EXPERIMENT 12. SPECTROSCOPIC STUDIES OF HCL AND DCL

Transcription

1 EXPERIMENT 12. SPECTROSCOPIC STUDIES OF HCL AND DCL High resolution infrared spectroscopy is one of the most useful tools for investigating the structure of small molecules. In this experiment you will practice some infrared techniques and analyses for one of the canonical problems in spectroscopy: obtaining the bond length of a diatomic molecule. You will learn about preparing isotopically enhanced samples of a gas and the operation of a Fourier transform infrared spectrometer. In the analysis you will review the quantum mechanics for a rotatingvibrating molecule and use the data to determine some of the molecular characteristics of HCl and DCl. Theory P HOTONS IN THE INFRARED range of the electromagnetic spectrum have the correct energy to excite molecular vibrational modes. Because of the selection rules for absorbing radiation, vibrational excitation is usually accompanied by rotational excitation. For energy levels near the bottom of the potential energy well of a diatomic molecule, the energies of the rotational-vibrational levels are given, in units of cm 1 by: # E v,j = " e v + 1 & % $ 2' ( )" x # v + 1 & % e e $ 2 ( ' 2 + B v J( J +1) ) D e J 2 ( J +1) 2 (1) where the first and second terms account for the vibrational energy, and the third and fourth terms account for the rotational energy. The fundamental vibrational frequency of the molecule is! e. The first anharmonic correction to the vibrational frequency is! ex e. B v is the rotational constant for a given vibrational level, and D e is the centrifugal distortion constant. The integers v and J are the vibrational and rotational quantum numbers respectively. They label the energy level of the molecule. B v may be obtained from the equilibrium geometry of the molecule using the relationships: $ B v = B e "# v + 1 ' & ) (2) % 2( B e ( cm "1 ) = h 2 ; I 8# 2 e = µr e ci e ; µ = m a m b m a + m b (3) Here B e is the equilibrium rotation constant, " is the anharmonicity correction factor to the rotational energy, I e is the equilibrium moment of inertia, µ the reduced mass, and m a and m b are the masses of the two atoms that comprise the diatomic molecule. The vibrational frequency! e, is related to the bond force constant k e by the expression: $ " e = 1 ' & ) k 1 $ ' 2 e & ) (4) % 2# (% µ ( Last updated: December 1,

2 Figure 1 Anatomy of a vibration-rotation band. Figure 1a shows rotational energy levels in their respective upper and lower vibrational energy levels, along with some allowed transitions. The spectral lines corresponding to these transitions are shown in Figure 1b. An actual infrared absorption spectrum for HCl is shown in Figure 1c. Note the splitting due to the H 35 Cl and H 37 Cl isotopic shift. The force constant k e is given by the second derivative of the bond s potential energy curve with respect to its displacement, evaluated at the equilibrium internuclear distance r e. The derivation of these equations are discussed in your textbook and will not be repeated here. Absorption of a photon can only occur when the photon energy is equal to the energy difference between two energy levels of a molecule. A further restriction on the absorption is that selection rules must be followed in the transition. For a diatomic molecule which is modeled as a harmonic oscillator (with a non-zero dipole moment), the selection rules for absorption are v = +1 and J = ±1. For an anhar- Last updated: December 1,

