Since we’re looking for the amount of NaOH needed, we will start with the HCl and convert it into the NaOH. It is important to know the chemical reaction that is occurring: 1HCl + 1NaOH –> 1NaCl + 1H2O
We know that we have 20 mL. And we also know the we have 0.100 M. I can rewrite the 0.100 M as
(0.100 mol / 1 L) because M = mol / L OR M = L / mol.
So now, I see that if I can get rid of that L, then I will know how many mols of HCl I have.
To do this, I will take the 20 mL, convert it into L by dividing by 1000.
Then I multiply the 0.020 L by the (0.100 mol / 1L) and I see that I now have 0.002 mols of HCl.
Now I use the chemical reaction to convert from HCl to NaOH. You’ll notice that It is a 1 to 1 conversion meaning that 1 mol of HCl will react with 1 mol of NaOH to make the products. This means that if I have 0.002 mols of HCl, it will neutralize 0.002 mols of NaOH.
Remember that part when I said M = L / mol? I can use this to find the amount of NaOH I need. So I multiply the 0.002 mols of NaOH with (1 L / 0.200 mols NaOH) = 0.01 L which I can then convert into mL by multiplying by 1000 to get 100 mL.
I know the text way makes it seem complicated. But all I did was multiply 5 times. I attached the mathematical representation of what I did. Notice how the top of the one fraction always matches the bottom of the next fraction. This allows my units to convert.