# You want to mop your floor and the back of the cleaner bottle recommends a 0.5M solution, but the...

## Question:

You want to mop your floor and the back of the cleaner bottle recommends a 0.5M solution, but the concentration of cleaner in the bottle is 12M. If you were going to make up a 2L mop bucket, how much of the concentrated cleaner should you use?

## Dilution of Solution:

For a prepared solution, there are one or more solutes (dissolved substances) inside, each with certain concentration values. Sometimes these concentrations may be too high for a given application, so you need to dilute the solution. This procedure is performed by adding more of the liquid solvent (e.g. water). This solvent may be added to the entire starting solution volume, or simply a sample portion of it. In both cases, the dilution procedure decreases the concentration of every solute substance.

The 12 M solution is the stock and the target 0.50 M solution is the diluted version. First we need the moles of the cleaning solute in 2 liters of the dilute solution:

• Molarity of dilute solution (given) = {eq}C_1 = 0.50 \ M {/eq}
• Volume of dilute solution (given) = {eq}V_1 = 2.0 \ L {/eq}
• Moles of cleaning solute in dilute solution = {eq}n = V_1 \times C_1 = 2.0 \ L \times 0.50 \ M = 1.0 \ mol {/eq}

Dividing by the stock molarity gives us the stock volume required:

• Molarity of stock solution (given) = {eq}C_2 = 12 \ M {/eq}
• Volume of stock solution required = {eq}\dfrac{n}{C_2} = 1.0 \ mol \times \dfrac{L}{12 \ mol} = \boxed{0.083 \ L }{/eq}

Calculating Dilution of Solutions

from

Chapter 8 / Lesson 5
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Learn what a solution is and how to properly dilute a new solution from a stock solution. Learn the dilution equation that combines molarity, the volume of stock solution and desired solution to determine how much stock solution is needed for the new solution.