3 monic oscillator (that is all real molecules) the selection rule for #v is not strictly followed; i.e. #v = +1, +2, One of the things you will explore in this lab is how strongly this selection rule (#v = +1) holds for DCl. Figure 1 illustrates the energy levels for the two lowest vibrational states of the molecule and shows some of the transitions that are allowed between the sublevels. Also shown is a hypothetical IR spectrum. What you should notice is the spectrum is separated into two branches, with a gap between them. The gap is where the infrared transitions would be if no change in the J value occurred, i.e. J = 0. This region is referred to as the Q branch and only involves a change in the vibrational quantum number. The low frequency branch consists of #J = 1 transitions and is called the P branch. The high frequency branch consists of #J = +1 transitions and is called the R branch. Note that the quantum numbers for the lower state in the transition are traditionally labeled with a double prime (v$ and J$) while those for the upper state are labeled with a single prime (v% and J%). You will notice that as you count away from the center of the spectrum the intensity of the individual lines increases, goes through a maximum, and then falls off in the wings. This pattern arises from a combination of two effects: the population of molecules in a quantum state and the number of quantum states at a particular energy. Within a band, the intensities are proportional to the population of molecules in the ground vibrational-rotational level. The population in state J is given approximately by the equation: N( J) = N 0 2J +1 ( ) # ( )exp " B 0J J +1 & % ( (5) $ k B T ' Where k B is Boltzmann s constant (and must have the proper units so that the argument of the exponential factor is unitless i.e. you must convert k BT to wavenumbers) and N 0 is the population in the state v = 0, J = 0. The (2J + 1) factor is the degeneracy of the rotational energy level and arises from the fact that 2J + 1 values of the m J (orientational) quantum number are possible for each value of J. The exponential factor is called a Boltzmann factor and gives the temperature dependence of the distribution. (Here we have neglected the possibility that a few molecules will be vibrationally excited.) Laboratory procedure The laboratory procedure has two main parts. In the first part you will prepare the sample. In the second part you will record the spectrum. The HCl fundamental band will occur at approximately 3000 cm 1. For DCl, the fundamental band occurs at around 2000 cm 1 and the first overtone occurs at around 4000 cm -1. Sample preparation We will be generating DCl using the reaction between deuterated sulfuric acid and sodium chloride. D 2SO 4(l) + NaCl(s) & NaDSO 4(s) + DCl(g) The presence of small amounts of water contamination will partially convert some of the DCl gas to HCl. Deuterated sulfuric acid is highly corrosive and extremely viscous. Be careful to avoid spills, and clean up immediately with copious amounts of water if you do spill any. Last updated: December 1,

4 A simple apparatus for carrying out this reaction is sketched out below. D SO 2 4 S ept um G a s C el l N ac l Procedure Figure 2 DCl generation apparatus. Clean the round bottom flask with a small amount of detergent and water. Rinse several times with distilled water, followed by acetone. Place in the oven to dry. For this experiment, we will use the Nicolet 380 FTIR spectrometer. Double-click on the EZ OMNIC icon on the desktop of the computer connected to the spectrometer. Select Hi Res HCl-DCl (PChem) from the experiment list. Last updated: December 1,

5 While the flask is drying, switch out the NaCl salt disc holder inside the FTIR for the gas cell holder. Place the empty gas cell in the FTIR and collect a background spectrum by clicking on the Collect Background (Col Bkg) icon on the menu bar. Remove the round bottom flask from the oven. Add about 2 g of NaCl to a 25-mL round bottom flask with a side arm. Insert rubber septa into the two openings on the top of the gas cell. Be careful not to touch the CaF 2 windows of the gas cell. Connect the gas cell as shown in Figure 2 above and Figure 3 below. Figure 3 DCl generation apparatus. Draw about 2-mL of concentrated D 2SO 4 into a plastic syringe. Use either a 3- or 5-mL syringe. Work quickly to minimize exposure of the D 2SO 4 to water vapor which will exchange the deuterium ions for hydrogen ions. Re-seal the D 2SO 4 bottle quickly, and return it to the desiccator. Pierce the septum on the round bottom flask with the syringe needle and add D 2SO 4 dropwise. Slow the rate of D 2SO 4 delivery to keep the froth away from the top of the flask. When all the acid has been added, and the frothing subsided, remove both needles from the gas cell. During clean-up (best done ASAP), wash the round bottomed flask, septa, and tubing with copious amounts of water, and let air dry. Dispose of the syringes and needles in the provided location. Last updated: December 1,

6 Recording spectra Place the HCl/DCl filled gas cell in the FTIR. Click on the Collect Sample (Col Smp) button on the menu bar. After scanning for a few minutes, the spectrum will appear on the screen. Making sure the cursor button is highlighted in the lower left corner of the window,!, draw a rectangle around the region of the spectrum you wish to enlarge. Once you have selected the region, single click with the mouse inside the rectangle. Last updated: December 1,

7 You can always zoom out by double clicking on the highlighted region of the mini-spectrum in the lower part of the screen. Click on the Find Peaks icon on the menu bar to locate the positions of the peaks in your spectrum. Last updated: December 1,

8 If you click on the screen, a horizontal line will appear at this location. Any peaks that go below the line will be picked, and their positions will be annotated on the spectrum. The sensitivity of the peak picking algorithm can be adjusted between Higher sensitivity settings may lead to noise and spurious peaks being identified. Once you are satisfied with the peak picking, click on the Replace button on the menu bar. You can zoom in on different regions of the spectrum and repeat the peak peaking routine. Small peaks that were not automatically picked by the software can be manually picked. Zoom in/out to the desired point on the spectrum and then click the Annotate button. It is located in the lower left corner of the window. Click close to the bottom of the peak you wish to peak, and its position will be recorded on your spectrum. Last updated: December 1,

