In my previous post we saw how really small molecules are. Another layer of complexity is revealed when we think about how many molecules are there. Again, it is a numbers game and due to the immense nature of this numbers it is very difficult for our brains to visualize the true significance of such huge amounts.
To try to overcome this difficulty, we can take advantage of several comparisons. In biology, the cell is the fundamental unit of life. By definition it is the minimal ensemble of molecules that when organized in a very particular way, as of today not very well understood, generates the phenomenon of life.
Some of the smallest cells are prokaryotes, a group that includes the bacteria. A typical bacteria can be considered a cylinder about 1 um wide and 2 um long. This corresponds to a volume of about 1.6 cubic micrometers.
Picture credit: http://www.sciencedaily.com/releases/2009/03/090329205447.htm
In a future post we’ll talk about how does bacterial size compare with the size of other cell types. In the meantime let’s compare the size of a typical bacterium with the size of a molecule
Consider pentacene, one of the molecules that we talked about last time. Now, pentacene will not likely be found in any living organism and it would probably be toxic anyway if it were, but I’d like to use this example because you already have an idea of pentacene’s molecular size (if you read my previous post; if not, go ahead and read it, we’ll wait for you…).
Ok, thanks for coming back… As we saw before, the volume of a typical bacteria is about 1.6 cubic micrometers. What does this mean? A more familiar volume measurement is the cubic centimeter, also known as cc or milliliter (mL). If you look at your pinky finger, the last bone will roughly be about 2 mL in volume, give or take depending on the specific bone structure.
Now each cubic centimeter has 1,000,000,000,000 cubic micrometers (um), by the way, how do we know that?
Picture credit: modified from: http://2012books.lardbucket.org/books/the-basics-of-general-organic-and-biological-chemistry/section_04_06.html
… therefore approximately 625,000,000,000 bacterial cells will fit in half the volume of the last bone in my pinky.
So far so good…
Ok, now let’s think about how many pentacene molecules will fit in a typical bacterium. What data do we have? for one, we have the typical volume of a bacterium, namely 1.6 um. Next, we need to calculate the volume of a single pentacene molecule. How do we do that?
We have various possibilities. In one of them we’ll need pentacene’s density (the amount of mass per unit of volume) which for pentacene happens to be 1.3 grams per cubic cm. We will also need to know its molecular weight, the mass of molecules per a special unit called a mole. A mole is 6,022,000,000,000,000,000,000 of anything, (abbreviated as 6.022×10^23). This is called the Avogadro’s number. For pentacene this number is 278.36 grams / Mol, meaning that a mole of pentacene molecules weights exactly 278.26 grams.
Then we play with the units
Still with me?
Please remember that there are 1,000,000,000,000 cubic micrometers per cubic centimeter, therefore: 2.81 x 10^21 molecules / 1,000,000,000,000 cubic micrometers = 2,810,000,000 molecules per cubic micrometer.
This means that if a typical bacterium has a volume of 1.6 micrometers:
… we can fit approximately 4,498,347,463 (about 4.5 billion) molecules of pentacene in a normal bacterium.
To get an idea of how big a billion really is, go here.
By the way, all these superscript numbers are in scientific notation. Here is why scientific notation is so useful.
It is past 2 am in my corner of the world and I am (finally) getting sleepy, so please double-check my numbers and let me know if I made any mathematical or logical “oops”. Also, tomorrow I will try to go over other ways of calculating pentacene’s volume and see how does it compare with what we did today.
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