[Rutherford]

For how long do you need to pass direct current (I=0.5A) through 50cm³ of a HCl solution (c=0.02mol/dm³) so that the pH is going to be 2?
I know that the pH will reduce because H⁺ ions take part in the electrolysis. I calculated that 5*10^-4 H⁺ ions need to take part in it. Now I wrote the electrolysis process:
K^-:2H⁺+2e^--->H₂
A⁺:2Cl^--->Cl₂+2e-
I used Faradey's law: nFz=It, t=nFz/I, because two electrons take part in the electrolysis I used for z=2 and I get that t=193s which is two times bigger than the right answer. I don't know where I've mistaken. Is it z?

[Borek]

z is 2 if you are looking for amount of H₂ produced, but 1 when calculating amount of H⁺ removed from the solution.

[Rutherford]

I don't understand. Is it related to the coefficients in the equation?

[Borek]

Just look at the reaction equation - there is one electron consumed for each H⁺ reduced (2 electrons per two H⁺) and two electrons consumed per each H₂ produced.

[Rutherford]

Thanks Borek.

[Rutherford]

I've done many problems correct thanks to your advice, but I came to this one:
100cm³ of KOH solution (c=0.01mol/dm³) is electrolysed for 20 hours (I=1A) using Pt electrodes. Calculate the concentration of OH^- ions after the electrolysis.

I figured out that the n of the OH^- ions remains the same-->1*10^-3mol. The cathode process is:
K^-:2H₂O+2e^--->2OH^-+H₂
Need to calculate the mass of water that is lost during the process. nFz=It n=It/(Fz). z is again the problem. For 2 moles of water, 2 electrons are spent, so I thought that for 1 mole of water 1 electron is spent and I used that z=1. I got two times more moles than I should, to get the right answer.

[Olympiad_Tutor]

what happens at Anode?

[Rutherford]

4OH^--->2H₂O+O₂+4e^-
The first one should be multiplied by 2. Still can't figure out what to do now.

[Olympiad_Tutor]

Try combining your half-reactions.

[Rutherford]

K^-:4H₂O+4e^--->4OH^-+2H₂
A⁺:4OH^--->2H₂O+O₂+4e^-
4 moles of water are spent, 2 moles are created. How can I combine these two reactions? Calculate the mass of the spent water and then the mass of the created water and substract them?

[Borek]

4 moles of water are spent, 2 moles are created.

So what is the overall change?

[Rutherford]

2 moles are spent, but how much is z? For those 2 moles z=4, for 1 mole z=2?

[juanrga]

I don't understand. Is it related to the coefficients in the equation?

z is charge of ion under study (z=1 for H⁺, for instance) not a stoichiometric coefficient

[Rutherford]

What would it be for the 2 H₂O moles?

[Olympiad_Tutor]

4e^- are needed to decompose 2 H₂O.

Combine the half-reactions aiming to cancel the electrons.  Even though the electrons are cancelled out, they are still responsible for the reaction.  Therefore you need to plug in 4 for moles of electrons into Faraday's law.