Ideal Toy Activity 7 Moving Molecules GOALS In this activity you will: Determine the effect of molecular size on molecular motion. Predict quantities of gas produced in chemical reactions. What Do You Think? Party balloons are often filled with air or helium. Predict which balloons ones filled with air or ones filled with helium will stay inflated longer. Explain why you predicted this. Record your ideas about this question in your log. Be prepared to discuss your responses with your small group and the class. Investigate 1. If your teacher were to open a bottle containing a substance with a strong perfume odor at the front of the class, estimate how much time it would take before you could smell it. Have your teacher tally the estimates at the board. a) Explain why you think the time for someone in the front of the class would or would not be different from someone in the back of the class. 2. Your teacher will now open the bottle. Raise your hand when you smell the odor so that the entire class can observe how the odor is traveling. a) Measure and record the time that elapses before you can smell the odor. 408
Activity 7 Moving Molecules 3. Dry air is composed of 79% nitrogen, 20% oxygen, 1% argon, 0.3% carbon dioxide, and trace amounts of other elements. a) Draw pictures of the internal views of two latex balloons. One balloon is filled with pure helium (He) and one is filled with air from your breath. Your pictures should show the size of the molecules as well as arrows depicting the speed and direction of the particles. The greater speeds will be represented by the longer arrows. 4. You are going to examine two gases under identical conditions to help you understand what might be happening in the balloons. You will use sandwich-sized plastic bags to represent the balloons. Before beginning, you must determine the amounts of chemicals required to fill the plastic bags with gas. 5. In one plastic bag, you will generate H 2 by reacting Zn with HCl (hydrochloric acid). a) In your notebook, write down the balanced equation for reacting Zn and HCl. Zn(s) 2HCl(aq) ZnCl 2 (aq) H 2 (g) b) Show that this equation is balanced. c) If you wish to fill the plastic bag with 0.85 L of H 2 gas, you will need to calculate the amount of zinc that will be necessary to do this. (Too much gas could burst the bag.) Since 1 mol of H 2 fills a volume of 22.4 L, calculate how many moles of H 2 will be required to fill a volume of 0.85 L. d) Since the mole ratio in the reaction shows that 1 mol of Zn produces 1 mol of H 2, write down the number of moles of Zn that will be required to create the number of moles of H 2 that will fill the volume of 0.85 L. e) Since 1 mol of zinc is 65.4 g (see the atomic mass on the periodic table), determine the mass of zinc to add to the HCl to produce the volume of 0.85 L of gas. You can also determine the required mass of HCl, but that is not necessary. If you have extra HCl, then the reaction will be limited by the amount of zinc. Zinc is called the limiting reactant. 6. In the other plastic bag, you will generate CO 2 by reacting NaHCO 3 (baking soda) with CH 3 COOH (vinegar). a) In your notebook, write down the balanced equation for reacting NaHCO 3 and vinegar (CH 3 COOH). NaHCO 3 (s) CH 3 COOH(aq) CO 2 (g) H 2 O(l) NaC 2 H 3 O 2 (aq) b) Show that the equation is balanced. c) Since you wish to fill the plastic bag with 0.85 L of CO 2 gas, calculate the amount of baking soda that will be necessary to do this. 7. Have your teacher approve your calculations. Set up your labeled plastic bags, and generate the different gases in each. Then measure the circumference of each bag. a) Record the circumference in your lab notebook. 8. Dispose of the materials as directed by your teacher. Clean up your workstation. 409 Safety goggles and a lab apron must be worn at all times in a chemistry lab. Wash your hands and arms thoroughly after the activity. Hydrogen gas is very flammable. Keep the bag away from sparks or a flame.
