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The Numbers Don’t Work

by James R. Barrante, Ph.D.

The major idea driving the greenhouse gas effect originates with the observation from the late 1800’s that planet Earth is warmer than similar planets of the same size and distance from their star.  The reason given by a number of scientists, including the physical chemist Svante Arrhenius, was that it was because Earth had an atmosphere containing specific gases that could absorb a portion of the infrared light radiated by the planet and return it to the planet.  The Earth receives light from the sun that warms the planet.  In turn, in order to maintain a constant temperature, Earth must radiate a portion of the light back to space.  The wavelengths of light radiated by the planet fall in a band in the infrared region of the light spectrum, controlled by the Earth’s temperature.  Any interference in this process, such as the absorption of this infrared radiation by atmospheric gases,  will upset the energy balance of the planet.

The two major gases able to intercept wavelengths of infrared light radiated by the planet are water vapor (its level varies with climate, so let us assume an average level of about 2%), and carbon dioxide (about 0.04%).  These two gases are known as “greenhouse gases.”  Just from the concentration difference alone, we can see that water vapor is the major player here.  Moreover, water vapor is able to absorb a much wider band of infrared light than is CO2.  Most scientists agree that of the total radiation absorbed, water vapor absorbs about 90%.

Based on calculations made by assuming the planet was a blackbody radiator, it was found that the planet was 33ºC warmer than it should be, supposedly caused by our atmosphere.  Assuming that the two major greenhouse gases are water vapor and carbon dioxide, carbon dioxide would be responsible for 10%, or 3.3ºC, of that warming.  That is, increasing the CO2 in the atmosphere from 0 ppmv (parts per million by volume) to the 1850’s value of 280 ppmv should have raised the temperature of the planet by 3.3ºC.  It is well known that the absorption of light by matter is not linear with concentration, but falls off exponentially or logarithmically.  In the late 19th century, Arrhenius suggested a simple equation to relate the amount of warming by a greenhouse gas to its level in the atmosphere to be

ΔT = T2 – T1  =  ln (C2/C1)

where k is an experimentally determined constant and ln is the natural logarithm.  We can see that this equation is problematic, if the concentration C1 is equal to zero.  So let us modify the equation by choosing some very small level of CO2 to represent zero concentration.  (It turns out that this choice is quite arbitrary, as long as it is very small).  The new equation becomes


Using the original premise that the presence of CO2 in the atmosphere raised the temperature of the globe by 3.3 degrees, we can determine the constant k.

3.3  =  ln (280/1 × 10¯¹º)

k  =  0.115ºC

We are now able to see how global temperature changes with increasing concentration of CO2.  It is clear that if you double the concentration of CO2 in the atmosphere, global temperature will increase by a whopping 0.08°C.  So, increasing the CO2 level from 0 ppmv to 100 ppmv, raised global temperature by 3.2°C; further increasing the level from 100 ppmv to 200 ppmv raised global temperature by 0.08ºC; and further raising the level from 200 ppmv to 300 ppmv raised global temperature by 0.05ºC.

A number of years ago climate scientists announced that the increase in CO2 level from its 1850’s value of 280 ppmv to the present value of about 380 ppmv raised global temperature by 0.8ºC.  Let’s see how that squares with our modified Arrhenius equation.

ΔT  =  0.115 ln (380/280)  =  0.035ºC

Not very good, is it!  Something obviously is wrong!  Whatever the case, it is apparent that associating a 0.8ºC temperature increase in global temperature with an increase in the CO2 level from 280 ppmv to 380 ppmv is not at all consistent with the CO2 and water vapor’s warming the planet by 33ºC as described by the climate-change crowd.  The numbers do not work!




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Ocean Acidification and Its Effect on Corals I

by James R. Barrante, Ph.D.

Ocean chemistry essentially involves the chemistry of the carbonic acid buffer system to which is added the chemistry of insoluble carbonates such as calcite and aragonite, CaCO3.  When the Earth formed, the atmosphere was approximately 95% carbon dioxide and water vapor.  No free oxygen or nitrogen gas was present.  As the planet cooled, however, the temperature dropped to below the boiling point of water, and the majority of the water vapor in the atmosphere along with outgassing vapors formed our oceans.  Because of its high solubility in water, the CO2 in the atmosphere began to dissolve into the oceans.  The high solubility of CO2 in water is mainly because CO2 reacts with water to form a weak acid, known as carbonic acid, H2CO3.  Carbonic acid in turn slightly dissociates in water giving:

Here the K‘s are the dissociation constants for carbonic acid and the a‘s represent the activities (effective concentrations) of the subscripted ions.

If we multiply the two dissociation constant equations together, we obtain an expression for the activity of CO3= .

As the concentration of CO3= increased in the oceans, it began to react with soluble salts of magnesium and calcium that found its way into the ocean to form insoluble carbonates.  These carbonates settled to the bottom of the oceans and became rock.  For example, marble is calcium carbonate.  The removal the carbonate ion from the ocean, allowed more CO2 to dissolve.  Eventually, the level of CO2 dropped to parts per million range and has remained there for millions of years.

The solubility of calcium carbonate (calcite and aragonite are two crystalline forms) can be described by the equation

where Ksp is the solubility product for CaCO3.  As a true equilibrium constant, it value is only a function of temperature.  To obtain concentrations from activities, however, require a knowledge of activity coefficients, and these are a function of the ionic strength of the solution.  In terms of concentrations, the above expression becomes

Here, γ ±2  represents the mean activity coefficient of calcium carbonate and () represent molar concentrations of the ions in solution.

Any solution of calcium carbonate in the presence of the carbonic acid buffer system must be electrically neutral.

Substituting the above equilibrium equations into this equation gives

The activity of dissolved CO2 (H2CO3) depends on the partial pressure of CO2 over the solution.  This is known as Henry’s Law

Here, kH  is the Henry’s Law constant and P is the partial pressure of CO2 in atmospheres.  Multiplying the above equation by  aH+2  and substituting Henry’s Law into the equation gives

We see this to be a quadric equation that can be solved numerically for pH as a function of CO2 pressure.  Once the pH is known, values of the other species can be determined.  The graph and Table below give values for pH, partial pressure of CO2, and activities of ionic species.  To get the concentrations from the activities, the high ionic strength of the sea water must be taken into account.  Concentrations could be significantly different from activities.  Other values at 298.2 K are:  K1  =  4.45 x 10-7, K2  =  4.69 x 10-11, kH  = 29.41 atm/M, Ksp = 6 x 10-9 (an average for the minerals marble and aragonite), and pH = – log aH+ .

It appears, looking at the activities of  Ca++ and CO3=, that as the partial pressure of CO2 in the atmosphere goes up, the activity of the Ca++  goes up, thus causing the activity of the CO3= to decrease.  The activity of the calcium ion represents the solubility of the CaCO3.  It is clear that the solubility of CaCO3 increases as the pH decreases.  What is not intuitively obvious is that the process is not linear.  Note that as the partial pressure of CO2 approaches 3000 ppm the concentrations of calcium and carbonate level off.  This would explain how the coral reefs could have formed in the first place at CO2 levels of 3000 to 4000 ppm.  The calculations producing the data in the graph were at 298.2K.


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