# Question #11820

##### 1 Answer

Here's my take on this.

#### Explanation:

Assuming that the question is not incomplete, your goal here is to figure out the **dilution factor**,

For starters, you know that the dilution factor tells you the ratio that exists between the volume of the diluted solution and the volume of the stock solution.

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

Now, you know that you take

This means that the dilution factor for the first dilution is equal to

#"DF"_1 = (250.00 color(red)(cancel(color(black)("mL"))))/(25.00color(red)(cancel(color(black)("mL")))) = color(blue)(10)#

Next, you take a

#"DF"_2 = (100.00 color(red)(cancel(color(black)("mL"))))/(25.00color(red)(cancel(color(black)("mL")))) = color(purple)(4)#

Now, if you want to figure out the **overall dilution factor**, you need to **multiply** the two dilution factors.

#"DF"_"overall" = "DF"_1 xx "DF"_2#

In your case, you have

#"DF"_"overall" = color(blue)(10) xx color(purple)(4) = color(green)(40)#

What this means is that the *initial solution* was diluted by a factor of **times less concentrated** than the solution that you diluted to get the solution

This is the case because the dilution factor also tells you the ratio that exists between the concentration of the stock solution and the concentration of the diluted solution.

#"DF" = c_"stock"/c_"diluted"#

So if you start with a sulfuric acid solution of concentration

#c_"A" = c_1/color(blue)(10)#

This tells you that solution **timess less concentrated** that the initial solution. Next, you have

#c_"final" = c_"A"/color(purple)(4)#

But since

#c_"A" = c_1/color(blue)(10)#

you can say that you have

#c_"final" = (c_1/color(blue)(10))/color(purple)(4) = c_1/(color(blue)(10) * color(purple)(4)) = c_1/color(green)(40)#

This tells you that the final solution will be **times less concentrated** than the initial solution.