The real FTIR spectrum of CO2 (wonkish)

I was reading through the comments on "Climate change is the world's most pressing problem"
and came across this bit of swill from one Chuck Wiese, Meteorologist - who also seems to have impressed the folks at Skeptical Science:

1/22/2015 7:16 PM

"Ample physical evidence shows that carbon dioxide (CO2) is the single most important climate-relevant greenhouse gas in Earth's atmosphere." Yes, water vapor is a greenhouse gas, but water vapor is limited to its equilibrium vapor pressure at a given temperature. Any more, and it condenses — a phenomenon we know well in the Northwest. Direct measurement of infrared absorption by CO2 — an experiment I have repeated many times with my chemistry students — is not affected by the presence of water vapor."

This statement by Jim Diamond is demonstrably false and as a chemistry professor, he ought to know better. Water vapor bands in the infrared are shared with CO2 in up to 37% of the absorption wavelengths from CO2, and CO2 IS NOT the "single most important climate- relevant greenhouse gas in the earth's atmosphere." The cross absorption and emission between these gases is very significant."

So I thought I would dig into the archives and see what I had on the infrared spectrum of CO₂. Here's a little bit of background on this type of experiment.

A Classic Physical Chemistry Experiment

The difference between adjacent vibrational states of a molecule usually lies in the infrared (IR) portion of the electromagnetic spectrum.
These energy differences can be related to physical properties of the molecule, such as the distance between atoms (bond length), the masses of the atoms, and properties related to the molecular potential energy surface.

These energy differences are measured by comparing the transmission of electromagnetic radiation through a region between a source and a detector, first, without a sample present, and second, with a sample present. The ratio of the latter to the former is called the the transmission coefficient, T. The differences are due to the presence of the sample.

Most modern IR instruments are Fourier-Transform (FT) rather than dispersive spectrometers. In either instrument, it is sometimes more convenient to determine the absorbance A of the species, rather than the transmission T. These are related through the Beer-Lambert equation:

• A₁₀ = - log₁₀ T 
• T = 10^-A₁₀

Although FT instruments are much less expensive and faster that dispersive instruments of the same precision, they have their own set of problems. Here's some information from the CH362 course Experimental Chemistry I at Oregon State:

The one minor drawback is that the FT instrument is inherently a single-beam instrument; it cannot use the "channel ratio" trick used in CW operation.  One result is that IR-active atmospheric components (CO2, H2O) will appear in the spectrum.  Usually, a "Background" spectrum is run, then automatically subtracted from every spectrum.  The spectrum... [above] is such a background scan.

You can see CO2 as the strong doublet [OG - due to the 'asymmetric stretch' mode] at around 2300 cm-1, and water as the "spiky" peaks in the 3800 and 1600 cm-1.  The "bell curve" shape of the spectrum reflects the output spectrum of the source:  strong in the middle, but falling off at the ends. [OG - The downward spike at about 670 cm^-1 is due to the bending mode of CO₂; notice that there is no overlap with the absorption due to water vapor in either the bending mode band or the asymmetric stretch band, so apparently Jim Diamond's assertion is demonstrably correct!]

This bending mode absorbance, although it looks insignificant in the background spectrum above, is responsible for the greenhouse gas properties of CO₂.

Outgoing spectral radiance at the top of Earth's atmosphere showing the absorption at specific frequencies and the principle absorber. For comparison, the red curve shows the flux from a classic "blackbody" at 294°K (≈21°C ≈ 69.5°F).  

It is possible, in a single measurement of the IR spectrum, to observe the rotational-vibrational spectra of all four isotopes of hydrogen chloride - ¹H³⁵Cl, ¹H³⁷Cl,²H³⁵Cl, ²H³⁷Cl. Under suitable conditions, one can see not only the rotational fine structure in the fundamental band,

but that in the first overtone as well - EIGHT different bands  - so that one can determine with great accuracy and precision five different molecular parameters for each of the four molecular isotopes:

• the harmonic vibrational frequency
• the vibrational anharmonicity - which also provides a crude estimate of the dissociation energy
• the rotational constant - from which one can determine the bond length
• the rotational-vibrational coupling constant
• the centrifugal distortion constant

For about $300, one can acquire a small (5L) lecture bottle of 99% DCl which contains both ²H³⁵Cl and ²H³⁷Cl, as well as smaller amounts of the more strongly absorbing ¹H³⁵Cl and ¹H³⁷Cl.

Problems with HCl/DCl

HCl/DCl is corrosive, so it must be shipped on land.

Packaging
5 L in steel cylinder
Shipping of this product by air freight is forbidden.
Outside of the U.S., ocean freight shipment is required and will result in substantial additional expense.
Standard 5 L quantity is packaged in a 450 mL carbon steel lecture bottle with stainless steel CGA 110/180 valve. Nominal gas pressure at 21ºC is 150 psig for 5 L . This pressure is slightly above atmospheric pressure. Care must be taken when extracting this product from the cylinder.

