# Suppose you wanted a 2:25 dilution of a stock solution, but you wanted 200 ml of it. How would you make this?

##### 1 Answer

#### Answer:

Here's what I got.

#### Explanation:

Your tool of choice here is the **dilution factor**,

- The ratio that exists between the volume of the diluted solution and the volume of the stock solution
- The ratio that exists between the concentration of the stock solution and the concentration of the diluted solution

So for any dilution, you have

#"DF" = color(white)(overbrace(color(black)(V_"diluted"/V_"stock"))^(color(blue)("volume ratio: diluted/stock"))) = color(white)(overbrace(color(black)(c_"stock"/c_"diluted"))^(color(blue)("concentration ratio: stock/diluted")))#

Now, you know that you're performing a

#2:25 = 1:color(blue)(12.5)#

dilution that will have

#"DF" = color(blue)(12.5)#

This tells you that the stock solution was **more concentrated** than the diluted solution and that the volume of the diluted solution is **times** the volume of the stock solution.

If you want the volume of the *diluted solution* to be equal to

#V_"stock" = V_"diluted"/"DF"#

Plug in your values to find

#V_"stock" = "200 mL"/color(blue)(12.5) = "16 mL"#

I'll leave the answer rounded to two **sig figs**, but keep in mind that you only have one significant figure for the volume of the diluted solution.

So, you can perform this dilution by taking