What is the pH of a mixture made with ammonia hydroxide and HCl?

[tyrant]

Homework Statement

A mixture is made by adding 25 ml of 0.100M HCl to 100ml of 0.025M ammonia hydroxide. Kd = 1.76 x 10^-5 . My task is to calculate the pH.

Homework Equations

I think this is the reaction that follows:
NH4OH + HCl <--> NH4 + H2O + Cl

The Attempt at a Solution

I have calculated the concentrations in the mixture:
c(NH4OH) = (0.025mol/l x 0.100l) / ( 0.100l + 0.025l) = 0.02 mol/l
c(HCl) = (0.100 mol/l x 0.025l) / ( 0.100l + 0.025l) = 0.02 mol/l

NH4OH + HCl <---> NH4 + H2O + Cl
Initial C 0.02M 0.02M 0
final C 0 0 0.02M

After this I'm not sure what happens, I have tried calculating the concentration of hydrogen ions formed by this reaction NH4 <---> NH3 + H ( I guess Kd is for this reaction) and calculating the pH then but it was wrong.
My teacher refuses to help me solve this and won't even tell me where I go wrong.

 

[Borek]

I have tried calculating the concentration of hydrogen ions formed by this reaction NH4 <---> NH3 + H

That's the correct approach, question is - what is Kd?

 

[tyrant]

I think Kd is a dissociation constant, the task was written as I wrote it to the problem statement. Kd is just given without specifically telling for what reaction it is.
Strangely I can't get the correct answer ( I don't know what the answer should be). I have double checked my calculations and there shouldn't be any errors in them. When I got my calculation back from my teacher there was only one mark and it said "wrong anwer and wrong solution". When I asked where exactly I had gone wrong he just mumbled something like check my lectures and I did but still no idea what seems to be the problem.

 

[Borek]

What if I tell you Kd is for NH₄OH dissociation?

 

[symbolipoint]

The Kd being 1.76 x 10^-5 is close enough to the dissociation constant for ammonia in water.

First task is use stoichiometry to determine which is in excess: ammonium hydroxide or HCl? If HCl is in excess, then use simple molarity of the excess HCl to find [H⁺] and pH. Otherwise, use dissociation constant expression formula to find pH.

Please note that we usually indicate dissociation constant of a weak base using symbol, K_b.