I want to master pharmacy through units and mathematical thinking

❶ Moles make the microscopic world easier to understand

Does anyone wonder why we use the unit called mol, or feel resistant to new units?

That makes sense. I understand because I felt the same way. Atoms and molecules are too small to count one by one.

But you see, if you collect an astronomical number of atoms or molecules, specifically
$${6.02×10^{23}}$$
of them, the weight becomes the atomic or molecular weight in grams.

The number of atoms or molecules far exceeds the world population; only by grouping them into such an unimaginably large mass does the weight become something we can grasp in everyday terms.

1 mol of water molecules is
$${6.02×10^{23}}$$
molecules and weighs 18g.

0.5 mol of water molecules is half that amount,
$${3.01×10^{23}}$$
molecules, and weighs 9g.

First, grasp the point to bring the overly microscopic world closer to our own perspective.

Now, we use moles to express concentration and perform calculations in analytical chemistry, but

The most important thing in analytical chemistry is, above all,
units and by aligning disparate units, you can prevent careless mistakes. During tests, units also served as a hint—albeit a somewhat desperate one—for which values to use in calculations.

As for how I memorized them, I would say,

once I understood what I wanted to express with concentration, I memorized the
units of concentration.

2. Molar concentration (mol/L): The number of moles of solute dissolved in 1L of solution

In calculations, units are basically the most important thing.

The volume of a solution is often expressed in ml. In that case, you have to convert it to L.

Let's try to find the molar concentration when 5.85g of salt is dissolved in 500ml of water.
Since 1L = 1000ml, you can convert it to the unit of L by dividing by 1000.
500ml = 0.5L of saline solution

To find how many moles of solute are dissolved, you just need to divide the grams of dissolved solute by the grams of solute per mole. Simply using NaCl as an example for mole calculation, 1 mole of NaCl is 58.5g. The 5.85g of NaCl dissolved is 5.85/58.5, which is 0.1 moles... Equation (1)

The molar concentration became 0.1 mol of NaCl / 0.5L of solution = 0.2 mol/L.

This is a huge aside, but
1 mol of NaCl is 58.5g
in other words, 58.5g per 1 mol

58.5g/mol
so it also means
Equation (1) is 5.85(g) / 58.5(g/mol)

Looking only at the units,
g/(g/mol) = g・mol/g = mol
Indeed, what I found in Equation (1) was mol.

This is what I secretly checked
so that I wouldn't get lost sometimes.
Sorry if this was unnecessary lol

Molar concentration (mol/L) = Number of moles of solute (mol) / Volume of solution (L)
Remember molar concentration as
moles of solute insolution /L

We want to be careful aboutwhether the denominator is solution or solventand similar units (so we don't fall into a trap!).

2. Being able to transform and interpret formulas according to the purpose

Avogadro's Law exists, right?
At the same temperature, pressure, and volume,
ideal gas follows

PV=nRT

Try playing around with
this formula
as if it were a game.

P = nRT/V
Since R is a constant, it doesn't change,
if you keep the temperature T and the gas volume constant

when the number of moles n increases,
the pressure P increases.
They are proportional.

Looking at it in the formula,
if n=1 mol, then P' = RT/V... n is 1, even though it's not written.
If n=2 mol, then P'' = 2RT/V = 2P'

You'll be fine once you get used to the symbols.
I just used P' because I substituted n=1.
I just used P'' because I substituted something different, n=2.

But P'' is twice P'.
The formula is telling us that when the number of moles doubles,
the pressure also doubles.

The number of moles,
to put it simply,
means the number of molecules or atoms has increased.

If the population? density of molecules increases,
pressure goes up, and the number of collisions with the sealed container increases,
which makes sense intuitively, right?

Using the same formula,
when the volume becomes 1/2
and when the volume doubles,

looking at what happens to P
is quite interesting.

Today, I talked about
convenient units to help us
feel the microscopic world while living in the macroscopic world,

and how you can understand many things
by manipulating mathematical formulas.
I hope this was helpful to you.