|CM2101 (Principles of Spectroscopy) |
|Experiment 1: Rovibrational Spectrum of Hydrogen Chloride |

AIM

To measure the infra-red (IR) spectrum of gaseous HCl using Fourier Transform Infra-Red (FTIR) spectrometer, and analyse the rotational fine structures.

ABSTRACT

The experiment aims to identify various parameters of gaseous HCl related to quantum mechanics by using high-resolution IR spectrum and graphical method of analysis. The values that are being investigated specifically are νe (equilibrium vibrational frequency), νeχe (product of equilibrium vibrational frequency and anharmonicity constant), k (force constant), B0 (rotational constant at n = 0), B1 (rotational constant at n = 1), Be (rotational constant at equilibrium internuclear distance), α (Coriolis constant) and re (equilibrium internuclear distance).

The spectrum obtained shows strong fundamental absorption band approximately between 3100 and 2600 cm-1, with the origin of the band approximately at 2880 cm-1. It is also characterised by the presence of P and R branches which spreads out from the origin, with the former being present at a lower wavenumber region than the latter. In addition, double peaks are observed due to the presence of two isotopes of chlorine: 35Cl and 37Cl.

INTRODUCTION

One of the areas being investigated in Quantum Chemistry is the vibrational and rotational aspects of a diatomic molecule. In this experiment, the diatomic molecule studied is the gaseous HCl. In understanding the vibrational energy levels of a diatomic molecule, the molecule is first approximated to a harmonic oscillator which obeys Hooke’s Law: an approximation which states that the extension of a spring is directly proportional to the load applied to it (Banwell, 1983 [A1]). In addition, with regards to the rotational energy levels of a diatomic molecule, the molecule is first approximated to a rigid rotor where its bond length does not change. Another important thing that is assumed is that there is no interaction between the vibrational and rotational motions of a molecule. Only after the properties of the molecule have been studied and understood, modifications to the harmonic oscillator and rigid rotor approximations are done, taking care the anharmonic properties, as well as the actual vibration-rotation interactions and centrifugal distortions of the bond to complete the picture.

The vibrational and rotational fine structures can be studied by obtaining an infra-red spectrum by using Fourier Transform Infra-Red (FTIR) spectrometer. IR radiation is passed though a sample, resulting in the absorption and transmittance of the radiation at a certain range of wavelengths. The signals are encoded in an interferogram which is then decoded via a mathematical tool of analysis known as the Fourier transformation. The spectrum obtained thus acts as a molecular fingerprint of the sample under consideration. The advantages of using FTIR over dispersive techniques include higher speed and sensitivity, as well as mechanical simplicity in which the moving mirror is the only continuously moving part in the instrument.

EXPERIMENTAL

|Chemicals |Concentrated H2SO4 solution |Solid CaCl2 |
| |Solid NaCl2 |Nitrogen gas |
| | | |

Preparation of Background Spectra

To the empty 10-cm IR cell, nitrogen gas was introduced in order to drive off any other gases that might interfere with the experiment. Two background spectra were subsequently obtained: one over the range of 4000 – 600cm-1 (resolution of 4 cm-1) and another over the range of 3200 – 2500 cm-1 (resolution of 0.5 cm-1). The spectra were saved in the system to be used later.

Determination of HCl Spectra

[pic]

Figure 1: Experimental setup to obtain gaseous HCl

As shown in Figure 1 above, solid NaCl was placed in a conical flask that was connected to a burette containing concentrated H2SO4 solution and a U-tube containing solid CaCl2. The U-tube was subsequently connected into the IR cell. Following that, a few drops of H2SO4 were allowed to come to contact with NaCl, resulting in the production of HCl gas that would be passed into the IR cell. The sample was then scanned over the range of 4000 – 600cm-1 (resolution of 4 cm-1) and another over the range of 3200 – 2500 cm-1 (resolution of 0.5 cm-1) after proper subtraction of the background readings had been done.

When the partial pressure of the HCl was too high as seen by the low transmittance of the peaks obtained in the spectra, the sample was diluted by introducing nitrogen gas into the IR cell.

