# Question #2a118

##### 3 Answers

Approx.

#### Explanation:

Note that

#### Explanation:

Here's an alternative approach to keep in mind when dealing with **dilutions**.

As you know, the underlying principle of a dilution is that you can **decrease** the concentration of a solution by **increasing** its volume while keeping the number of moles of solute **constant**.

This implies that *increasing* the volume of the solution by a **factor**, let's say *decrease* by the **same factor**

This factor is called **dilution factor** and can be calculated like this

#color(blue)(|bar(ul(color(white)(a/a)"DF" = V_"diluted"/V_"concentrated" = c_"concentrated"/c_"diluted"color(white)(a/a)|)))#

In your case, you know that the initial volume of the solution, i.e. the volume of the *concentrated solution*, is equal to *diluted solution*, is equal to

#0.500 color(red)(cancel(color(black)("L"))) * (10^3"mL")/(1color(red)(cancel(color(black)("L")))) = "500 mL"#

This means that the concentrated solution was diluted by a factor of

#"DF" = (500 color(red)(cancel(color(black)("mL"))))/(100color(red)(cancel(color(black)("mL")))) = color(blue)(5)#

As a result, the concentration of the diluted solution will be

#c_"diluted" = 1/color(blue)(5) * "0.0234 M"#

I make it 0.00468 M.

#### Explanation:

I tend to think of it like this:

Work out how many moles of solute are contained in the original sample by multiplying the molarity by the number of litres (0.0234 x 0.1) = 0.00234 moles.

The number of moles in the final dilution will be the same, but the total volume will change from 100 ml to 0.5 l .

So the molarity at the end will be 0.00234 / 0.5 which is 0.00468 M.