Ideal Toy 9. Allow the bags to sit for several days. a) Record your observations and new circumference measurements in your log each day. 10. Your teacher may have generated the gases in the balloons a few days earlier so that you can compare the volume of the balloons after several days. A pair of balloons is shown in the diagram, so that you can complete this activity rather than halt everything for the days it may take for your balloons to change. a) Describe the differences between the gases you generated that might account for the differences you observe in the two models. b) How could these differences explain your observations? MOLECULAR SIZE AND MOLECULAR MOTION OF GASES Small-particle Model of Gases Scientists have adopted the following model for gases: Gases consist of tiny particles (atoms or molecules) which are separated by relatively large distances. For water, the particles are about 1000 times further apart in the gas phase as in the liquid phase. Gas molecules are in constant, random motion, and travel in a straight line between collisions. They do collide frequently with other gas molecules and with the walls of their container. Gas pressure is related to the sum of all of these collisions with the walls during a given time. 410
Activity 7 Moving Molecules At any given temperature (Kelvin scale), the average kinetic energy of all the molecules of gas is directly proportional to that temperature. However, some of the molecules will be moving faster than the average, some slower. At the same temperature, all gases have the same average kinetic energy in their molecules. As the temperature increases, so do the average velocities and kinetic energies of the molecules. Diffusion When the perfume or other odors left the bottle and traveled about the room, you observed that the students closest to the teacher smelled the perfume first. Diffusion is the spontaneous mixing of one gas (or liquid) with another that occurs because of the random movement of the molecules. This occurs with perfumes because the fragrant gaseous molecules move freely through the widely spaced air molecules to reach your nose. (In typical classrooms, with radiators, air conditioners, open windows, students moving around, etc., convection currents are much more important in distributing gases than diffusion.) The process of diffusion is complete when the molecules of the gases are evenly spread within the room. Diffusion is purely a physical phenomenon. The rate of diffusion has to do with the speed of the gas molecules. All gases at the same temperature have the same average kinetic energy. However, gases with a large molar mass have slow speeds while gases with small molar mass have fast speeds. The velocity (v) of a gas molecule is related to its kinetic energy (KE): KE 1 2 mv 2 where m is the mass of the molecule. Since two gases have the same kinetic energy, you can derive the relationship from the equation above. Assume that you have a gas with a large mass, m L and one with a small mass, m S. Since their kinetic energies are equal: 1 2 m L v2 L 1 2 m S v 2 S v L ms vs m L Chem Words diffusion: the spontaneous mixing of one gas (or liquid) with another that occurs because of the random movement of the molecules. The velocity of large-mass gases is smaller than the velocity of small-mass gases and its diffusion is also slower. For example, if the ratio of the masses of the gases is 1:9, then the ratio of speeds will be 1:3. If you make the mass of the particles nine times larger, the speed decreases by a factor of 3. 411
Ideal Toy Chem Words effusion: the movement of a gas through an extremely tiny opening into a region of lower pressure. Graham s Law of Effusion: a law that states that the rate of escape of a gas from a container through a pinhole (effusion) is inversely proportional to the square root of the molar mass of the gas. Effusion When the balloon deflated over time, it was due to the leaking of the gas through tiny openings in the latex of the balloon. These holes in the material are much, much smaller than a puncture. The effusion of a gas is its movement through an extremely tiny opening into a region of lower pressure. In the Investigate section, you observed the effusion to be much greater for the hydrogen gas than for the carbon dioxide gas. You might think that the smaller hydrogen molecules are able to fit through the tiny holes and therefore escape faster. However, since the larger carbon dioxide molecules can also fit through the holes, the difference in the rate of effusion must be dependent on another property of the gases. A Scottish scientist, Thomas Graham (1805 1869), studied the rates at which various gases effuse. He found that the more dense the gas is, the slower it effuses. The exact relationship between rate and gas density, d, is called Graham s Law of Effusion. Graham s law states that the rate of effusion of a gas is inversely proportional to the square root of the density of the gas. Since equal volumes of gas at the same temperature and pressure contain equal numbers of gas molecules, the rate of effusion is also inversely proportional to the square root of the molar mass of the gas. The gas with the lowest molar mass effuses the fastest. Once again, since the kinetic energies are identical: 1 2 m L v2 L 1 2 m S v 2 S v L ms vs Look at the velocities of the two gases in the activity hydrogen and carbon dioxide. The molar mass of hydrogen is 2.0 g/mole. The molar mass of carbon dioxide is 44.0 g/mole. What is the rate of effusion of hydrogen to carbon dioxide? v H2 v CO2 44.0 2.0 m L 4.7 Solving the equation gives a ratio of 4.7:1. This tells you that at the same temperature, hydrogen molecules have a velocity 4.7 times greater than carbon dioxide molecules. It was the higher velocity that allowed the 412
