Question

A 57.0 mL aliquot of a 0.400 M stock solution must be diluted to 0.100 M. Assuming the volumes are additive, how much water should be added

Answer 1

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=(0.400 M*0.057 L)/(0.100 M)`

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