Question #5f23b

1 Answer
Dec 23, 2017

Answer:

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"#