Question

If I have 2mL of a substance and dilute it to 5mL. Then I take 1mL of the 5mL solution and dilute it to 10mL. How diluted is the original sample?

Answer 1

Let the initial concentration of the solution be 'M' mol / L or 'M' mmol / mL

Hence moles of the substance in 2 mL of the solution = (M mmol/mL) x 2 mL = 2M mmol

Now when the slution is diluted to 5 mL , the concentration of the diluted solution

= 2M mmol / 5 mL = 2M/5 mmol/mL

Now moles of the substance present in 1 mL of the above diluted solution = (2M/5 mmol/mL) x 1 mL = 2M/5 mmol

Now 1 mL of the above diluted solution is further diluted to 10 mL

Hence concentratation of the further diluted solution = mmol in 1 mL / V(mL) =  2M/5 mmol / 10 mL

= 2M / 50 mmol/mL = M/25 mmol/mL or M/25 mol/L

Hence the original solution is diluted by 25 times (answer)