CM1011 Exp8_Graham's Law_Fa23

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Dec 6, 2023

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Name ________________________________________ Section __________________ Experiment 8 Graham’s Law CM1011 Fall 2023 1 Diffusion of Gases and Graham’s Law In your text (Chang and Goldsby 7 th Ed) : Chapter 5, especially Section 5.6 According to the kinetic molecular theory of gases , a gas consists of atoms or molecules 1 that are separated by distances so much larger than their own dimensions that they can be modeled as points with mass but with negligible volume. They are in rapid, random motion, with frequent collisions. Intermolecular attractions or repulsions are also considered to be negligible, and kinetic energy is conserved upon collisions, i.e. the collisions are perfectly elastic. The distribution of molecular speeds follows a Boltzmann distribution. The average kinetic energy (KE) is proportional to the temperature of the gas in Kelvins. Any two gases at the same temperature will have the same average kinetic energy. The average kinetic energy per molecule is ࠵?࠵? #### molecule = ! " ࠵?࠵? " ### Eq. 1 Where ࠵? ’ is the average molecular speed, multiplying by Avogadro's number, N A , yields the average kinetic energy per mole (since N A ࠵? = ࠵? , the molecular weight): ࠵?࠵? #### mole = ! " ࠵?࠵? " ### Eq. 2 From kinetic molecular theory, it can be shown that the average kinetic energy per mole of an ideal gas is: ࠵?࠵? #### mole = (3/2) RT Eq. 3 Equating Eq. 2 and 3 yields: (3/2) RT = (1/2) M ࠵? ࠵? #### Eq. 4 from which the root mean squared (rms) velocity is extracted: ) ࠵? ࠵? #### = ࠵? ࠵?࠵?࠵? = * ࠵?࠵?࠵? ࠵? Eq. 5 Note that the average KE ∝ T, but that the speed is proportional to √T and inversely proportional to √M . At a fixed temperature, the distribution of molecular speeds for lighter molecules will be shifted to higher speeds, in the familiar Boltzmann form, as shown in Fig. 2. 1 For simplicity, we will use only the term “molecules” in the discussion, with the understanding that gases can be either atomic or molecular or, in mixtures, both. 2 Unless otherwise noted, all figures are from Chang, Chemistry, 9 th edition MHHE, 2007 . Fig. 1 Distribution of molecular speeds (Boltzmann distribution) for N 2 at various temperatures

Name ________________________________________ Section __________________ Experiment 8 Graham’s Law CM1011 Fall 2023 2 Fig. 2 Distribution of speeds of differing MW at the same temperature. Fig. 3 Schematic of molecular random walk, showing net motion resulting from multiple collisions . Fig. 3 illustrates how the random collisions of molecules results into overall net translation. Molecules with higher average speeds will have a higher rate of net translation. For example, after opening a container containing substances we can smell, such as perfume or food, the volatile molecules will eventually travel from the container to our noses, albeit by a very indirect path. This is an example of gas diffusion , the gradual mixing of molecules of one gas with another due to their kinetic properties. Gas effusion is the related process, whereby gas under pressure passes through a small opening or porous plug from one compartment to another, as shown in Fig. 4. In 1829, Thomas Graham experimentally established a quantitative relationship between the relative rates Graham’s Law: ! ! ! " = ! " " " ! Eq. 6 Where r 1 = rate of effusion of gas 1 r 2 = rate of effusion of gas 2 d 1 = density of gas 1 d 2 = density of gas 2 At a given temperature and pressure, the rate of both diffusion and effusion is ultimately dependent on the Fig. 4 Gas effusion

Name ________________________________________ Section __________________ Experiment 8 Graham’s Law CM1011 Fall 2023 3 average molecular speed, so it is not surprising that Graham’s Law applies to both diffusion and effusion. For an ideal gas (and, to a very good approximation, many actual gases under wide, T, P ranges), density, d ∝ M , molecular weight: d = P M / ( RT ) Eq. 7 Therefore, at constant temperature and pressure (T, P), Eq. 6 can be restated in terms of molecular weight. ! ! ! " = ! # " # ! Eq. 8 The rate of diffusion, r , in cm s +! ࠵? = distance travelled, cm time elapsed, s = ࠵? ࠵? Eq. 9 If the distance travelled, x , is fixed, Eqs. 8 and 9 can be expressed in terms of time elapsed, t : $ " $ ! = ! # " # ! Eq. 10 This form would be most useful where the experiment involved measuring the time needed for gases to diffuse or effuse a fixed distance. In this experiment, hydrogen chloride gas, HCl (g), and ammonia gas N H , (g) will diffuse from opposite ends of a tube. When they meet, they react and form a visible product, N H - Cl (s), NH , (g) + HCl (g)  N H - Cl (s, white) Eq. 11 [view on computer before printing, gas cloud hard to see] Fig. 5 shows cloudy white N H - Cl formed from the contact of the two species when NH , and HCl vapor diffuses. Note that the N H - Cl cloud is closer to the HCl container, because the lighter gas, NH , , diffuses further. The two containers are opened at the same time, so the time that the gases diffuse is fixed. The gases diffuse different distances (x), depending on their molecular weights. Combining Eq. 8 and 9, we get: % ! % " = ! # " # ! Eq. 12 Fig. 5 Formation of N ࠵? ࠵? Cl (s)

