Problem about Nitrate electrodeposition

[cuigm371]

Homework Statement

Hey guys,
I am preparing a technical exam and am facing an exam problem below:

Ni is electrodeposited from an aqueous sulphate solution that has a composition that fluctuates from 1 to 0.01M due to changes in the feed composition of the process.
a) what is the pH range that this electrodeposition can be conducted in order to avoid hydrogen gas evolution and nickel hydroxide precipitation? Given:
Ni 2+ + 2e- <-> Ni , E0 = -0.25V
Ni 2+ + 2H2O <-> Ni(OH)2 (s) + 2H+ log K = -12.73

Homework Equations

Ksp= [Ni(OH)2] * [H+]^2/[Ni+]

The Attempt at a Solution

a. pH range: take Eh-PH of H2O with respect to H2/H+ where:
[H2/H+] = -0.0592 pH = E0 = -0.25 V
so pH = 0.25/0.0592 = 4.22 to avoid hydrogen gas evolution

For Ni(OH)2 precipitation:
Ksp= [Ni(OH)2] * [H+]^2/[Ni+]^2 = 10^(-12.73)

this is where I was stuck- how to calculate the [Ni(OH)2] and the [Ni+]? using 1M and 0.01M respectively?

 

[Borek]

Your formula for Ksp is wrong.

 

[cuigm371]

Your formula for Ksp is wrong.

Thank you for pointing out. the formula should've been:

Ksp= [Ni(OH)2] * [H+]^2/[Ni+] = 10^(-12.73)

I still am not clear what to do next. Could you please advise?

 

[Borek]

No, this is still not a correct formula for solubility product. It is not a matter of a wrong exponent, it is conceptually wrong (and that's what stops you from solving the problem).

 

[cuigm371]

Ni(OH)2 <-> Ni 2+ + 2 (OH)-
and Ksp = [Ni2+] [OH-]^2/[Ni(OH)2]

this seems more reasonable. Correct?

 

[Borek]

No, you are making the same error again and again. Please check with your textbook.

 

[cuigm371]

No, you are making the same error again and again. Please check with your textbook.

I believe it is right as below. THANK YOU VERY MUCH!

H+ + OH- = H2O Kw
Ni(OH)2= Ni2+ + 2OH- Ka

so, for Ni2+ + 2H2O = Ni(OH)2 + 2H+
K = Kw^2/Ka

 

[Borek]

Nope, it is not a solubility product.

http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch18/ksp.php

 

[cuigm371]

Nope, it is not a solubility product.

http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch18/ksp.php

Refer to the textbook page attached.

Ni(OH)2 = Ni2+ + 2(OH)-
Ks = [Ni]2+ x (OH)-^2 = 10^(-12.73)
Ni+ ranges from 1 to 0.01M, so OH- can be calculated accordingly. Is this right now?

 

[Borek]

Yes, when you have a correct formula for Ksp it is as trivial as solving for OH^- and converting it to pH.

 

[cuigm371]

Yes, when you have a correct formula for Ksp it is as trivial as solving for OH^- and converting it to pH.

Thank you very much indeed!
looking back I think I was confused initially by the way it was given,
Ni 2+ + 2H2O <-> Ni(OH)2 (s) + 2H+

and forgot to go to the definition of the solubility product. this is a good lesson learned.