Floating in a Dream

Sometimes when I teach chemistry, I wonder if I’m not just an educated salesman. Thanks to an efficient hippocampus and amygdala, I contrast my present emotions towards the subject with those from my high school and college days, and although I always liked the subject, the present zeal was not as intense back then. And would I teach for free and still think about the subject as often if I suddenly woke up financially independent?

Then last night I had a dream about buoyancy that my students and I had discussed recently while reviewing. It could have been just a coincidence, one of the brain’s memory-housekeeping functions twinkling in our sleep.

If you tie a bunch of grapes to a helium balloon, one of three things can happen: if they’re light enough, the balloon will still rise. Too heavy, and they’ll sink. But if their combined weight(with that of the balloon and string) is equal to the buoyant force, the assembly will just be suspended in midair.

In my dream I was suspended from a balloon like grapes. (Ironically, my surname means grapes in Italian.) Along with a newspaper reporter we were floating above traffic. In reality the tension in the straps around by torso would have to counter the weight of my body, but in the dream they weren’t perceptible. Besides, the floating reporter was far prettier than the balloon, so I never noticed it. But being a married teacher, instead of dwelling on her, I should calculate the volume of the balloon.
F_buoyant = F_gravity
m_air*g = m_load*g + m_He*g
The g which equals gravitational acceleration cancels:
m_air= m_load + m_He
If we express mass as the product of volume and density, then:
V*d_air = m_load + V*d_He , where V= balloon’s volume + load’s volume.
Rearranging the equation, we get:
V = m_load/(d_air-d_He).

The Subtleties Of the Volumetric Pipet

To the uninitiated, the volumetric pipet is just an oddly-shaped glass tube used to measure the volume of liquids. To researchers accustomed to fancy piston-driven micropipettes, the simple pipet is a throwback to a different age.

But although it continues to serve as a useful tool in preparing solutions and accurately measuring out volumes for titration experiments, the pipet is a great starting point to illustrate important analytical concepts and even some basic science.Why is it shaped the way it is?

By having a bulge in the midsection like some middle-aged man, it holds the bulk of its volume there. But where the bottom of the meniscus meets the volume-marker, it is extremely thin. This is deliberately done since any extra amount of liquid will have little room to spread horizontally and will rise instead. Errors will become obvious, and so this piece of glassware is far superior to a graduated cylinder, which has a wider diameter. 

A 50.00 ml pipet has an uncertainty of
±0.05 mL , introducing an error of only 0.1%. In a 50.0 ml graduated cylinder, the uncertainty is 8 times as large.

As with the use of a thermometer or burette, the meniscus has to be read at eye-level. Otherwise every other angle  would lead to a different perception. The pipet’s pointy tip is designed to trap the last drop, providing consistency. The desired volume delivered from the pipet is calibrated by taking that trapped volume into account, and so it should not be forced out.

The proper use of the pipet leads to precision. In science precision means that measurement can be reproduced. In other words, if 50.00 ml is measured repeatedly, it will deliver the same amount within ±0.05 mL. This could be verified by comparing the mass each time, and it will show consistency.

Does precision necessarily imply accuracy? Not necessarily. What if the manufacturer had placed the marker delineating the 50.00 ml spot in the wrong place? Then even though the corresponding mass would be obtained repeatedly, it would still not match the real mass of that perceived volume. If the temperature and density of the liquid are known to enough decimal places, then together with the mass, the volume can be calculated and the pipet’s supposed 50.00 ml can then be checked against the calculation for accuracy.

Finally how is the volume of liquid sucked into the pipet in the first place? In science, the word “sucks” sucks because it does not allow us to picture the behaviour of molecules.

Imagine a pipet immersed into a liquid with the bulb being squeezed and then released while it’s still attached to the pipette. Since the liquid is in the way, the only air that can reenter the pipette comes from the pipette itself. As the bulb regains its original shape, the total available volume for the air becomes greater than the original, lowering pressure inside the bulb and pipet. (the pressure drops because there are less molecular collisions in the more spacious volume).

The atmospheric pressure is now greater than the internal pressure of the bulb-pipette system, and so there is a net force that pushes the liquid into the pipette.

From Breasts To Structural Formulas

In his voyage to the land of the giants, the so-called Brobdingnag, Gulliver does not exactly perceive breasts the way Hugh Hefner would.

The nipple was about half the bigness of my head, and the hue both of that and the dug, so varied with spots, pimples, and freckles, that nothing could appear more nauseous.

What the clergyman-writer did not realize is that although breasts can have pimples, the areolar bumps that he was probably referring to were sebaceous glands. They secrete a fluid consisting of wax monoesters, triglycerides, free fatty acids and squalene, a terpene also found in shark oil. The Montgomery tubercles (also known as areolar glands), a type of sebaceous gland, play an important role in breastfeeding. Secretions from these pregnancy-enlarged glands lubricate the breasts, protecting them from trauma and infection. Also, lactating women emit volatile compounds that can reliably activate behavioral and autonomic responsiveness in human newborns. Smooth muscle bundles are also found in these glands, which extend into the tips of the breasts. If it were not for those variations that Swift found unappealing, nipples would also not pucker up in the cold or during a state of arousal.

_{Response of nipple and areola to cold; smaller protrusions are Montgomery tubercles. Source: Ana Dias photography}

Sebum, the mixture of fats released by sebaceous glands, is found in all mammals, and so it also serves to lubricate hair. The exact composition varies among species, but there is one fatty acid that is only released by humans. Appropriately enough, it is called sapienic acid.

sapienic acid: source chemspider.com

Is there any way that the total number of double bonds and structural rings can be predicted from its molecular formula of C₁₆H₃₀O₂?

We could use the formula 1+C–H/2= i.u, where i.u.= to the index of unsaturation,

C = number of carbons in the formula,
H = number of hydrogens.

Notice that when the compound contains oxygen, they are ignored in the formula. If there had been nitrogen atoms, one hydrogen would have to be removed for every N. Finally if there had been halogens, each would have to be replaced with hydrogen.

In this case, 1+16 -30/2 = 2. And there are indeed two double bonds in the structure of sapienic acid.

From breasts to structural formulas—only in the mind of a chemist!

(source for featured image: From an original painting by Emily Balivet)