You have 100 mL of a 12 M solution of HCl, and you need to dilute it to 1.5 M for an experiment. How many liters will your new solution be?
When working with dilutions we usually use this formula:
Vi * Mi = Vf * Mf
Where, Vi and Mi are the initial volume and the initial molar concentration (before the dilution) and Vf and Mf are the final volume and final molar concentration (after the dilution)
The concentration before the dilution is 12 M and the volume of solution that we have is 100 mL.
Vi = 100 mL
Mi = 12 M
We want to prepare a 1.5 M solution and want to know the volume.
Vf = ?
Mf = 1.5 M
We can replace these values in the formula and solve it for Vf to get the final volume.
Vi * Mi = Vf * Mf
Vf = Vi * Mi/Mf
Vf = 100 mL * 12 M/(1.5 M)
Vf = 800 mL
But we need the answer in L. We know that there are 1000 mL in 1 L.
1000 mL = 1 L
Vf = 800 mL = 800 mL * 1 L/(1000 mL)
Vf = 0.800 L
Answer: The new solution will have a volume of 0.800 L.