So out of all the science disciplines, people may think biology is the least mathematical out of them all. You know like physics have the way with quantum mechanics and general relativity or chemistry has its way with energy and thermodynamics. I guess the more abstract the ideas are, the higher the need for an equation to represent it.
But then we have biology. Even though this trend is changing, and its changing fast with the increased involvement of computational tool and physics and genetics, biology is changing into more quantitative. And for however much the biology has changed, there will be 1 equation that all biologists love: C1V1 = C2V2.
Oh the equation for how you calculate everything, from dilution of that sodium chloride solution to making up the loading buffer for your western blot, C1V1=C2V2 always proved to be useful. But do you ever think where does this equation come from or why this equation the way it is? Well, you came to the right place :)
I am no mathematician and my time for maths has long gone since the day I left Vietnam to pursue my dream in biology. But there's one thing I always bring with me where ever I go and has been extremely helpful for me in biology, it's chemistry!
So in chemistry, you have the famous equation to calculate the number of molecules in a quantity of substance, you know it as moles ( or the symbol for it is n). To calculate n of a solute in a solution, you need the concentration of that substance (C) and the volume of liquid that the solute is dissolved in (V):
n = C * V
So imagine you have that 1 drop of liquid and the pink circles are the solute molecules while the cyan part is the solvent. So the
number of mole of the pink solute (n1) = C1 (its concentration) * V1 (the volume of liquid it's in)
Now you drop that drop of liquid into a beaker that already contains another solvent with the volume V2 and now all your pink particles are disseminated all over the place. Now, to calculate the number of mole of the pink solute in the second beaker, you'll do the same:
n2 = C2 * V
But remember, V is now the total volume of the drop and the volume V2 of the beaker so
V = V1 + V2
So now: n2 = C2 * (V1+V2)
But did you notice that the number of pink solutes is exactly the same before and after? You did not take anything away or adding anything to it, all you did is dissolve it into a bigger volume, and that's all you did! Every single pink particle from the first drop is now in the beaker! So n1 is exactly the equal to n2
And there we have the famous equation: C1V1 = C2(V1+V2)
But because now you have the same number of pink particles in a bigger volume, the concentration will be different, and that is C2. C2 is not not the same as C1.
Hmmm, but it doesn't seem right, is it? Why V1+V2? We never did that.
Well, you are right and wrong. Technically, it is V1 + V2, the volume of the drop plus the volume of the liquid in the beaker. BUT in biology, we always deal with teeny tiny amounts of liquid, like a few microliters that really is not going to change much of the volume after adding them together. So, with V1 is teeny tiny, V1 + V2 will approximately V2.
So there you have it: C1V1 = C2V2 And by rearranging them, you'll get C2 = C1V1/V2 and you can work out what is new concentration!
There you go, so now you understand why we do what we do. And it's important to always bring the knowledge you have from other disciplines to apply that to what you are doing now. Biology really is the playground for other disciplines, and you should be really proud of being a part of it! :)
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