Category Archives: Basic Physical Chemistry

Ocean Acidification and its Effects on Corals III. Temperature

by James R. Barrante, Ph.D.


In OA I and OA II we considered the ocean chemistry of the carbonic acid system at constant temperature.  Under these circumstances, it is apparent that if the partial pressure of carbon dioxide in the atmosphere increases, the pH of a buffered ocean must drop.  We were able to show in OAII that increasing the partial pressure from 280 ppmv to 380 ppmv will decrease ocean pH from a values of approximately 8.2 to 8.1. pH units.  In OAIII we shall consider the effect of temperature on these equilibria.  Since we are working with activities rather than concentrations, it is not necessary to consider ocean salinity here.  A significant amount of research has been done concerning the temperature dependence of the equilibrium constants.  This data can be found online.  A typical set of equations are:

ln K1 =  – 1596.1/T  –  9.2597

ln K2 =  – 2174.5/T  – 16.467

ln kH =  – 2400/T  +  11.431

ln Ksp =  2388.9/T  – 27.213

where K1 is the first dissociation constant of H2CO3, K2 is the second dissociation constant of H2CO3, kH is the Henry’s Law constant, and Ksp is the average solubility constant of CaCO3.

The equation relating the pH of ocean water to the partial pressure of atmospheric CO2 at temperature  is


This equation was derived in OAII.  There are obviously a number of variables in this equation that could be changing at the same time.  It might be interesting to approach the problem as one does with PVT data and look at a surface graph.  First note that because the concentration of calcium ion in the oceans is so large, we can assume that the activity is constant at 0.00123.

It is well-known that pH is a sensitive function of temperature.  Consequently, to assume that the pH of our oceans depends only on the concentration of dissolved CO2 is a sophomoric definition of the boundaries of the system.  To express the data graphically, it is necessary to do so on a surface.  Slices of the three-dimensional graph are easily seen by following isotherms or CO2 isobars.  Note that the change in pH with temperature is not insignificant.  It has been noted that the pH of the oceans has dropped about 0.1 pH units in 150 years.  This normally is incorrectly attributed to the absorption of atmospheric CO2, and while atmospheric CO2 does come into play here, one should note that as little as a 2-degree C increase in ocean temperature can decrease ocean pH by as much as 0.05 pH units.  Moreover, assuming that the concentration of dissolved CO2 increases in a solution in which its temperature increases is not consistent with Henry’s Law.

Below is the P-pH-T representation of ocean pH.  Keep in mind that the system is highly buffered.  For clarity, the pH at various intersections of the curves is given.  Because of the three-dimensional nature of the graph, to find temperatures and pressures, be sure to follow the intersections along lines to their respective axes.  The temperature range was taken to represent global SST in zones from the equator at 303K to Antarctica at 273K.  Note the variation in ocean pH between these two temperatures on any isobar.  At today’s value of 400 ppmv, the pH changes from 8.30 to 8.00.  This would suggest that describing an average ocean pH has no physical meaning.  I would imagine that a similar effect occurs going from surface temperature to deep-water temperature.  It’s clear that using a secondary school chemistry course definition of pH in this complex system serves no useful purpose and leads one to the wrong conclusions about ocean acidification.


    P-pH-T Data for Ocean pH.


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Applied Mathematics for Physical Chemistry


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January 26, 2016 · 9:31 am

Scientific Folly of Averages

by James R. Barrante, Ph.D.


There is a misunderstanding among many scientists that using average values to do science is acceptable under any condition.  This is actually not the case.  To understand this, we must look at Error Theory.  Scientists are generally interested in two types of errors:  random error and systematic error in their measurements.  Random error is related to inherent errors in measuring devices, particularly when these measuring devices are being used near their limitations.  This type of error is associated with the precision of the measurement, how close individual measurements of the same parameter are to each other.  Systematic error is related to experimental design.  This type of error is associated with the accuracy of the measurement; that is, how close individual measurements of the same parameter are to the “true” value.   The precision of a measuring device can be increased by making the measurement more than once and taking an average only if the following is true:  the measurement must be made using the same measuring device on exactly the same sample over and again thousands of times.  Thus, the precision of the average or mean value will be greater than the precision of a single measured value.

No statistical analysis will affect the systematic error.  The average will be no more accurate than a single measurement.  What, then, is the advantage of measuring a sample several times and taking an average.  The reason is to insure that no systematic error was made in the measurement, a possibility if the measurement was made a single time.  For example, if you were determining the mass of an object, to insure that you did not misread the balance, you might take three consecutive readings, each one after zeroing the balance.  If they are all within the random error of the balance (generally supplied by the manufacturer), you can be sure that no error was made reading the scale of the balance.  Does this mean that the average of the three is accurate.  Not in the least.  If the balance had not been calibrated, the average could be precise (e.g., 24.55; 24.52; 24.54), but not accurate.  For example, the true weight could be 16.24.  Calibrating the balance is necessary to minimize systematic error.  It’s part of experimental design.

