7-Graphical Determination of an Order of Reaction

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Apr 3, 2024

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Graphical Determination of the Order of a Reaction generating H 2 (g) Introduction In lecture you have been exposed to the idea that reactions occur at different rates. Through mathematics, we can express the concentration dependence on time in the form of an integrated rate law. To chemists, 3 important integrated rate laws (in their linear form) for the consumption of reactant ‘ 𝐴 ’ are 0?ℎ ????? → [𝐴] = −?? + [𝐴] 𝑜 (1) 1?? ????? → ln([𝐴]) = −?? + ln ([𝐴] 𝑜 ) (2) 2?? ????? → [𝐴] −1 = ?? + ([𝐴] 𝑜 ) −1 (3) where [𝐴] is the concentration of reactant 𝐴 at time ? , ? is the rate constant, and [𝐴] 𝑜 is the initial concentration of reactant 𝐴 . Because each reaction order produces a different linear equation, a graphical analysis of concentration and time data (and a test for linearity) will show whether a reaction follows equations (1), (2), or (3), and thus provides insight into the reaction order. In this lab we will be focusing on the production of hydrogen gas via the single replacement reaction between solid magnesium and hydrochloric acid: 𝑀𝑔 (?) + 2 𝐻𝐶? (𝑎?) → 𝐻 2 (𝑔) + 𝑀𝑔𝐶? 2 (𝑎?) . (4) While this reaction involves 2 reactants, the magnesium is present in its solid form. At this stage of your progression through chemistry, we do not consider the solid as having an overall effect on the reaction rate, beca use it “doesn’t have a concentration”. In truth, the amount of solid will affect a rate of reaction, however, the surface area of solids exposed to other reactants is the important physical property associated with increasing or decreasing a reaction’s ra te. In our experiment, we will use enough magnesium to assure that the surface area remains relatively unchanged during the chemical process we enact. This isolates the effect of HCl’s concentration on the reaction, and thus the rate law becomes ?𝑎?? = ?[𝐻𝐶?] 𝑥 . (5) Note that in this case, the rate constant is actually a pseudo rate constant, as information regarding the surface area of Mg has been taken into account within ? . However, given the isolation of the effect of HCl, and noting the form of the equations (1), (2) and (3), one can determine 𝑥 , which is the order of HCl. To enact the analysis prescribed above, one needs concentration v. time data. To obtain this data, consider the following experimental setup for a water displacement volumetric gasometer (which should be present in the lab as you enter):

The leftmost 50 mL Erlenmeyer flask contains a coiled piece of Mg: This flask will be stoppered during a run, but a tube in the stopper will allow generated gas to flow to the middle 250 mL Erlenmeyer, which is nearly filled with water. This flask has a stopper as well, but it contains two tubes. Please note that the second tube in this flask is submerged: as the hydrogen gas enters the 2 nd Erlenmeyer flask, it will force an equal volume of water from this reservoir into a 50 mL graduated cylinder. Monitoring the amount of water that reaches the graduated cylinder will allow us to infer the volume of hydrogen gas generated. This volume of gas will be converted to mol using the ideal gas law, and then the reaction shown in (4) can be used to infer how many mols of HCl were used to generate that amount of gas. Knowing the initial concentration of HCl and noting that the volume of the reaction solution can be assumed to 50 mL EM 250 mL EM 50 mL Grad. Cyl. Tube for gas Tube for water

be constant, one can deduce the concentration of HCl in the leftmost flask at any time during the r eaction’s progress, and thus the aforementioned graphical analysis can be completed. Procedure Prepare your initial HCl solution: Obtain 6 mL of 1 M HCl and place it in a 50 mL graduated cylinder. Fill the graduated cylinder until a total volume of 45 mL is obtained. Pour this solution into a beaker and set it aside for now (labelled). Testing your setup: If there is not a 50 mL graduated cylinder in place to collect water, place the rightmost tube (tube for water) within your own. Make sure that the middle 250 mL Erlenmeyer contains water up to its neck (if it doesn’t fill it until it does). Take the leftmost stopper out of the 50 mL Erlenmeyer flask. Hook a different tube from your cabinet to the air nozzle on the benchtop and turn the nozzle until a GENTLE flow of air can be heard. Place the air flow tube next to the stopper you have removed from the 50 mL Erlenmeyer and observe at least 10 mL of water running from the 250 mL Erlenmeyer and into your graduated cylinder. If this is observed, you can be confident that your experimental setup is correct . “Reset” your graduated cylinder by putting any water inside it down the sink. Running the reaction: Become familiar with the operation of a stopwatch provided by your instructor. When you are ready to proceed with your reaction, simply pour your 45 mL HCl solution into the leftmost 50 mL Erlenmeyer flask, and place the single-hole stopper (with the “tube for gas”) into it (you do not have to force it down dramatically but push with sufficient force to ensure that no gas will escape from it). Observing the reaction and recording data: IMPORTANT → there will be a lag in collection of water in the graduated cylinder. As the vapor pressure of the hydrogen gas builds, you may not see any initial drops of water, or you may see a drop here and there. Do NOT start the timer until the drops into the graduated cylinder are steady and continual. This lag period may last up to 7 minutes, during which you will NOT record data but will observe your set- up…you will certainly be able to tell the difference once the steady drops start to manifest inside the graduated cylinder. Once they do, start the timer, and record the volume of water in the graduated cylinder once a minute for 10 minutes total. Note that you should have a total of eleven data points, as at time zero you can state that 0 mL of water have reached the graduated cylinder. Extra info needed: You will be using the ideal gas law during your calculation. Before you leave, be sure to record the temperature of the room (assumed to be the temperature of the gas) and the pressure of the atmosphere (assumed to be the pressure of your gas at each step). Cleanup: Once your ten-minute run is done, simply remove the stopper from the 50 mL Erlenmeyer flask containing the reaction, and dump the solution it contains into the waste container in the hood. Rinse the flask once with water, while keep the Mg inside. Stopper the flask (use a stopper without a hole).

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