RESULTS AND CALCULATION

Low-Resolution Spectrum

From the low-resolution spectrum, it can be confirmed that there is one strong absorption band with two branches from wavenumbers of approximately 3100 to 2600 cm-1. Also, the origin of the band is found at approximately 2880 cm-1.

Determination of νeχe, νe, χe and k

The first and second overtone bands of HCl are known to lie at the wavenumbers 5668 and 8347 cm-1 respectively. The first overtone is known to be the energy gap between the quantum numbers n = 0 and n = 2, while the second overtone is known to be the energy gap between the quantum numbers n = 0 and n = 3. The following vibrational energy formula can be employed in order to obtain various useful parameters.

En = νe (n + ½) – νeχe (n + ½)2

In the above equation, Eν is the vibrational energy at n vibrational state, νe is the equilibrium vibrational frequency and χe is the anharmonicity constant.

νe (2 + ½) – νeχe (2 + ½)2 – [νe (0 + ½) – νeχe (0 + ½)2] = 5668
2νe – 6νeχe = 5668 --- (1)

νe (3 + ½) – νeχe (3 + ½)2 – [νe(0 + ½) – νeχe (0 + ½)2] = 8347
3νe – 12νeχe = 8347 --- (2)

Solving simultaneous equations (1) and (2), it is found that: νeχe = 51.67 cm-1, νe = 2989 cm-1 and χe = 0.01729, corrected to 4 significant figures.

μ = [(1 x 35) / (1 + 35)] x 1.67 x 10-27 kg = 1.624 x 10-27 kg (4 s.f.) νe = [pic]
Force constant, k = μ(2πcνe)2 = 515.5 Nm-1 (4 s.f.)

High-Resolution Spectrum

The presence of double peaks in the high-resolution spectrum can be explained by the existence of the two isotopes of chlorine, 35Cl and 37Cl. Considering each double peak, the peak of higher wavenumber corresponds to H35Cl, while the peak of lower wavenumber corresponds to H37Cl. This is because H37Cl has a higher reduced mass (μ), which results in a lower νe since μ is inversely proportional to νe. This is also confirmed by the fact that the intensity of the peak with lower wavenumber has higher intensity than the peak of lower wavenumber since the natural abundance of 35Cl exceeds that of 37Cl in a 3:1 ratio (ChemGuide, 2010 [B1]).

Determination of B0, B1, Be, α and re

In the assignment of lines for H35Cl in the high-resolution spectrum, it is important to note that the P branch occurs at lower wavenumbers than the R branch. In addition, while the R branch starts with R(0), the P branch starts with P(1). The details will be discussed in the Discussion section. The following formulae are used.

∆0(J) = R(J) – P(J + 2)
∆1(J) = R(J) – P(J)

|J |P(J) / cm-1 |R(J) / cm-1 |Δ0(J) / cm-1 |Δ1(J) / cm-1 |
|0 |- |2906.39 |62.68 |- |
|1 |2865.16 |2925.92 |104.39 |60.76 |
|2 |2843.71 |2944.97 |145.87 |101.26 |
|3 |2821.53 |2963.29 |187.33 |141.76 |
|4 |2799.10 |2981.13 |229.04 |182.03 |
|5 |2775.96 |2998.25 |270.27 |222.29 |
|6 |2752.09 |3014.64 |311.49 |262.55 |
|7 |2727.98 |3030.31 |352.48 |302.33 |
|8 |2703.15 |3045.26 |393.22 |342.11 |
|9 |2677.83 |3059.49 |433.73 |381.66 |
|10 |2652.04 |3072.99 |473.75 |420.95 |
|11 |2625.76 |3085.77 |- |460.01 |
|12 |2599.24 |- |- |- |

Table 1: Experimental values obtained for P(J), R(J), Δ0(J) and Δ1(J)

[pic]
Figure 2: Plot of Δ0(J) (cm-1) against J

y = 41.159x + 63.681
Δ0(J) = R(J) – P(J + 2) = 2B0 (2J + 3) = 4B0 J + 6B0
Gradient = 41.159 = 4 B0 → B0 = 10.29 cm-1 (4 s.f.)

[pic]
Figure 3: Plot of Δ1(J) (cm-1) against J

y = 39.954x + 21.888
Δ0(J) = R(J) – P(J) = 2B0 (2J + 1) = 4B1 J + 2B1
Gradient = 39.954 = 4 B1 → B1 = 9.989 cm-1 (4 s.f.)

