Question

what volume of 1.5 M NH4 OH is needed to make 500.mL of a 3.00 M solution?

Answer 1

You need to double the concentration, from 1.5M to 3.0M, so the volume needs to be cut in half. The only way to increase the concentration of this solution is to allow water to evaporate until you get a concentration twice as large. This means starting with a volume twice as large as what you need to finish with. 1000mL of 1.5M solution, when evaporated to 500mL, will have a concentration of 3.0M.