Someone on the NASA Facebook site asked, “Has the Tonga volcano (the name of the volcano is actually Hunga, which erupted off the coast of Tonga) put enough dust into the atmosphere to affect the global average temperature, as Mt. Pinatubo did back in 1991?”

The next day someone at NASA took the time to answer the question,:

“The main climate impacts of volcanic eruptions is not from their carbon dioxide emissions (small compared to that coming from human activities) but from the short-term cooling induced by their sulfur dioxide (SO2 ) aerosols emitted.

The total SO2 mass from the Tonga eruption was 0.4 teragrams — 400 million kilograms — of SO2 , which is well below what could significantly alter global climate.

For instance, the Mount Pinatubo eruption in 1991 released 15 to 20 teragrams (1 teragram represents 1,000,000,000 [1 billion] kilograms) of SO2 high into the atmosphere, resulting in a 0.6 degree Celsius (1 degree Fahrenheit) drop in global temperature over the next 15 months. That amount is 37.5 to 50 times greater the relatively small amount of SO2 emitted from the Tonga eruption.”

1. Amplified Explosion. The fact that the volcano is located in relatively shallow water (150 m) led to a bigger explosion. The steam generated from the contact between magma and seawater led to additional gas pressure that could not be offset enough by the overhanging pressure of the seawater at that depth.
2. The Shock Wave. “The blast produced a shock wave in the atmosphere that was one of the most extraordinary ever detected, said Corwin Wright, an atmospheric physicist at the University of Bath in England. Satellite readings showed that the wave reached far beyond the stratosphere, as high as 60 miles up, and propagated around the world at more than 600 miles an hour.” (NY Times, Here’s What Scientists Know About the Tonga Eruption, Jan19, 2022″.
3. Volcanic Lightning. In the title-picture we notice a beautiful bolt of lightning. This was not caused by a coincidental storm but by the ash itself. The rapidly expanding particles from the ash have enough kinetic energy to cause electrons to move out of the dust, leading to massive static. If the charges are separated in the eruption-cloud there could be enough voltage to cause a discharge.

More Details About Pinatubo and Atmospheric Perturbations from Volcanoes:

1. The Pinatubo eruption was the 2nd largest of the 20th century, spewing ash to a height of 40 km, which is in the upper stratosphere, home of the ozone layer.
2. The combined effect of volcanic particles and anthropogenic reactive chlorine led to record low levels of stratospheric ozone. (Nature volume 373, pages399–404 (1995))
3. How? The particles that the eruption injected into the stratosphere provided sites for heterogeneous chemical reactions, akin to the way polar stratospheric clouds(PSFs) accelerate ozone depletion over Antarctica. The set of reactions lowers reactive nitrogen species, which are needed to act as an important buffer to ozone loss. For example, NO2 is involved in reactions which convert reactive chlorine into non-reactive forms, preventing it from destroying more ozone. But if NO2 is sequestered by either PSFs or volcanic aerosols, then more catalyst(Cl) is available to wreak havoc.
4. Pinatubo killed over 800 people, damaged farmlands and thousands of homes. It also caused about \$100 million of damage to aircraft.

How Well Do You Know Your Volcanoes?

1B, 2C, 3E, 4A, 5D

# Figuring Square Roots Without a Calculator or Without Newton’s Method

People knew how to calculate square roots thousands of years before they had any knowledge of calculus. So how did they perform the feat? I saw this on Dr. Peyam’s Youtube channel of mathematics, where he points out that Heron’s method (the Babylonoian method) is essentially an algorithm disguised as Newton’s method. He probably considered it too pedestrian to reveal why, but after showing the Babylonian method like he did, we will prove how it ends up being the same series of calculations, even if the Babylonian way involves no derivatives.

Suppose you want to find the square root of 3. Since 1.52 = 2.25 and 22 = 4, we know the root of 3 lies somewhere between 1.5 and 2.

We begin with the higher value of 2, which will be our first guesstimate of b. To get the next guesstimate, we will do the following:

= (1/2) ( b + a/b) , where a is the number we are square rooting, so

= (1/2 )(2 + 3/2) = 1.75

We can do better than that by using this new estimate and plugging it back into: = (1/2) ( b + a/b) = (1/2 )(1.75 + 3/1.75) = 1.73214…

One more iteration and we have the square root of 3, accurate to 8 decimal places: (1/2 )(1.73214… + 3/1.73214…) = 1.73205081

So why is the method equivalent to Newton’s?

In Newton’s method, we also use successive approximations but this time they’re defined by x = x1 – f(x1)/f'(x1), where f(x) = x2a. Since the derivative of x2a = 2x, if we replace our guesstimate, x1, with b, in x = x1 – (x12a)/2x we get

x = b – (b2a)/ (2b ). Obtaining a common denominator for b and the fraction that we are subtracting it from:

x = [2b2– (b2a)]/ (2b) = [2b2b2 + a]/ (2b) = [b2 + a]/(2b) = (1/2) (b + a/b), which is exactly the formula used by the Babylonians!

Is there a way of coming up with the formula (1/2) ( b + a/b) without using calculus? Yes.

Again let a= be the number we are square rooting.

Then a = the square of the sum of the approximate square root of a, which we will call b again and the error, e, involved:

a = (b+ e)2

Now expand the above and solve for e :

a = b2+ 2be + e2

a = b2+ e (2b + e)

e = ( ab2 )/ (2b + e)

Since e << 2b in the denominator:

e ~ ( ab2 )/ (2b)

If we substitute the above into a = (b+ e)2

If we add the approximate expression for e to our estimate of b:

The new estimate = b + ( ab2 )/ (2b) = (b2 + a)/ (2b) or = (1/2)(b + a/b).