At equilibrium internuclear distance, re, of HCl, the following formula can be used to find the rotational constant, Be.

Be = Bn + α(n + ½)

In the above equation, Bv is the rotational constant at n vibrational state and α is the vibration-rotation interaction constant (Coriolis constant).

Be = B0 + α(0 + ½) = 10.29 + 0.5α --- (3)
Be = B1 + α(1 + ½) = 9.989 + 1.5α --- (4)

Solving simultaneous equations (3) and (4), it is found that:
Be = 10.44 cm-1 and α = 0.3010, corrected to 4 significant figures.

In order to find the equilibrium internuclear distance, re, the following formula can be used.

Be = h / (8π2cI) = h / (8π2cμre2) {since I = μre2}

re = √[h / (8π2cμBe)] = √[(6.626 x 10-34) ÷ (8π2 x 3.0 x 1010 x 1.624 x 10-27 x 10.44)] = 1.284 x 10-10 m = 1.284 Å (4 s.f.)

DISCUSSION

Introduction

The heteronuclear HCl molecule exhibits a rovibrational spectrum since it has a permanent dipole moment which shifts upon vibration. In addition, the strong fundamental band observed in the low-resolution spectrum is a result of transition from n = 0 to n = 1. Since HCl is a linear diatomic molecule with only one normal mode of vibration as given by the equation 3N – 5, where N is the number of atoms in the molecule (which is 2), it is relatively easier to study the spectrum as compared to bigger molecules which have many more vibrational and/or rotational modes of transition.

Experimental Setup

It must be ensured that the experimental setup is tight so that moisture from the surroundings will not come inside the setup. In addition to this, solid CaCl2 is placed inside the U-tube in the setup. Solid CaCl2 is strongly hygroscopic. Moisture that passes through the solid will be absorbed, resulting in the formation of hydrated calcium chloride salt as shown in the equation below (Absolute Astronomy, 2010 [B2]).

CaCl2 (s) + 2H2O (g) → CaCl2.2H2O (s)

It is necessary to minimise the presence of moisture in the experimental setup which may otherwise dilute the gaseous HCl formed upon the addition of concentrated H2SO4 solution onto the solid NaCl (as shown in the equation below). When the concentration and/or the partial pressure of the gaseous HCl inside the gas cell are too low, the intensity of the absorption peaks may be too low for effective analysis of the spectrum.

NaCl (s) + H2SO4 (l) → HCl (g) + NaHSO4 (s)

Quantum Chemistry

In an ideal molecule which is perfectly harmonic in nature, the selection rule is only limited to Δn = ±1. However, since real molecules are slightly anharmonic, the wavefunctions are slightly asymmetrical, and hence the integral evaluation of the two wavefunctions of distinct vibrational levels (apart from the n = 0 and n = 1 levels which gives the fundamental band) never goes to zero. It will definitely retain a small value so that the selection rules for anharmonic oscillators include transitions of Δn = ±1 (fundamental band), ±2, ±3, etc (overtone or hot bands). Since the larger the value of the overlap integral, the higher the intensity of the peak as they are directly proportional to one another, the overtone bands have very small intensity relative to the fundamental band. Hence, the spectrum of HCl is expected to show a very intense absorption at approximately 2880 cm-1 (fundamental band), a relatively weak one at 5668 cm-1 (first overtone band) and an even weaker one at 8347 cm-1 (second overtone band). The effect of anharmonicity to the vibrational energy can be described by the product between equilibrium vibrational frequency and the anharmonicity constant (νeχe) as shown below. The minus sign precedes νeχe such that the value of νeχe will be positive.

En = νe (n + ½) – νeχe (n + ½)2

The high intensity of the fundamental absorption band of HCl can be explained by the Boltzmann distribution, which states that there is only one most probable state occupied by a system. At room temperature, the HCl molecules largely occupy the ground state (vibrational level at n = 0) and can transit into the next higher vibrational energy level at n = 1. The overtone or hot bands in which Δn = ±2, ±3, etc. may not be observed, possibly because there is not enough thermal energy for the molecules to make such a large transition in vibrational energy. Another possible reason is that even though these hot bands are detected by the spectrometer, its intensity must be very limited to the point that the peaks may be masked by occurrence of noise in the spectrum.

