thing applies on the other side to go to moles of A for example. 00:25:12.500 --> 00:25:17.000 We spent a deal of time doing mole to mole conversion and also mass to mass conversions. 00:25:17.000 --> 00:25:24.100 All we are going to do now, we are going to apply our knowledge of stoichiometry to gases. 00:25:24.100 --> 00:25:31.700 If everything is about pretty much getting to moles first, we have an ideal gas law that helps us do that. 00:25:31.700 --> 00:25:40.000 Typically for gas stoichiometry problems, we are going to use ideal gas law where n is equal to PV over RT. 00:25:40.000 --> 00:25:43.900 If we are at standard temperature and pressure, we could take a shortcut. 00:25:43.900 --> 00:25:52.400 We can just use the molar volume to get to moles because we know that one mole equals 22.4 liters. 00:25:52.400 --> 00:25:57.100 In this case, the ideal gas law not needed. 00:25:57.100 --> 00:26:01.000 But again this is only at STP. 00:26:01.000 --> 00:26:05.800 Let's go ahead and do a sample problem then; the question is the following. 00:26:05.800 --> 00:26:13.100 How many liters of oxygen gas at standard temperature and pressure are needed to form 10.5 grams of water vapor? 00:26:13.100 --> 00:26:22.400 As soon as I see the letters STP, I know that I am dealing with 1 atm pressure and 273.15 kelvin. 00:26:22.400 --> 00:26:30.200 I also know that one mole of a gas is going to be equal to exactly 22.4 liters. 00:26:30.200 --> 00:26:38.100 The first thing you always do in stoichiometry is to make sure the chemical equation is balanced like we have always done. 00:26:38.100 --> 00:26:45.400 Here we are going to need two hydrogens and two waters. 00:26:45.400 --> 00:26:53.400 What do we have here?--we have the mass of the water vapor. 00:26:53.400 --> 00:27:02.100 Somehow we want to go from mass of water vapor all the way to liters of O2 gas. 00:27:02.100 --> 00:27:07.100 Because I am at STP, the liters of O2 gas is going to 00:27:07.100 --> 00:27:21.500 come from molar volume which is one mole is equal to 22.4 liters. 00:27:21.500 --> 00:27:30.900 But in order to get the moles of O2, I first need the moles of H2O. 00:27:30.900 --> 00:27:36.300 Before moles of H2O, we then have our mass of H2O which is given. 00:27:36.300 --> 00:27:40.500 There is our basic flow chart; it is pretty much three main steps. 00:27:40.500 --> 00:27:44.400 Let's go ahead and do this. 00:27:44.400 --> 00:27:59.400 10.5 grams of water vapor times 1 mole of water divided by its molar mass of 18.016 grams of water. 00:27:59.400 --> 00:28:01.000 That gives me moles of A. 00:28:01.000 --> 00:28:04.000 Now from moles of A to moles of B using the mole to mole ratio 00:28:04.000 --> 00:28:10.100 which is 1 mole of O2 over 2 moles of H2O. 00:28:10.100 --> 00:28:13.200 Finally now that I am at moles of O2, I can go ahead and 00:28:13.200 --> 00:28:17.100 use molar volume as a conversion factor to go and get volume. 00:28:17.100 --> 00:28:22.700 22.4 liters for every one mole of O2. 00:28:22.700 --> 00:28:26.800 When all is said and done, we get a volume of 6.5 liters that are 00:28:26.800 --> 00:28:34.900 required at STP for this reaction to make 10.5 grams of water vapor. 00:28:34.900 --> 00:28:39.600 Let's now go ahead and summarize this lecture. 00:28:39.600 --> 00:28:43.000 We started off today's lecture with the kinetic molecular theory of gases. 00:28:43.000 --> 00:28:48.300 It is basically five postulates which describe ideal gas behavior. 00:28:48.300 --> 00:28:52.600 We then proceeded to tackle the simple gas laws which basically relates the 00:28:52.600 --> 00:28:59.800 four parameters used to characterize gases--pressure, volume, kelvin temperature, and moles. 00:28:59.800 --> 00:29:05.200 When we culminated all of these simple gas laws, we arrived at the ideal gas law. 00:29:05.200 --> 00:29:14.100 The ideal gas law allows us to come up with many applications including density and its relationship with temperature. 00:29:14.100 --> 00:29:23.900 Finally all of our stoichiometry skills that we established previously can easily apply to gas problems. 00:29:23.900 --> 00:29:29.400 That is our summary; let's go ahead and do a series of sample problems. 00:29:29.400 --> 00:29:35.500 Here is sample problem one; you have a 827 milligram sample of a gas. 00:29:35.500 --> 00:29:44.200 It occupies 0.270 liters when measured at a temperature of 88 degrees Celsius and a pressure of 975 millimeters of mercury. 00:29:44.200 --> 00:29:48.400 Calculate the molar mass of the gas; let's take it one by one. 00:29:48.400 --> 00:29:56.800 Here we have mass; here we have volume, temperature, and pressure. 