When do averages have no scientific meaning?  The study of climate change is a perfect example.  The idea of an average global temperature as it relates to an average global atmospheric CO2 level has about as much scientific meaning as the average diameter of a football has to its shape.  Knowing that the average diameter of a standard football is 9.00 inches tells you nothing about its shape.  In fact, the average presented as a single number would suggest that the football is spherical.  The average value of some measured parameter of a system (like pressure or temperature) is scientifically significant only if 1) the system is very small; 2) its boundaries are well-defined; and 3) measurements are made with the same measuring device on various points over the system where these measuring points have the same environment.  The globe satisfies none of these requirements.

You can certainly determine the temperature of the globe at various points around the globe and obtain an average that is valid as an average temperature.  But you cannot do anything scientifically meaningful with that number.  For example, suppose we wish to determine how atmospheric CO2 level affects that average.  For this to be scientifically meaningful, it would have to be true that only CO2 level could affect the temperature at every single measuring point over the entire system.  When the Soviet Union fell, a number of temperature measuring stations in Siberia were closed.  The average global temperature suddenly increased.  Climate change theory would have you believe that a sudden increase in CO2 level caused the sudden increase in average global temperature.  Another example, the average atmospheric CO2 level is found to suddenly increase.  It is assumed that this sudden increase in CO2 level was caused by an increase in burning fossil fuels.  In actuality, the opening of a coal-burning power plant occurred at one measuring point, while a volcanic eruption occurred at another measuring point.  Different causes, same effect.

Where cause and effect is meaningful is when the system is small with well-defined boundaries.  A small cylinder holding a gas is heated from 300 K to 400 K.  A pressure gauge on the cylinder measuring average pressure increases from 1.0 bar to 1.3 bar.  The average pressure change is consistent with the average temperature change, because the cylinder is a system that satisfies the three conditions mentioned above.  This is the nature of the natural sciences and it cannot be changed within the realm of the scientific method.  Unfortunately, many climate scientists do not seem to understand this.

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Let’s Do P-Chem Homework!

by James R. Barrante

From the author of “Applied Mathematics for Physical Chemistry,” 3rd ed., a new textbook on solving physical chemistry problems in the iBook Store.  Only $9.99.  See it today.


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Physical Chemistry for the Biological Sciences


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September 11, 2014 · 12:19 pm


Author of best selling supplement, Applied Mathematics for Physical Chemistry, 3rd Edition, James R. Barrante has a new textbook, Physical Chemistry for the Biological Sciences, an iBook for iPads, iPhones, or Macs with OS X Maverick.  To download a sample chapter, go to the iBookstore.  At $9.99 it makes a great supplement for any physical chemistry course.


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August 19, 2014 · 1:15 am

Can Infrared Light Pass Through Glass?

by James R. Barrante, Ph.D.

There seems to be some controversy, particularly by laypersons, as to whether infrared light can pass through glass.  The correct answer is, “That depends!”  Infrared radiation spans a wide region of wavelengths.  At the shorter wavelength end, near visible red, the behavior of infrared light is not that different from visible light, except, of course, humans cannot see it. This radiation, called near infrared, does pass through glass. A better way to look at it is to say that it is not absorbed by the glass. It’s energy is too large to excite atoms in molecules to higher vibrational states. If you own an electric stove, you will experience this light just before the coils begin to glow a dull red. If you doubt that it is there, put your hand near a coil. Your skin actually “sees” this light.

The middle band of wavelengths, generally referred to as thermal infrared, is infrared light produced by matter around room temperature.  It is this band of infrared that cause atoms in molecules to jiggle, and jiggling atoms generate heat.  This radiation is strongly absorbed by matter, and will not pass through glass.  It is also the radiation absorbed by CO2.  So any demonstration that attempts to show that a glass jar filled with CO2 will heat up faster and to a higher temperature than a jar filled with air by shining infrared on both jars has been staged. Oh, the gases in both jars will heat up. If you heat up any container, glass or otherwise, any gas inside the container also will heat up.

At the other end of the infrared spectrum, the far infrared, the light is significantly lower in energy, approaching that of microwaves and radio waves.  This type of radiation generally is produced by colder substances.  It is a more controllable heating radiation and is the type used in infrared heaters and saunas.

As a final reminder, infrared radiation is a form of light, not heat.  Heat is transferred by molecular collisions and is relatively slow.  Infrared radiation moves at the speed of light and is fast.  We associate infrared light with heat only when it interacts with matter and excites vibrational modes of motion of atoms in molecules.  In order for that to happen, a vibrational mode must set up an oscillating electric field in the molecule that can couple with the electric field component of the infrared wave.  While the nitrogen atoms in N2 vibrate, they are unable to create an oscillating electric field.  Consequently, N2 is not infrared active.  Carbon monoxide, CO, is a polar molecule and therefore will set up an oscillating electric field when the carbon-oxygen bond stretches.  It is infrared active.


Filed under Basic Physical Chemistry, Basic Science