Final buffer question?

Question

If 500.0ml of 0.100M HCl is added to 300.0ml of 0.200M solution of ammonia, what will be the pH of the resulting buffer?

It would be great if you could go through it step by step

Answer 1

1. work out moles of HCl
2. work out moles of NH3 (which is greater)
3. all the HCl is turned into (NH4)+
4. work out remainder of NH3 moles
5. work out total volume
6. work out molarities of NH3 and (NH4)+
7. look up Kb, and work out Ka for (NH4)+
8. apply [H+] = Ka x [(NH4)+]/[NH3]
9. calculate pH