Dilution help

Trojan

I'm looking for some help figuring out a dilution calculation.

Theoretically, I have a 19M NaOH solution that I need to use to make a 500ml solution which is 2.75M in Na+.

Therefore I need to calculate how many moles of Na+ in the resulting solution, how many is equivalent in the original 19M, and what volume that is of the 19M.

I was trying to find a way to apply the equation "Molarity = Mass of solute / (Molar mass x Volume of solution)" as I was able to use this to successfully calculate the mass of the solute in a previous problem using this, but I'm getting lost and wondering if it's pulling me down the wrong rabbit hole.

Via trial and error, I do know that the approximate mass is 69-73g +/- a bit, but I don't know how to get there through calculation, which is really what I'm trying to learn.

Using the above formula:
Molarity = 2.75M (end result we want)
Mass of solute = (unknown)
NaOH molar mass = 39.9971 g/mol
Volume of solution = 0.5L

2.75 = x / 19.9985
54.996 = x

So 54.996g is mass of solute according to our formula... but we're talking about diluting a dense liquid, NaOH is 2.13 g/cm³ in density and multiplying that out gives 117.1415 which if used as mL seems way out.

Appreciate any and all advice on how to approach this.

Furez

Im a bit rusty at this stuff, maybe your over complicating things or I dont know what Im at.
Assuming you are working from a flask containing 19 M NaOH solution.

19 M = 19 mole/L = 19 mole/1000 ml
So
1 M = 1000/19 = 52.63 ml/L
2.75 M = 52.63*2.75 = 144.74 ml/L or 72.37 ml made up to 500 ml.

Again this may be wrong as I dont see why you need the MW or density. Im interested to see how this works out as a refresher.

kc90

Furez wrote: »

Im a bit rusty at this stuff, maybe your over complicating things or I dont know what Im at.
Assuming you are working from a flask containing 19 M NaOH solution.

19 M = 19 mole/L = 19 mole/1000 ml
So
1 M = 1000/19 = 52.63 ml/L
2.75 M = 52.63*2.75 = 144.74 ml/L or 72.37 ml made up to 500 ml.

Again this may be wrong as I dont see why you need the MW or density. Im interested to see how this works out as a refresher.

This is how I would do it too. Because no matter what volume of that solution you take, it's always 19M, you don't need to look at density or molar mass.

The most important part is this: 1 M = 1000/19 = 52.63 ml/L
So when you take a fraction of 1L (1/19th here), and dilute it to 1L, this will be a dilution to the fraction you took.

Trojan

Furez wrote: »

19 M = 19 mole/L = 19 mole/1000 ml
So
1 M = 1000/19 = 52.63 ml/L
2.75 M = 52.63*2.75 = 144.74 ml/L or 72.37 ml made up to 500 ml.

Again this may be wrong as I dont see why you need the MW or density. Im interested to see how this works out as a refresher.

Bang on. Confirmed correct.

I was waaaay over complicating things with the density - you brought some much needed simplicity to it, thank you!