9 Once you are done annotating, click on the selection tool in the lower left corner ( ). You should carefully locate all the peaks corresponding to the HCl fundamental band (~3100 cm 1 ), and the DCl fundamental band (~2100 cm 1 ). If you are unsure whether a particular peak is signal or noise, then record the peak location, but make a note in your lab notebook as to the tentative nature of your assignment. Note: since chlorine consists primarily of two isotopes: chlorine-35 (~75% abundance), and chlorine-37 (~25% abundance), you should see each peak split into two signals: the larger peak corresponds to the chlorine-35 containing molecule, the smaller one chlorine-37. At this point, you should save your spectrum by selecting Save As in the File menu. You should also print out each region of interest. Last updated: December 1,

10 It is possible to extract the picked peak positions from the data file. Click on the information button ( ) in the top left corner of the spectrum. This displays all the collection parameters. Click on the Annotations button to see a list of all picked peaks. By clicking on the title X Position, all these peaks will be highlighted. Press the Copy button to transfer all this information to the clipboard. Open up Microsoft Excel, and then Paste in these peaks to the spreadsheet window. You can then save this file to a USB jump drive for data analysis. This method avoids the manual data entry of several hundred peak positions. Last updated: December 1,

11 Saving your data You should save your data in two ways:!! Clean-up Select Save As from the File menu. Select the folder you wish to save the file in and hit open, then click Save. This will save the spectrum in the SPA format, which is only readable on the computer attached to the instrument. Be sure to record the filename in your lab notebook. In order to save the spectrum in a format readable on other computers, you will have to save it in CSV format. To do this, Select Save As from the File menu. Change the "Save as type" scrolldown menu to CSV and hit Save. You can import this file into Microsoft Excel, and use it to plot the spectra in your lab report. When you are finished with the gas cell, remove both septa in a fume hood, and leave overnight to flush out the DCl/HCl gases. Do not wash the gas cell. Return it to the provided desiccator when finished. Be sure to replace the gas cell holder with the NaCl disc holder. Return the gas cell holder to its proper location. Last updated: December 1,

12 Data analysis Assigning the spectrum The first step in obtaining spectroscopic constants is to assign your spectrum. Several method may be used, but the most obvious way for a diatomic molecule is to count outwards from the gap between the R and P branches. You must label the transitions with the J$ quantum number; i.e. the P(1) line is the J$ = 1 & J% = 0 transition, the R(0) line is the J$ = 0 & J% = 1 transition, and so on. (Be careful to use the correct value of J$ for the first line in each series and the rest are easy.) Next you need to tabulate the transition frequencies of each isotope for later manipulation (H 35 Cl, H 37 Cl, D 35 Cl, D 37 Cl). The isotopic abundance of 35 Cl to 37 Cl is approximately 3:1. The intensity of the absorption peaks 1 should also reflect this ratio. You may wish to lay out your data in Excel, or some other spreadsheet, similar to Figure 4 below. Figure 4. A sample spreadsheet layout for the HCl/DCl data. Finding rotational constants, Bv Consider the v = 1 level. Note that if you subtract the frequency of the P(J) line 2 from that of the R(J) line, the difference is given by: R(J) P(J) = B 1[(J+2)(J+1) (J)(J 1)] D e[(j+2) 2 (J+1) 2 J 2 (J 1) 2 ] (6) This equation may be written as R(J) P(J) = 2B 1(2J+1) 4D e(2j+1)(j 2 +J+1) (7) And further rearranged to [R(J) P(J)] (2J+1) = 2B 1 4D e(j 2 +J+1) (8) A plot of [R(J) P(J)] (2J + 1) vs. (J 2 + J + 1) should be linear with a slope equal to 4D e and an intercept equal to 2B 1. 1 Since the FTIR is being run in transmission mode, stronger absorption corresponds to lower percent transmission. 2 In this analysis, J is simply a variable that can take any allowed value. For example, if J = 2, then R(J) P(J) refers to the difference between the R(2) and P(2) lines, and R(J 1) P(J + 1) refers to the difference between the R(1) and P(3) lines. Last updated: December 1,

