what volume (in litres) of 17.6M NaOH will be used to prepare 0.5M NaOH in 50,000ml?

Answer 1

you are diluting it 17.6/.5= 35.2 times
which means 1 part original, 34.2 parts water.
so total solution=50 liters, which means each "part" is 50/35.2=1.42 liters
so the volume of NaOH is 1.42 liters, and the volume of water to dilute it 1.42*34.2 = 48.56 liters