shortcut - pH and volume ?

[xD_aQt]

Hydrochloric acid of pH 1 is added to 20 mL of 0.1 M sodium hydroxide solution, resulting in a
solution of pH 4. The volume of the hydrochloric acid used is closest to

Is there a shortcut in solving this problem?

[coletrain]

C1V1=C2V2

[xD_aQt]

I'm not sure what the answer is because apparently the answer given for that question is wrong too. It says its 20.04ml

[xD_aQt]

how did you come about solving it?

[Linkage1992]

nevermind, i think it's the wrong answer, because when i work backwards i keep getting a pH of 3...

[Linkage1992]

ah, i know what i did wrong. their answer is right, it is 20.04mL

okay, so the fact that the final solution is acidic means that there is an excess of H+ ions.
First work out the concentration of the final solution, which will just be 10^-4 M.

This concentration has been determined by the number of moles of excess H+ ions divided by the new total volume of the system. The total volume will be x + 0.02, where x is the volume you want to find.

Thus, the number of moles of H+ in the final solution (since n = cv) is 10^-4 *  (x + 0.02)

This is the amount of moles left over after the H+ ions have reacted with the OH- ions.

Thus, n(H+) initial - n(OH-) initial = 10^-4 * (x + 0.02)

n(OH-) will equal 0.02 * .1 which is 0.002

n(H+) will equal x * .1 (since the pH is 1, the concentration will be 0.1)

Sub these values into the equation to get:

.1x - .002 = 10 ^-4 * (x + 0.02)

solving this equation gives x = .02004 which is 20.04mL

sorry for my pretty crappy explanation.

[xD_aQt]

Mmm I asked my teacher and they said it was wrong but they are yet to get back to me with their answer.
Just out of curiosity, is anyone able to confirm Linkage1992's answer?

[fady_22]

Mmm I asked my teacher and they said it was wrong but they are yet to get back to me with their answer.
Just out of curiosity, is anyone able to confirm Linkage1992's answer?

That's what I got as well (using the same method).
Neap 2010, right?

[xD_aQt]

Yeah

[Martoman]

Two ways. You can just be intuitive and say: think of the ph curve when you react a strong base and acid. Once you add 20ml of HCL the solutions is neutral. A VERY SMALL INCREASE in the volume dilivered sends the pH FLYING down the curve near 1. So a very small increase in volume is, with a few seconds thought, A.

Being really mathy:

let x be the volume you add in litres.

if ph1 HCL then [H] = [HCL] = 0.1

Now if the solution is ph4 there is some excess acid.

so to find this excess its

To find the concentration of this you add the volumes of the acid and the base.



For a solution of 4 ph this resultant concentration must be 0.0001



x = 0.02004 = 20.04 ml.