In addition, the empty gas cylinder must be treated as hazardous waste! This greatly inflates the cost of the experiment.

I seem to remember a couple of poster presentations about alternatives.

• Constructing a green alternative to a traditional physical chemistry experiment, the moderate-resolution infrared spectra of carbon dioxide: Analysis of weak absorption bands  

CHED 1382
Catherine Marie Clark,  and Christopher Robert Braden. Department of Chemistry, Linfield College,  McMinnville, OR 97128

In order to demonstrate the potential for CO₂ gas to replace HCl gas in a common physical chemistry experiment, FTIR spectroscopy was performed on CO₂. Techniques such as the inclusion of P₂O₅ in the gas cell were applied to reduce interference by water. This allowed for the resolution of bands resulting from rotational-vibrational coupling, which are necessary in determining molecular constants.

• Developing a green physical chemistry experiment 

I&EC 136
Christopher Robert Braden, Catherine Marie Clark, and Jim Diamond. Department of Chemistry, Linfield College, McMinnville, OR 97128

We investigated the use of CO₂ as a substitute in order to find a green alternative to a common physical chemistry experiment, the analysis of the rotational fine structure in the IR spectrum of a hydrogen halide. While HCl provides an easily analyzed spectrum with clear overtones and readily obtained isotopes, it is a corrosive substance that requires disposal as hazardous waste regardless of the method of preparation. CO₂ can be easily obtained from the atmosphere, and isotopically enriched samples are easily obtained as well. The CO₂ spectrum requires little effort to resolve and shows overtones and combination bands at moderate pressure. Though the spectrum is more complex than HCl, it is no more difficult to analyze, and the experiment provides a richer experience for undergraduates. Overall, our findings indicate that CO₂ is a safe and satisfactory substitute for HCl.

The Green Chemistry Alternative to HCl/DCl: The Rotational Fine Structure in the Fundamental Bending Mode Band of CO₂

We tried FTIR measurement of CO₂ with various methods of sample preparation, looking for a fast, easy, green alternative to HCl/DCl.

• CO₂ in the atmosphere (about 400 ppm);
• CO₂ in respired breath (about 4% by volume);
• CO₂ obtained from sublimation of dry ice pumped into an evacuated 10 cm gas cell with KBr windows at various pressures after being dried with P₂O₅.
• CO₂ obtained from sublimation of dry ice pumped into an evacuated 10 cm gas cell with KBr windows at various pressures without drying.
•  CO₂ obtained from sublimation of dry ice directly in the FTIR sample chamber without use of a cell.

The last method was easiest but the partial pressure of CO₂ was unknown. Given the lack of overlap between water vapor and CO₂ absorption bands [see above],we settled on measuring CO₂ obtained from sublimation of dry ice pumped into an evacuated 10 cm gas cell with KBr windows at various pressures without drying. A partial pressure of 100 torr provided strong, sharp spectra.

The FTIR Spectrum of CO₂

Here are the actual results of a set of experiments from 2007.

FTIR Spectrum of CO₂(g) from 370 cm^-1 to 7000 cm^-1

All of the "negative" absorbances represent absorption of water vapor in the background spectrum, weaker stronger than absorption of water vapor in the sample spectrum. From right to left, the observed bands represent:

1. poor transmission of the KBr windows below 400 1/cm
2. water vapor absorption between 400 and 500 1/cm
3. the bending mode band,between 500 and 750 1/cm
4. water vapor absorption, between 1300 and 2000 1/cm 
5. the asymmetric stretch band, between 2200 and 2400 1/cm
6. the only overlapping band in this spectrum, showing both  CO2 absorption and water vapor,  between 3400 and 4000 1/cm
7. a very weak combination band of CO2 between 4800 1/cm to 5200 1/cm
8. weak water vapor absorption, between 5200 and 5600 1/cm
9. gradual attenuation of the signal above 6000 1/cm due to both windows and detector.

Some of the features in the bending mode band are visible only with higher resolution.





Bending mode band, from 500 cm^-1 to 750 cm^-1

Besides the prominent Q band in the center, the other features are: a Fermi resonance to the high-energy (left) side of the Q band; the weaker (1.1%) 13CO2 Q band; the low-energy component of the Fermi resonance in the CO2 band; and emergence of the the low-energy component of the Fermi resonance in 13CO2. There are many lines present in the rotational fine-structure.

Here is an interesting zoom into the combination band, show the absorption spectrum (in black), and its second derivative (in blue). Note that absorption maxima correspond to minima in the second derivative. 

 

A linear regression of peak position versus a cubic function of an index related to the rotational quantum number is sufficient to determine the molecular parameters described above with a great deal of precision. There is about a 1/3 chance that there is a significant difference in B0 and r0 between this result and that of Herzberg. The band origins are, on the other hand, significantly different, but we had a laser.

Not too bad, considering we were working with data that is demonstrably false!