Acid Base reaction, pH and POH

[Alex Santos]

Homework Statement

[/B]
NH3(aq) is a weak base with Kb = 1.8*10-5, Calculate [OH-] in a solution that is made by mixing togeather 500ml of 0.20M NH3(aq) and 500ml of 0.20M NH4CL(aq), what is the value of Ph?

Homework Equations

Henderson Hasselbalch: ph = Pka + log([conj.base/acid])
As well as another approach on the example, the regular one.

The Attempt at a Solution

To start with I am always a bit confused on how to set up the example and giving me the right inital values, for example I have NH4Cl---->NH3 + Cl + H. Now can I use my initial values, as NH3 in terms of moles
moles NH4Cl: 0.5L*0.2M = 0.1 moles
moles NH3: 0.5*0.2M = 0.1moles

using the " normal method" I get PH = 5.13 and by using the Hendersone Hasselbalch I get PH = 9.25.

I will send an attachment of my calculation because I write everything on an Ipad, so you can see clearly what I am doing.
Please correct me and tell me what is wrong and which method is wrong in my case.
Thank you

 

[Borek]

Solve full quadratic for the ICE table method.