Dr. F. Responds to a New Study (Help with the Math)

[BigEgo]

So there was a cell study published recently that took human and rat lung cells and exposed them to both cigarette smoke and e-cig vapor (with and without nicotine). Dr. Farsilinos responded saying that the study was bogus based on a detail he saw in one of the charts.

What happened is they were measuring the nicotine in molarity and not in milliliters. For those of you unfamiliar, 1M = 1 molar of solute in 1 liter of a solution. So, essentially 1 molar (1M) = 1 mol/L.

Dr F. concluded that they were using concentrations of nicotine that would never been seen in real life conditions (see the link above where he explains).

Dr. F's detraction resulted from a chart that listed the following concentrations of nicotine they applied to the cells. They were:

.1 mM
.5 mM
2.5 mM
5 mM
10 mM

(A mM = millimole or 1/1000th of a mole).

Now, the molar mass of nicotine is 162.23g/mol. This means that 1M of nicotine = 162.23g. Since 1M = 1mol/liter, this means that there would be 162.23g of nicotine in one liter of their solution.

Now here's where I am wondering if Dr. F messed up his calculation. A millimole = .001 M. Thus a millimole of nicotine = .16223g (let's round to .16g). That would be .16g/L.

Now .1 mM of nicotine = 160g x 0.0001 = .016g/L. And so on for the rest of the chart presented in the paper. Here would be the conversions in grams per liter:

.5 = .08g/L
2.5 = .4g/L
5 = .8g/L
10 = 1.6g/L

Now, you are probably thinking, "Yes, but you have grams per liter. We need milligrams per milliliter. Therefore, you would need to move the decimal three places to the right. Hence, .016g/L would equal 16mg/mL. Right?"

Wrong. 0.016g/L = 0.016mg/mL. It's the same. It's something we learn in elementary school called cancellation.

The density of pure nicotine is 1.01g/cm^3. This equates 1:1 with mg/mL. Thus, the density of pure nicotine (undiluted) would be 1.01g/mL or 1010mg/mL.

Dr. F, is claiming that 10 mM =1600mg/mL. This is impossible as that is more nicotine than is possible to fit into one mL, even if it was pure and undiluted. (As I said above, pure nicotine is 1010mg/mL).

I conclude that Dr. F. is wrong when he says they were using 16mg/mL, 80mg/mL, 400mg/mL, 800mg/mL, and especially 1600mg/mL (impossible), etc. He moved the decimal place over when he shouldn't have. Or perhaps I am completely wrong and talking out my behind (I am not a chemist and admit I could be totally confused about molarity and the densities and masses of the chemicals here).

I know we have chemists here. I would like it if an expert would show me the error of my ways, which I fully admit is possible. Again, I am no expert. I'm just a guy who thought that surely these researchers cannot be so silly as to use outrageous amounts of nicotine such as 1600mg/mL!

 

[bwh79]

I never did quite get the concept of a mole but aside from that, yeah your math all looks good.

 

[InTheShade]

Nobody can possibly understand the concept of a mole.

Seriously, I would contact Dr. Farsalinos with your question / explanation. He's very active with replies to his studies, on Twitter and on his website and I am sure he would be happy to either revise his rebuttal or let you know how he reached his conclusion.

 

[Bunnykiller]

I think I found your error..... 1/1000 = .001 this bumps up the mass by 1 magnitude

nevermind... that was .1 mm not 1mm

and... 162 g/l = 162mg/ml...

I always hated math being dyslexic and all...

 

[Bunnykiller]

ahhh but I did find something that doesnt look right

.016g/L = 16mg/ml this seems more correct

 

[Bunnykiller]

this has become a challenge for me now...
umm
if 1M = 162g/L
then .1M = 16.2g/l
and 1mM = .162g/L
therefore 10mM must = 1.62g/L
and to get mg/ml
thats 1620 mg/L which umm goes to
1.6mg/ml?

good thing Im not a rocket scientist.... the lunar lander would have ended up on Jupiter after going thru the sun...

 

[Bunnykiller]

Everything is now ok with the chart Dr. F posted.... I notified him and he made the proper adjustments....

 

[caramel]

I think I found your error..... 1/1000 = .001 this bumps up the mass by 1 magnitude

nevermind... that was .1 mm not 1mm

and... 162 g/l = 162mg/ml...

I always hated math being dyslexic and all...

C'mon, no need to feel bad, it happens with the big guys too:

http://www.cnn.com/TECH/space/9909/30/mars.metric.02/p

 

[BigEgo]

this has become a challenge for me now...
umm
if 1M = 162g/L
then .1M = 16.2g/l
and 1mM = .162g/L
therefore 10mM must = 1.62g/L
and to get mg/ml
thats 1620 mg/L which umm goes to
1.6mg/ml?

good thing Im not a rocket scientist.... the lunar lander would have ended up on Jupiter after going thru the sun...

You are correct, just as I said in my original post. 10mM = 1.6g/L = 1.6mg/mL.

Basically the crux is that when you convert from g/L to mg/mL, nothing changes. 1.6g/L is still 1.6mg/mL. It is *not* 1600mg/mL as Dr. Farsilinos originally said.