13 Consider the v = 0 level. The above analysis relied upon the fact that both transitions R(J) and P(J) terminated on the same rotational level in the v = 0 vibrational state. This leads to cancellation of the B 0 terms. If we require that our pair of transitions originate from the same rotational level in the v = 1 vibrational state then the B 1 terms will cancel, leaving us with B 0 terms in the expression. R(J 1) and P(J + 1) lines terminate at the same rotational level, J. R(J 1) P(J + 1) = B 0 (J + 1)(J + 2) B 0 J(J 1) D e [(J + 1) 2 (J + 2) 2 J 2 (J 1) 2 ] (9) Which simplifies to [R(J 1) P(J + 1)] (2J+1) = 2B 0 4D e (J 2 +J+1) (10) A plot of [R(J 1) P(J + 1)] (2J + 1) vs. (J 2 + J + 1) should be linear with a slope equal to 4D e and an intercept equal to 2B 0. Finding molecular parameters Figure 5. An energy diagram showing the difference between the two analyses above. Using your calculated B v values and equation (2), you can obtain B e for each isotopically labeled hydrogen chloride molecule. Subsequently, you can calculate the equilibrium bond length, and the average bond length for each isotope and vibrational level. If the assumptions we have made are all correct, r e and " should be independent of isotope. Is this true within the precision of the data? Sample Calculations Given that B v = B e "(v + ½) solve the following set of equations B 0 = B e "(0 + ½) B 1 = B e "(1 + ½) by subtracting (b) from (a) to yield B 0 B 1 = ". Once you evaluate ", substitute it back into equation (a) and determine B e. Using equations (3), solve for r e. For your report you should have a table of B 0, B 1, D e, B e, ", and r e for both isotopes of HCl and DCl. Compare your results with that of the literature. Provide references to your literature values. Calculate percent errors assuming the literature values to be correct. Be sure to calculate the standard error in all your B and D values obtained from your graphs. Propagate the errors to calculate the error in ". (a) (b) Last updated: December 1,

14 Questions 1.! Derive equations (6) and (7) from equation (1). Hint: R(J) corresponds to the difference in energy between which initial and final values of v and J? R(J) = E final v, final J E init v, init J. Do the same for P(J). When you substitute into the left hand side of the expressions in equations (6) and (7), what do you end up with? 2.! Use equation (4) to compute the force constant of the H 35 Cl and the D 35 Cl bond. Do these force constants differ? Is so, why? If not, why? Note: take! 0 as being exactly halfway between the first line of the P-branch and the first line of the R-branch. Use the equation:! 0 =! e! 2! e x e to calculate the value of! e. Literature values 3 of x e! e are cm 1 and cm 1 for H 35 Cl and D 35 Cl respectively. 3.! Do the values of the spectroscopic constants B e, B v, and! e vary with isotope and/or with vibrational level in a way that you would expect. Explain your answer. 4.! Equation (5) can be used to predict how a change in temperature will alter the ro-vib spectrum of 1 H 35 Cl. Using your experimental value of B 0, calculate the relative proportion [N(J)/N(0)] for the J = 0, 4, 8, and 12 rotational levels at 50 K, 150 K, and 300 K. Be sure to show all work. Given that the absorptions of the P(J) and R(J) lines are proportional to the number of molecules in each rotational state, what would you expect the ro-vib spectra to look like at these three temperatures? Hint: the wavenumber to Joule conversion is given in the front cover of McQuarrie and Simon. 5.! Using equation (4), calculate the theoretical ratios of! HCl! DCl for the chlorine-35 and chlorine-37 containing isotopomers. How do these compare with your experimental values? 3 K.P. Huber and G. Herzberg, Molecular Spectra and Molecular Structure, v. 4, Constants of diatomic molecules, Van Nostrand, Toronto, Canada, Last updated: December 1,

15 Pre-Lab Questions 1. Read pp of McQuarrie and Simon. 2. Calculate B e (in units of cm 1 ) for 14 N 17 O if r e is equal to Å. The masses of 14 N and 17 O are and respectively in atomic mass units. 3. Calculate " (in units of cm 1 ) for 14 N 17 O if k = 1550 N/m. 4. Calculate the ratio of " ( 1 H 35 Cl) / " ( 2 H 35 Cl), assuming the force constants and bond lengths are the same for the two species. The masses of 1 H, 2 H, and 35 Cl are , , and respectively in atomic mass units. 5. What are the selection rules in a ro-vib transition? 6. What value does P(3) and R(1) have in the following ro-vib spectrum? Last updated: December 1,