Question

Question #59b26

Answer 1

`"0.05 M"`

Explanation:

The trick here is to realize that diluting a solution will cause its concentration to decrease by the factor as its volume increases.

`"DF" = V_"diluted"/V_"stock" = c_"stock"/c_"diluted"`

Here `"DF"` is the dilution factor.

In your case, the volume of the stock solution increases by `"875 mL"` to a total value of

`V_"diluted" = "125 mL" + "875 mL"`

`V_"diluted" = "1,000 mL"`

This means that the dilution factor is equal to--remember, we're using the volume of the diluted solution and the volume of the stock solution here!

`"DF" = ("1,000" color(red)(cancel(color(black)("mL"))))/(125color(red)(cancel(color(black)("mL")))) = color(blue)(8)`

So if the volume increased by factor of `color(blue)(8)`, it follows that the concentration must have decreased by a factor of `color(blue)(8)`.

`color(blue)(8) = c_"stock"/c_"diluted"`

You will thus have

`c_"diluted" = c_"stock"/color(blue)(8)`

`c_"diluted" = "0.400 M"/color(blue)(8) = color(darkgreen)(ul(color(black)("0.05 M")))`

The answer is rounded to one significat figure because when you're adding the two volumes, the answer, i.e. `"1,000 mL"`, has one significant figure and no decimal places.