The derivation of the rotational selection rule in this case is much more complicated than the rules for vibrational modes of transition, but the rule can be summarised as ∆J = ±1. In the fundamental band, the two branches correspond to the P and R branches as mentioned in the Exercise section, with the P branch at lower range of wavenumbers as compared to the R branch. The R branch starts with the R(0) peak where ∆J = +1. On the other hand, the P branch starts with the P(1) peak where ∆J = -1. There is no P(0) peak since this peak would mean that there is a transition to the J = -1 rotational quantum number which is impossible. Another point to note is that the Q branch is not observed since ∆J = 0 is forbidden so that there is a relatively larger gap between the P(1) and R(0) peaks as compared to the gap between the P peaks or the R peaks.

Besides anharmonicity, the other two modifications that need to be taken into account in explaining real molecules are the fact that the diatomic molecule bond is not rigid, unlike the one described by the rigid rotor. When a molecule is rotating in a very fast speed, centrifugal forces stretch will stretch the bond, causing a change in the bond length. As such, an extra term can be added to the rotational energy expression, which is the centrifugal distortion constant, DJ, as shown below.

EJ = BJ(J + 1) – DJJ2 (J + 1)2

Again, a minus sign precedes the centrifugal distortion constant such that the value of the constant will be positive. The constant is in the order of approximately 10-6 cm-1. As such, for most practical purposes, this constant is considered to be negligible. However, it is important to note that as J (rotational quantum number) increases, the contribution of the centrifugal distortion becomes greater.

The other modification to be considered is the vibration-rotation interaction. As a molecule is vibrating and rotating at the same time, at a higher vibrational state, its equilibrium bond length tends to be slightly longer than the theoretical value due to the anharmonic nature of the potential energy curve. The consequence to this is that there will be a slight decrease in the value of the rotational constant, B, since it is inversely proportional to the square of the bond length. To account for this effect, the vibration-rotation interaction constant (also known as the Coriolis constant), α, is introduced as shown below.

Bn = Be – α(n + ½)

The vibration-rotation interaction breaks down the Born-Oppenheimer Approximation which essentially describes that nuclear motion can be separated from electronic motion, and that vibrational modes of transition are independent rotational modes of transition (Banwell, 1983 [A1]). Also, this means that the rotational constant is no longer a constant as a function of n, but it will decrease slightly as n (vibrational quantum number) increases. Due to this effect, it can be observed that the gaps between the adjacent absorption peaks of the fundamental band in the high-resolution spectrum are decreasing in width with increasing wavenumbers.

IR Spectroscopy

IR spectroscopy is a modern, commonly used spectroscopic technique to determine the chemical functional groups in the sample which is ultimately crucial in structural elucidation. It is simply the absorption measurement of different IR frequencies by a sample positioned in the path of an IR beam as different functional groups absorb characteristic frequencies of IR radiation. Vibrational absorption occurs in the IR region, where the energy of radiation is insufficient to excite electronic transitions (Skoog, 1996 [A2]). When the frequency of a specific vibration (stretching or bending) is equal to the frequency of the IR radiation directed on the molecule, the molecule absorbs the radiation and transits from one vibrational energy level to the next (of higher energy level). It is important to note that the vibration of one bond is independent and unaffected by other vibrations. As bond length and polarity of a particular bond is unique, it has a specific force constant value, resulting in a unique energy gap for each transition. As such, different functional groups would absorb at different wavelength. Also, variations in rotational levels may give rise to a series of peaks for each vibrational state. With liquid samples, however, rotation is often hindered or prevented, and the effects of these small energy differences may not be detected (Skoog, 1996 [A2]). The specific type of IR spectroscopy used in this experiment is the FTIR spectroscopy as mentioned in the Introduction section.

