If CO2 gas concentration (or partial pressure) in air doubles, then solubility of CO2 gas in ocean and water doubles. This is water everywhere, i.e., ocean, lakes, soil, plant and animal tissues, and raindrops.
When CO2 gas concentration in air decreases, then CO2 gas solubility in water decreases by the same proportion.
When temperature of the surface of the water increases, then the ratio of CO2 gas emissions from that liquid surface increases compared to CO2 absorption into the liquid surface. The ratio of this partition of a gas between the liquid phase matrix and the gas phase matrix is known as the Henry’s Law coefficient.
Henry’s Law coefficients are also known as Arrhenius Constants, which vary with temperature.
This law was discovered by the many experiments on many combinations of gases and liquids documented by Dr. William Henry in England in the early 1800’s. These are documented in editions of the Royal Society of London (England). One of the peer reviewers of Dr. Henry’s works was John Dalton, who founded our existing system of atomic and molecular weights and some of the Ideal Gas Laws.
TKH = c(l)/c(g)
Where T is surface temperature is in Kelvin
KH = Henry’s Law constant
c(l) = concentration of the unreacted gas in the liquid surface
c(g) = concentration of the unreacted gas in mixture of the gases above the liquid surface.
There are many different uses for Henry’s Law in industry (blood gases, anesthesia, carbonated beverage, ammonia production, etc) so the equation has been derived for different purposes, for example solubility, volatility, and fugacity. Great care must be taken with the units in converting from one form to another. The above dimensionless version of the equation is convenient for CO2 (and other atmospheric gas discussions) because the defacto gold standard for CO2 by NOAA Mauna Loa is micromoles of net CO2 per mole of dried air, a dimensionless ratio, reported as ppm. They do not measure CO2 by volume (ppmv) because the water and water vapor have been removed by freezing which changes the sample volume.
Henry’s Law is a constant at a fixed given temperature for a given combination of gas and liquid because diffusion of a gas in a liquid is a function (inverse of thee square root of the molecular weight of the gas), which is constant.
Gases in atmosphere are always colliding with the surface. The absorption rate relative to the emission rate of the gas from the surface is the KH coefficient, i.e., the Henry’s Law constant. The absorption rate of all gases is inversely proportional to the temperature of the liquid. More gas is absorbed by colder water. Each gas and liquid combination has a unique KH, which is referenced onlinefor a given temperature.
A short video by a University of California chemistry professor, sorry I do not know his name.
The graphic below describes the hydration reaction of CO2 gas and water. As you can see it is a reversible reaction. (Stumm, Werner. Aquatic Chemistry. 1996)
The reaction products of the hydration reaction are not included in the Henry’s Law calculation. Only the unreacted gas is included in the Henry’s Law calculation. The reaction products are bicarbonate ions and carbonic acid ions. The ions become part of Dissolved Inorganic Carbon (DIC) and removed from KH. When the hydration reaction reverses, which it easily does by warming of the surface, CO2 gas is generated in the liquid surface re-entering the KH equation. That reverse reaction product CO2 gas can be emitted from the surface. Surface warming increases the rate of CO2 emission (and all gas emission) from ocean surface. Ocean holds about 50 times more CO2 than atmosphere, with deep water holding more CO2 than surface.
In the following graphic is by Daniel Mazza, PhD, professor of chemistry.
In the following graphic from the attached paper by Roger Cohen, PhD and William Happer, PhD describes the rate of change of Molar concentration of the CO2 hydration reaction products versus rate of change CO2 concentration in air. Note the unreacted CO2 gas dissolved in ocean is the nearly flat green line near the horizontal axis. Most CO2 gas becomes bicarbonate ion (HCO3–). Brackets [ ] indicate stoichiometric amounts.
In the following graphic by Jamal Munshi, PhD, professor of business statistics, we can see that the trend (i.e., rate of change) of CO2 gas concentration in air measured by NOAA Mauna Loa is not correlated with the trend of estimated CO2 generated from estimated fossil fuels usage. Adding CO2 from fossil fuels to air does not increase concentration of CO2 in air, because the increase is offset by an equal increase in solubility of CO2.
The rate of emission from the surface is faster than the rate of absorption because air is much less dense than water and thus migration away from surface is faster in air. There is a lag time between absorption and emission. The lag time varies with temperature of the surface. The late Murry Salby, PhD, professor of atmospheric physics, calculated the average global lag time for CO2 at about 6 months. The graphic below from Werner Stumm, PhD illustrates the non parallel rates of emission and absorption.
In conclusion, higher concentration of CO2 in air would be better for plants and all life on earth, but humans burning fossil fuels contribute almost nothing to the CO2 concentration and any increases or decreases are only temporary until the Henry’s Law constant partition ratio is rebalanced for the local surface area. CO2 in air increases and decreases locally, mostly based on warming and cooling of the local surface, ocean being about 70% of earth’s surface. There is no climate crisis and attempts to reduce CO2 are futile and extremely wasteful of resources.
References:
- Compilation of Henry’s law constants (version 5.0.0) for water as solvent By Rolf Sander, PhD. Air Chemistry Department, Max Planck Institute of Chemistry, P.O. Box 3060, 55020 Mainz, Germany. Published: 6 October 2023. https://henrys-law.org
- U.S. National Institute of Standards and Technology (NIST.) https://webbook.nist.gov/cgi/cbook.cgi?ID=C124389&Units=SI&Mask=10#Solubility
- Stumm, Werner, 1996. Aquatic Chemistry, https://archive.org/details/aquaticchemistry0000stum/page/192/mode/2up)
budbromley 
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