00:29:56.800 --> 00:30:00.000 The question is asking for molar mass. 00:30:00.000 --> 00:30:04.800 Molar mass, we all know to be in units of grams per mole. 00:30:04.800 --> 00:30:12.400 We have the grams already; that is the 827 milligrams or the 0.827 grams. 00:30:12.400 --> 00:30:14.800 All we have to get then is the moles. 00:30:14.800 --> 00:30:21.400 Once we have that, we can divide the two numbers to give us the molar mass. 00:30:21.400 --> 00:30:25.900 We need to get the moles of this gas which is n. 00:30:25.900 --> 00:30:34.200 We are given pressure, volume, and temperature; that is three out of the four parameters. 00:30:34.200 --> 00:30:38.500 We can go ahead and use the ideal gas law to help us do this. 00:30:38.500 --> 00:30:45.600 Moles is equal to PV over RT. 00:30:45.600 --> 00:30:50.900 Pressure is 975 millimeters of mercury. 00:30:50.900 --> 00:30:53.500 We have to then go ahead and convert this to atm remember. 00:30:53.500 --> 00:30:57.400 That is our restriction. 00:30:57.400 --> 00:30:59.900 We are going to multiply this by the volume in liters. 00:30:59.900 --> 00:31:02.700 It is already in liters. 00:31:02.700 --> 00:31:10.900 We are going to divide this by the universal gas constant. 00:31:10.900 --> 00:31:16.500 We are going to then multiply this by the kelvin temperature. 00:31:16.500 --> 00:31:29.000 88 plus 273.15; this gets us 0.012 moles. 00:31:29.000 --> 00:31:32.500 Now we can go ahead and proceed to solve for the molar mass. 00:31:32.500 --> 00:31:39.000 0.827 grams over 0.012 moles. 00:31:39.000 --> 00:31:47.600 That is going to be equal to roughly 69 grams per mole for molar mass. 00:31:47.600 --> 00:31:50.900 This is another nice application of the ideal gas law. 00:31:50.900 --> 00:31:58.900 It can be used to determine the molar mass of a gas that follows ideal behavior. 00:31:58.900 --> 00:32:03.100 Let's go ahead and now proceed on to sample problem two. 00:32:03.100 --> 00:32:10.600 What mass of silver(I) oxide is required to form 388 milliliters of O2 gas 00:32:10.600 --> 00:32:16.700 when measured at 734 millimeters of mercury and 25 degrees Celsius? 00:32:16.700 --> 00:32:20.500 Mass is what we want to get; we are given volume. 00:32:20.500 --> 00:32:25.400 We are given pressure; we are given temperature; guess what? 00:32:25.400 --> 00:32:31.000 You have chemical equation here which pretty much means you have a stoichiometry problem. 00:32:31.000 --> 00:32:34.700 Always the first step is to balance. 00:32:34.700 --> 00:32:42.400 When we go ahead and balance this, we are going to need 2 silver oxides and 4 silvers. 00:32:42.400 --> 00:32:47.000 We want to go from basically the following. 00:32:47.000 --> 00:32:51.200 We are given the pressure, the temperature, and the volume of O2. 00:32:51.200 --> 00:32:53.500 That is three out of four parameters. 00:32:53.500 --> 00:32:55.800 We can go ahead and get the moles of O2. 00:32:55.800 --> 00:33:00.900 n of O2 is equal to PV over RT. 00:33:00.900 --> 00:33:14.200 That is going to be equal to 734 millimeters of mercury times 1 atm divided 760 millimeters of mercury. 00:33:14.200 --> 00:33:19.700 Going to multiply that by the volume in liters which is 0.388 liters, 00:33:19.700 --> 00:33:28.800 divided by the universal gas constant, 0.08206 liters atmosphere K mol, 00:33:28.800 --> 00:33:34.700 times the temperature in kelvin, 25 plus 273.15. 00:33:34.700 --> 00:33:43.400 Then the moles of O2, we get 0.015 moles of oxygen gas. 00:33:43.400 --> 00:33:47.500 We want to go from moles of O2 which is what we have. 00:33:47.500 --> 00:33:52.600 Somehow we want to go all the way to the mass of silver(I) oxide. 00:33:52.600 --> 00:33:53.600 We know how to do that. 00:33:53.600 --> 00:33:58.400 This is really now just a matter of doing something we have already learned. 00:33:58.400 --> 00:34:07.700 We are going to go from the moles of O2 to the moles of silver(I) oxide using the mole to mole ratio. 00:34:07.700 --> 00:34:15.500 Then on from there is to the mass of silver(I) oxide using the molar mass. 00:34:15.500 --> 00:34:17.800 Let's go ahead and finish this up. 00:34:17.800 --> 00:34:22.500 You have 0.015 moles of O2. 00:34:22.500 --> 00:34:32.400 The mole to mole ratio is going to be 2 moles of silver(I) oxide for every 1 mole of oxygen gas. 00:34:32.400 --> 00:34:38.500 Then we are going to go ahead and multiply this by the molar mass of silver(I) oxide to get to grams. 00:34:38.500 --> 00:34:49.100 Its molar mass is 231.74 grams for every 1 mole of silver(I) oxide. 00:34:49.100 --> 00:34:57.100 We get roughly 7.0 grams of silver(I) oxide that are required. 00:34:57.100 --> 00:35:02.100 That is another stoichiometry problem that involves gases. 00:35:02.100 --> 00:35:06.000 Thank you all for your attention; I will see you all next time on Educator.com.