Student activity: Calibration at Mauna Loa (continued)

How can we be certain that CO2 levels are indeed increasing from decade to decade? It would be expected since most economies are growing and based on fossil fuels, but the only way to make sure that the excess CO2 is not being absorbed by plants, oceans and minerals is by continuously measuring the CO2 in the air.

That’s what takes place at Mauna Loa on the “Big Island” of Hawaii. To understand how it’s measured, scientists use the fact that CO2 absorbs infrared (heat energy). This property not only makes it possible to measure the concentration of CO2, but it is the reason CO2 has a worrying effect on the climate.

1)   Draw the Lewis Dot diagram for carbon dioxide. What is the shape of the carbon dioxide molecule?

Notice that fig. 1a is the same as  fig. 1b.

The number of vibrational modes (different types of vibrations) in a molecule is 3n-5 for linear molecules such as CO2, where n = number of atoms in the molecule.

Ball-and-spring representation of carbon dioxide.

Fig. 1a, b: Models of carbon dioxide.


2)   Using this formula determine the number of different types of vibration for carbon dioxide.

Does this agree with Fig. 2?

Ball-and-spring model showing directions of vibration.

Fig. 2: Vibration modes of carbon dioxide. The arrows indicate the directions of motion. Vibrations labeled A and B represent the stretching of the chemical bonds in CO2. C and D represent bending vibrations.

3)   Diatomic molecules such as oxygen (O2) and nitrogen (N2) cannot absorb infrared radiation. That’s why most of the gases in air are not greenhouse gases. Now the vibration in A (Fig. 2) does not lead to infrared absorption either. Apply physics to chemistry: what does diagram A (Fig. 2) have in common with diatomic molecules?
Hint: For a molecule to absorb infrared, the vibrations or rotations within a molecule must cause a net change in the dipole moment (a net force is required) of the molecule.

A nice animation of the vibrations of carbon dioxide, oxygen and nitrogen can be found on the Windows to the Universe website.

4)   Easier question: Are bending and stretching vibrations the   only movements associated with carbon dioxide gas? (Think of other gases in answering the question).

The concentration of CO2 in the atmosphere is measured at Mauna Loa, Hawaii using infrared spectroscopy. Ambient air at the site (taken from the top of a 38 m tower to avoid contamination from humans) is dried and passed through an observation cell continuously. The monitoring light beam is at a wavelength that is absorbed by carbon dioxide (due to motions B,C and D, Fig 2). The light that makes it through is converted into a voltage signal, which varies with concentration of CO2.

To calibrate the voltage response, three reference samples are monitored. Below is data of Voltage Output from Mauna Loa CO analyser for November 17, 2006.2

Graph of voltage versus hour.

5)   Use the data on the previous page to fill out the x values. First find W1, W2 and W3 on the graph. Respect significant figures and make sure to estimate the last digit in measurement!

X (voltage in V) Y (concerntraion of CO2 in ppm
W1 370.5
W2 373.93
W3 389.72

6)   For each pair of (x,y) coordinates, substitute them in the     equation y = ax2 + bx + c.

That means you should have three equations with ab and c as unknowns.

7)   Use substitution or elimination to solve for ab and c. Do your calculations on a separate page.




Use your answers to write an equation in the form of y = ax2 + bx + c that relates concentration(y) to voltage(x).


8)   Use your equation to get the actual concentration range of carbon dioxide between the years 2006 and 2009.

Table of year beside voltage ranges obtained and respective ranges of concentrations of CO2.

9)   Why is there variation from season to season within the same calendar year? Think about rates of reaction.

10)  Based on these data, is the CO2 concentration increasing from year to year? Why?

Notes and references

  1. Students can solve the system of equations using substitution or elimination but it might be a good opportunity for them to use Solver in Excel. There are plenty of online examples for students to follow.
  2. The reference is slightly changed since 2010 and is found at

Selected answers (for teacher use):

5) W1 = 1.43 V
W2 = 1.85 V
W3 = 2.28 V

6) y =  0.3706x2  +  21.24x  +  339.4 (An extra significant digit was conserved for future calculations.)

7) minimum concentration of CO2 in 2006 was 379 ppm; maximum concentration of CO2 in 2009 was 390 ppm.