The Babylonians used a base 60 numerical system. Their approximation for the root of 2 comes from:

# Ideas & Tricks Behind the Jargon of Organic Chemistry

To someone not familiar with baseball, the following part of a score card seems like a meaningless mishmash of lines, numbers and letters.

In reality, each numbered column is one of 9 chapters of a game called an inning. The horizontal rows represent the numbers and names of the players of the two teams playing against each other. Inside each box is a summary of what the batter did during his “at bat”. A “K” for example  is a strike out.

Notice, however, that each explanation involves the introduction of more jargon that has to be clarified if the reader is completely clueless about baseball.

There are strong parallels between a box score and the skeletal formulas of organic chemistry, which appear everywhere from coffee mugs to the Merck Index and from student homework to published research papers whose subject is not necessarily pure chemistry. I often use them in my blogs and I have underestimated how opaque they can be, even if the reader has taken chemistry courses and generally enjoys reading science.

In the same way that we forget that baseball is obscure outside of the USA, Canada, and some Latin American and Asian countries, those who use skeletal structures underestimate how much basic chemistry people forget after studying it during a brief part of their lives.

Convinced that most of the world is missing out on something fun and of importance, let me proceed!

Here are two coffee cups with two slightly different skeletal structures of the caffeine molecule.

Each capital letter is the symbol of a chemical element that makes up part of the universe. Sometimes writers incorrectly state that everything consists of atoms, which is not true, given that visible light, all other energy forms, subatomic particles and dark matter do not consist of atoms. What they mean is that all solids, liquids, gases and part of plasma consist of atoms and/ or some combination of atoms. For example, each caffeine molecule is an assembly of carbon(C), nitrogen(N), oxygen(O) and hydrogen atoms(H). To be sure you have caffeine, you not only need the right number of atoms as revealed in the subscripts of its formula, C8H10N4O2, but they have to be in the order shown by the skeletal formula. (For some other molecules, the skeletal will also reveal 3D structures that are also a crucial part of a molecule’s identity.)

Why is that important? A skeletal structure identifies key functional groups that give chemists clues about caffeine’s behaviour towards solvents and other reactants. It furthermore serves as a blueprint to make the compound in the lab or or to try to synthesize similar molecules.

Of course you may ask, why does caffeine’s C8H10N4O2 indicate 8 carbons and 10 hydrogens while the skeletal structure shows only 3 C’s and only 9 H’s in the structure on the left hand side and none on the right ! The latter uses a “lazy” convention of leaving out a CH3 group at the end of any outward bond ( shown as a line segment sticking out). It’s also understood that at every corner there is a carbon. A structural formula, as opposed to a skeletal one, will reveal that. Watch:

Now you can see all 8 carbons and the tenth hydrogen has also appeared. Why did they leave out that hydrogen? Well, an organic chemist or student is expected to know that in such molecules, each carbon will make 4 bonds with other atoms, so that if you see only 3 lines connected to the C, a fourth bond is really there and the electrons ( what the line segment really represents) are being shared with a hydrogen. Look throughout the molecule, and you will see that there are four lines connected to each carbon. The structure on the right has expanded the CH3 groups so that you could see those bonds too.

But why does each hydrogen, oxygen and nitrogen only make 1, 2, and 3 bonds, respectively? To find out the number of bonds made by caffeine’s elements (and by fluorine(F), chlorine(Cl) or by any other element in the so-called halogen column), you can consult the periodic table.

Carbon(C) is the fourth element in its row. Why? It has 4 valence electrons in its outermost energy level and with four more ( what it takes to get to the end of the second row) it will stabilize. The way to get 4 more is to form four bonds. To get to the end of hydrogen’s row, you only count up to one; hence each hydrogen makes only one bond. From nitrogen you count to three to get to the end of the row; thus three bonds for nitrogen. O makes two bonds; fluorine, chlorine, bromine and iodine, only 1.

Finally let’s do a little math. Is there a way that we can predict how many bonds there are in the caffeine molecule simply from looking at C8H10N4O2 ? Yes. (1) Multiply each atom by the number of bonds they make; (2) add up those numbers, and finally (3) divide by two since each bond involves two atoms. Thus, there should be a total of ( 8 × 4 + 10 × 1 + 4 × 3 + 2 ×2 ) ÷ 2 = 29 bonds. Go back to figure 1 and you will indeed count 29 bonds.

There’s more. From C8H10N4O2 you can also predict the index of unsaturation, in other words the total number of ringed structures (like pentagons and hexagons in the skeletal structure) and extra bonds in the form of double or triple segments. Each ring structure or double bond counts as 1 (1 extra bond) and a triple counts as 2 ( two extra bonds). The formula is the following: index of unsaturation= (2C+ 2 – H)/2 but with the following adjustments: ignore any oxygens; remove 1 hydrogen for every nitrogen; and replace any halogen with a hydrogen. So for caffeine , C= 8; H =10- 4 = 6 due to the four nitrogens and we ignore the 2 oxygens. The index of unsaturation= (2 × 8 +2 – 6)÷2 = 6.

And indeed there is a sum of 2 rings plus four double bonds for an unsaturation- index of 6.

If you are still reading, would you like to practice more?

EXAMPLE 1 What is the molecular formula associated with this skeletal structure?