From the low-resolution IR spectrum, it has been deduced that the strong fundamental absorption band is approximately between 3100 and 2600 cm-1. However, there is another relatively significant absorption peak which occurs at approximately 2400 cm-1, possibly pointing to the asymmetrical O=C=O stretching mode of vibration of carbon dioxide gas. This is possible since atmospheric carbon dioxide gas molecules may get stuck inside the gas cell used, even though nitrogen gas has initially been introduced into the cell to force other gas molecules out of the cell. Even though the concentration of carbon dioxide gas in the atmosphere is only around 0.04%, very small compared to nitrogen and oxygen gas (~70% and ~21% respectively), there are no absorption peaks that point towards the modes of vibration of nitrogen-nitrogen triple bonds nor oxygen-oxygen double bonds since these modes of vibration are essentially IR inactive. This is also the reason why nitrogen gas is used to force other gases which are potentially IR active, such as carbon dioxide, out of the cell since it will not affect the absorption spectrum of HCl obtained. After subtraction of the background spectrum from the spectrum obtained for the sample, the interfering peaks that may have come from the surrounding air would have been removed.

There are other peaks of relatively low intensity that may also point to carbon dioxide, as well as water molecules. The peaks found between 700 and 600 cm-1 may point to the C=O bending of carbon dioxide (the literature value is approximately 660 cm-1). On the other hand, the peaks at around 1800 to 1400 cm-1 may point to the O-H bending of water molecules (the literature value is approximately 1600 cm-1). Lastly, the peaks occurring between 3900 and 3600 cm-1 may point to the symmetric and asymmetric O-H stretching of water molecules (literature states that it is above 3600 cm-1). As such, it can be confirmed that there are carbon dioxide and water molecules present in the gaseous form inside the gas cell during the measurement of gaseous HCl. However, as seen from the relatively low intensity of the peaks that correspond to carbon dioxide and water molecules, there is only a small amount of carbon dioxide and water molecules present in the cell which does not significantly impact the fundamental absorption band of HCl.

Another important point to note is to keep the wall of the gas cell clear, e.g. not to touch the wall where light is going to pass through during the spectroscopic analysis. Fingerprints left on the wall may result in inaccuracies in the absorbance readings obtained.

Other Concerns

Since the value of the equilibrium internuclear distance obtained experimentally (1.284 Å) is close to the literature value (1.274 Å) with difference of only 0.78%, this shows that the values of parameters obtained in this experiment is largely accurate, and thus reliable. Should there be more time for the experiment, a repeat could be done in order to ensure the reproducibility of the results obtained.

All chemicals used in the experiment must be handled with care since they can pose health risks. Chemicals such as solid NaCl and CaCl2 can be irritating to the eyes upon contact. Hence, goggles must be worn at all times during the experiment. In addition, he concentrated H2SO4 solution used is extremely corrosive and will cause serious burns. Gloves should be worn during the experiment to ensure that direct skin contact with the chemicals does not happen. Another precaution to take is not to inhale any of the chemicals used as they may cause irritation of the respiratory tract when inhaled for too long. All the reactions must thus be performed in the fumehood. As such, safety precautions need to be observed closely at all times during the experiment to prevent unnecessary accidents.

CONCLUSION

For H35Cl, from the high-resolution IR spectrum obtained, as well as the graphical method employed, the important parameters found are as follows (corrected to 4 significant figures): νeχe = 51.67 cm-1 νe = 2989 cm-1 χe = 0.01729 k = 515.5 Nm-1
B0 = 10.29 cm-1
B1 = 9.989 cm-1
Be = 10.44 cm-1 α = 0.3010 re = 1.284 Å

REFERENCES

|Books: |
|[A1] |Banwell, C.N. Fundamentals of Molecular Spectroscopy, Third Edition. Berkshire: McGraw-Hill Book Company (UK) Ltd, 1983. 73, |
| |82, 89-90 pp. |
| | |
|[A2] |Skoog, West and Holler. Fundamentals of Analytical Chemistry, 7th Edition. |
| |The USA: Saunders College Publishing, 1996. 592-593, 596 pp. |
| | |
| |
|World Wide Web sites: |
|[B1] |ChemGuide, 2010. The Mass Spectra of Elements. Available from: |
| |http://www.chemguide.co.uk/analysis/masspec/elements.html (accessed 23-10-10) |
| | |
|[B2] |Absolute Astronomy, 2010. Calcium Chloride [online]. Available from: |
| |http://www.absoluteastronomy.com/topics/Calcium_chloride (accessed 24-10-10) |