Question

Question #5f23b

Answer 1

Here's what I got.

Explanation:

The idea here is that you can use the `"pH"` of the solution to find the initial concentration of hydroxide anions, `"OH"^(-)`.

You know that an aqueous solution at `25^@"C"` has

`color(blue)(ul(color(black)("pH + pOH = 14")))`

This means that you have

`"pOH" = 14 - "pH"`

`"pOH" = 14 - 14 = 0`

Since you know that

`"pOH" = - log(["OH"^(-)])`

you can say that the concentration of hydroxide anions will be

`["OH"^(-)] = 10^(-"pOH")`

`["OH"^(-)] = 10^(-0)`

`["OH"^(-)] = "1 M"`

Now, when the `"pH"` of the solution is equal to `7` at `25^@"C"`, the solution is actually neutral, meaning that you have

`"pOH" = "pH" = 7`

In this case, the concentration of hydroxide anions, which is equal to the concentration of hydronium cations, `"H"_3"O"^(+)`, is equal to

`["OH"^(-)] = 1 * 10^(-7)color(white)(.)"M"`

So, you know that you must decrease the concentration of hydroxide anions by a factor of

`"DF" = (1 color(red)(cancel(color(black)("M"))))/(1 * 10^(-7)color(red)(cancel(color(black)("M")))) = color(blue)(10^7)`

Here `"DF"` is the dilution factor. Now, in order for the concentration of the solution to decrease by a factor equal to `"DF"`, its volume must increase by a factor of `"DF"`.

This means that you have

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

`V_"diluted" = "DF" * V_"stock"`

In your case, the volume of the diluted solution must be equal to

`V_"diluted" = color(blue)(10^7) * "0.2 mL"`

`V_"diluted" = 2 * 10^6color(white)(.)"mL"`

So in order for the `"pH"` of the solution to decrease from `14` to `7`, the volume of the solution must increase from `"0.2 mL"` to `2 * 10^6` `"mL"`.

You can thus say that you can dilute this solution by adding enough water to get the total volume of the solution to `2 * 10^6` `"mL"`, which, for all intended purposes, is equal to

`V_"water" = 2 * 10^6color(white)(.)"mL" - "0.2 mL"`

`V_"water" = "1,999,999.8 mL"`

However, keep in mind that you only have one significant figure for the volume of the initial solution, so you must round the answer to one significant figure.

`V_"water" = "2,000,000 mL"`