# How do I work out the original concentration of a solution after taking an aliquot and further diluting it for analysis?

I'm trying to work backwards to obtain the original concentration of a 1 litre solution. I feel my calculations have gone wrong and need another set of eyes to have a look.

To start, a tablet containing arginine was dissolved in water and made up to 1 litre solution. A 250 μL aliquot was taken from the solution and diluted to 25mL.

Analysis was done and a concentration value for the 25mL sample was 4.25 x10^-5 mol/L.

When I tried to work backwards from that concentration value and determine what the original concentration is in the 1 litre solution, I got 17 mol/L. Which seems excessively high for what was suppose to be a tablet.

I then need to give the value of mass of arginine (172.2 g/mol) in the tablet, but using the 17 mol/L, gives a value ~3kg.

What do I need to do to get the concentration value for the 1 litre solution?

## 1 Answer

You took an aliquot of $0.25 ml$ with unknown concentration. You diluted 100 times by adding 100(-1) times the volume of your aliquot. The result was $4.25*10^{-5} mol/L$, or, $$4.25*10^{-5} mol/L * 172.2 g/mol = 7.38*10^{-3} g/l$$

You diluted 100 times, so going back it becomes 100 times more concentrated: $100*7.38*10^{-3} g/l = 0.738 g/l$.

A good habit, even if you're not stuck, is to write the units corresponding to the values. This way it is very easy to spot when you've for example multiplied by a molar weight you should have divided by.