2016, 91362 Chemistry Paper, Q3, b)

I don’t understand what the thought process was within [NH4+] = 0.320 x (20 / 30) = 0.213 molL-1.
Why did they times 20/30? Please help.

HI Hajun and welcome to Studyit.
The reason behind the 20/30 is the dilution factor that always occurs in a titration. Because the acid is twice as concentrated as the base we only need to add half the volume to reach the endpoint (n=CxV). In this case we start with 20 mL of the base but at the endpoint we have added another 10 mL of the acid so the total volume is now 20+10 = 30 mL.
This means that the concentration of the species in the solution at the endpoint (such as the ammonium ion) all need to be multiplied by the dilution factor of 20/30 (initial volume/final volume) as the number of moles of the product is spread out over a bigger volume.
Hope this clarifies.