Activity 7 Moving Molecules hydrogen to leave the latex balloon faster than the carbon dioxide. Diffusion and effusion have the same mathematical relationship. They also sound very much the same. They also both deal with gases. This certainly leads to confusion. Diffusion has to do with the random motion of the gases across space. Effusion has to do with the random motion of the gases through the tiny openings. Checking Up 1. Explain diffusion of a gas in your own words. 2. What is meant by the effusion of a gas? 3. Two equal-sized boxes with identical small openings contain different gases. One contains carbon dioxide (CO 2 ) and the other contains helium (He). Which gas will effuse faster? 4. How is the average kinetic energy of gas particles related to temperature? What Do You Think Now? At the beginning of this activity you were asked: Predict which balloons ones filled with air or ones filled with helium will stay inflated longer. Explain why you predicted this. How would you answer this question now that you have completed this activity? What does it mean? Chemistry explains a macroscopic phenomenon (what you observe) with a description of what happens at the nanoscopic level (atoms and molecules) using symbolic structures as a way to communicate. Complete the chart below in your log. MACRO NANO SYMBOLIC What visual evidence do you have that supports Graham s Law of Effusion? Describe what is happening at the nanoscopic level when two gases of different masses are escaping from tiny holes in their containers. Use an equation to represent Graham s Law of Effusion. 413
Ideal Toy How do you know? Using the molar mass of H 2 of 2.0 g and an approximation of the molar mass of air to be 28.6 g, what is the rate of effusion of H 2 to air? From this information, what would you predict for the leak rate of air-filled and hydrogen-filled balloons? Why do you believe? A tennis ball contains a mixture of gases. Why does a tennis ball lose its bounce over time? Why should you care? If your toy uses a gas to propel or otherwise support the way it is used, what considerations will you need to keep in mind as you design it? If the toy must contain a constant amount of some gas, will choosing the heaviest gas available always be the best decision? Explain your answer using examples to support your thoughts. Reflecting on the Activity and the Challenge In this activity you explored the effect of gas size on effusion rates. You found that the more massive the gas, the slower its rate of effusion. For example, H 2 has a molar mass of 2; He has a molar mass of 4; and N 2 has a molar mass of 28. Using Graham s Law, you would predict that H 2 would effuse at a faster rate than helium or nitrogen. You have probably seen the effect of mass on effusion with party balloons lots of times but had never really tested what might be occurring. You might apply your new knowledge of what is occurring to the toy model your team is proposing. Your proposal will have to explain the advantages and disadvantages of using one particular gas over another. The use of different gases might impact the behavior of your toy. Consider how you could make that knowledge work to your advantage in the toy design. 414
Activity 7 Moving Molecules 1. If latex balloons are filled with the following gases and allowed to sit for two days, which balloon will have the most volume? Which would have the least volume? Rank them all in order of smallest to largest volume. Explain your reasoning. a) H 2 (molar mass = 2.0 g/mol) b) He (molar mass = 4.0 g/mol) c) O 2 (molar mass = 32.0 g/mol) d) N 2 (molar mass = 28.0 g/mol) e) CO 2 (molar mass = 44.0 g/mol) 2. Two cotton plugs are placed simultaneously in each end of a glass tube, 12 cm in length. On one end the cotton is soaked with aqueous NH 3 and on the other end the cotton is soaked with aqueous HCl. Within minutes a white ring of NH 4 Cl appears about 4 cm from the HCl side. NH 4 Cl has formed as the HCl reacted with the NH 3. Explain why the reaction occurred much closer to the HCl than to the NH 3 side. 3. Which of the following gases would most likely keep automobile tires inflated the longest: CO 2, air (average molar mass 29 g/mol), or He? Why? 4. Given the molar mass of carbon dioxide (44.0 g/mol) and oxygen (32.0 g/mol), determine the rate of effusion of the CO 2 to O 2. 5. The rate of effusion of Gas A to Gas B is 1:2. Which gas has the higher molecular mass? 6. Preparing for the Chapter Challenge Different gases could be used in the toy that you are proposing. Based on your toy s design, certain criteria will determine what the best gas to use will be. List the key criteria to consider and tests that would need to be carried out on the gases to be used in a toy proposal. Inquiring Further The cost factor If you wanted to generate as much carbon dioxide gas as possible, but had only $1 to spend, how much baking soda and vinegar would you purchase? Assume that the cost of baking soda is 5 per gram and the price of vinegar is 3 per gram. 415