Name ________________________________________ Section __________________ Experiment 8 Graham’s Law CM1011 Fall 2023 4 Procedure Note: Aqueous NH , reacts with water, forming N H - OH. The reagent bottles may be labeled either NH , (aq) or N H - OH (aq) – it is the same thing. Obtain a clean, dry glass tube, approximately 60 cm in length and 1.5 cm in diameter. In the hood, clamp the tube to a ring stand so that it is almost lying flat on the bench in the hood, but held steady by the clamp. It is much easier to see the formation of the cloudy white ring of N H - Cl when looking down on the tube, with the dark hood bench surface underneath it. Make sure the tube is level. Put on your gloves . Obtain watch glasses, pre-cut parafilm squares and two 50 mL beakers. Under the hood , pour concentrated HCl and NH , into different beakers and place them at opposite ends of the tube. Keep the beakers covered with watch glasses when not in use, to minimize the amount of escaping fumes. Do not carry uncovered containers or glass wool soaked in HCl or N H , through the lab. Each partner takes one end of the tube and use a pair of tweezers to dip their glass wool wad into the HC1 or NH , , respectively. Each partner now jams their wetted wad of glass wool into the opposing ends of the tube at same time, keeping the glass wool twisted up in a tight bunch. Start the timer as soon as the glass wool wads enters the end of the tube. Seal the ends off with pre-cut parafilm squares (stretch the parafilm square over the tube ends, like using plastic wrap in the kitchen). Keep the two beakers (HCl and ࠵?࠵? ࠵? ) as far apart as possible, covered, and away from the glass tube, in order to avoid a premature reaction between the two vapors. Carefully observe the full length of the glass tube, watching for evidence of the formation of a white ring of solid N H - Cl. Note the time when the white ring appears, to the nearest second. Mark the precise location of the ring on the glass tube, using a wax pencil or Sharpie marker. Usually it takes 6-7 minutes at room temperature for the formation of the ring. If you see nothing after 10 minutes, consult your instructor. The ring broadens and is less intense at later times so waiting too long to observe it will actually cause a problem. Hazards: Both concentrated NH , and concentrated HCl are toxic and corrosive. The fumes of both concentrated NH , and concentrated HCl are toxic, corrosive, and irritating. Wear your goggles. No contact lenses!!!! Avoid contact with your eyes, skin, and clothing. Permanent fogging of soft contact lenses may result from NH , vapors. Avoid inhaling vapors and ingesting these compounds. In case of a spill, immediately notify your laboratory instructor. The experiment and all transfer of liquids must be performed in the hood.

Name ________________________________________ Section __________________ Experiment 8 Graham’s Law CM1011 Fall 2023 5 Measure and record the distances, to the nearest 0.1 cm, from the mark where the ring first formed to the nearest end of each of the soaked glass wool plugs. Carefully note which distance corresponds to the diffusion distance of the NH , and which corresponds to the diffusion distance of the HCl. Use a pair of tweezers to remove the glass wool from the tube. Place them in the appropriate covered beaker for use in the next run. Thoroughly rinse the glass tube with tap water. Then, rinse the tube with 10 mL of distilled or deionized water. Finally, use a small beaker to fetch about 10 mL of acetone, and rinse the inside of the tube with acetone. Pour the acetone rinse into the container designated by your laboratory instructor. To dry the tube, hold a hose attached to the air line to the end of the tube, so that air is blown through the tube. Make sure the tube is completely dry. Repeat the same procedure twice more and record the observations in data sheet. Dispose of all reagents and glass wool in the waste disposal in the hood by the lab door. Do not carry uncovered containers or glass wool soaked in HCl or ࠵?࠵? ࠵? through the lab. Wash your hands thoroughly with soap or detergent before leaving the laboratory. Calculations Do the following calculations for each determination and record the results on the indicated lines on your Data Sheet. 1. Find the total elapsed time for the determination. 2. Total elapsed time = (time of first N H - Cl observations) — (time of glass wool insertion) Express the elapsed time in seconds, line (3). 3. Given a molar mass for NH , of 17.0 g/mol, calculate the molar mass of HCl, using Equation 12, line (7). 4. Find the mean (average) molar mass of HCl, line (8). 5. The accepted molar mass of HCl is 36.5 g/mol. Determine the percent error in the mean molar mass of HCl for this experiment, using Equation 13, in the Sample Calculation below. Enter on line (10).

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