Answer:
The amount of water to add is 171 mL
Step-by-step explanation:
A solution is a homogeneous mixture of two or more substances.
A dilution is a solution with a lower concentration than the one you start from, called the stock solution.
In other words, dilution is the procedure followed to prepare a less concentrated solution from a more concentrated one, and it simply consists of adding more solvent. In other words, in a dilution the amount of solute does not vary, but the volume of the solvent varies: as more solvent is added, the concentration of the solute decreases, since the volume (and weight) of the solution increases.
The formula used in dilution is:
Ci*Vi = Cf*Vf
where
- Ci: initial concentration
- Vi: initial volume
- Cf: final concentration
- Vf: final volume
In this case:
- Ci: 0.400 M
- Vi: 57 mL= 0.057 L (being 1 L=1,000 mL)
- Cf: 0.100 mL
- Vf: ?
So:
0.400 M* 0.057 L= 0.100 M*Vf
Solving for Vf:
Vf=0.228 L
Assuming that the volumes are additive, the final volume is equal to the initial volume plus the amount of water added:
Vf= Vi + Vwater added
Then:
0.228 L= 0.057 L + Vwater added
Solving:
Vwater added= 0.228 L - 0.057 L
Vwater added= 0.171 L= 171 mL
The amount of water to add is 171 mL