# Question #cbbe3

##### 2 Answers

I have given both the shortcut method and also explained in detail what makes the shortcut work

#### Explanation:

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The wording; "diluted to" is stating the

Thus, expressed as a fraction we have:

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What

To change this to percent we need to have

For a moment lets think of the

If we can retain this ratio but change the bottom number (denominator) to 100 we have our answer

Known:

So if we multiply

The

#### Explanation:

Let me offer a more chemical-oriented approach to this problem.

As you know, a solution's molarity is defined as the number of moles of solute divided by the volume of the solution - expressed in liters.

#color(blue)("molarity" = c = "moles of solute"/"liters of solution" = n/V)#

Now, the idea behind diluting a solution is that you can **decrease** its concentration by

keeping the number of moles of soluteconstantincreasingthe volume of the solution byincreasingthe volume of the solvent

The underlying principle of a dilution

So, your initial sample has a total volume of

The target solution has a total volume of

The **number of moles of solute** present in these solutions will be

#n_1 = c_1 * V_1" "# and#" "n_2 = c_2 * V_2#

Since a dilution **implies** keeping the number of moles of solute constant

#n_1 = n_2#

you will get

#color(blue)(c_1V_1 = c_2V_2) -># the equation for dilution calculations

Your goal is to determine the dilution factor, so you can rearrange the above equation to get

#c_1/c_2 = V_2/V_1#

Plug in your values to get

#c_1/c_2 = (20 color(red)(cancel(color(black)("mL"))))/(0.25color(red)(cancel(color(black)("mL")))) = 80#

Therefore, the initial solution was **eighty times as concentrated** as the target solution

#c_1 = 80 xx c_2#

And that's how you find the dilution factor. Simply divide the **final volume** of the solution by the **initial volume** of the sample

#color(blue)("D"."F" = V_"final"/V_"initial") -># the equation for finding the dilution factor

A dilution factor of