I remember when I took Chemistry 101 in college that density is equal to mass divided by volume (D = M/V). This is about all I remember from my semester of chemistry (lol). Moles and molarity is something I was never familiar with as I had always brushed it off as some chemistry mumbo-jumbo that isn't relevant to me. So I did some digging and I learned what both of them mean (mole and molarity are different, but related).

A mole is an SI unit of measurement that expresses the amount of chemical constituents (atoms, molecules, ions, etc) in matter. Basically it is a count of molecules in a chemical compound (or atoms in a molecule, etc). Instead of counting these constituents individually, a mole was devised as a standard unit of measurement. An analogy I came up with off the cuff: A pound of sugar, a pound of water and a pound of feathers are all one pound, even though they are different substances with different masses (and densities). You can still have 1 pound of each even if it takes a larger volume of feathers to make 1 pound than it does sugar. A better analogy than a pound would be a dozen. You can have a dozen eggs, a dozen cars, a dozen trees, etc. Even though they are different, have different physical properties and weights, everyone knows what you mean when you say "a dozen." So, a mole is like a molecular version of a dozen. A mole of oxygen is a still 1 mole. A mole of hydrogen is still 1 mole. Ok, but I am sure you're asking "What the hell *is* a mole? How is it defined?" Well, 1 mole was standardized to equal the number of atoms in 12 grams of the isotope carbon-12. I am not a chemist so I am not sure why this was chosen, but it likely has to do with some special property of carbon (or its simplicity or prevalence in organic chemistry or something). This constant is known as Avogadro's constant with a value of 6.02 × 10^23. This means there are 6.02 x 10^23 atoms in 12 grams of carbon-12. That in regular decimal notion means that 602,000,000,000,000,000,000,000 atoms comprise 12g of carbon-12. This also means there are 6.02 x 10^23 atoms in 1 mole of oxygen. It means there is 6.02 x 10^23 atoms in 1 mole of hydrogen. So, as you can see, 1 mole of hydrogen will "weigh" differently than 1 mole of a more complex substance (especially complex molecules). So even though you can have a mole of any atom (or molecule), the gram weight of each substance will be different. So, basically a mole is a way of converting individual molecular masses (atom count) to grams.

Molarity is a bit different than a mole, but related. Basically it is 1 mole (defined above) in 1 liter of a solution. If you have 1 mole per 1 liter, then you are said to have 1 molar (1M). So if someone says they have 1M of nicotine, that means they have 1 mole of nicotine concentrated in 1 liter of a solution (1 mol/L). Together, the 1 mole of nic and the 1 liter of solution = 1 molar (1M).

The difference in 1 mole of nicotine and 1 mole of, say, oxygen will depend on the atomic weight of each molecule. Nicotine's chemical structure is C10H14N2. This means 1 molecule of nicotine contains 10 carbon atoms, 14 hydrogen atoms, and 2 nitrogen atoms. Now, each atom in the periodic table has an atomic number and an atomic mass. The atomic number is the number of protons in the nucleus. The atomic mass (or weight) is the total number of protons and neutrons in the nucleus. Since atoms typically have the same number of protons and neutrons, this is why on the periodic table the atomic mass of any given element is about twice the atomic number (not exactly, but close). There are isotopes that skew the averages a bit, but this is close enough for our purposes.

So what is nicotine's mass? Well as I said above, we know that 1 molecule of nicotine (which is the smallest possible amount of nicotine you can have) contains 10 carbon, 14 hydrogen and 2 nitrogen atoms. In order to calculate the molecular weight of nicotine, we perform simple arithmetic and add the atomic weights of each atom that comprises it. Looking at the periodic table, the atomic mass of hydrogen is 1.0079, the atomic mass of carbon is 12.0107, and the atomic mass of nitrogen is 14.0067. We take each of these values and multiply them by how many atoms we have. So:

H = 14 x 1.0079 = 14.1106
C = 10 x 12.0107 = 120.107
N = 2 x 14.0067 = 28.0134
-----------------------------------
Total = 162.231

Now, where have we seen that number 162.231 before? Yep, 162.231g of nicotine makes up a mole. So this is how 1 mole is determined for any substance. You simply take the molecular weight of a chemical, put the gram symbol behind it and that gives you 1 mole of that chemical compound. Now, as I explained, 1 molar of nicotine means there is 162.231g (concentration) suspended in 1 liter of a solution. (Don't confuse a mol with a molar).

So, this is where all of this confusion started. We started with 162g/L and this is where Dr. F. went wrong with his conversion. The authors of the paper in question used millimoles for the measurement of nicotine they applied to their cell cultures. A millimole, of course, is simply 1/1000th of a mole. Therefore, 162.231/1000 = .162231g or .16g rounded. That means 1 millimole (1 mM) of nicotine is .16g/L. I will refer you to my original post for the rest of the numbers. But I will say that the highest concentration they used on the cells (10 mM) comes out to be 1.6mg/mL. That is less than the concentration most people use in dripping atomizers.