You want to make 300 mL of a 0.2000 M dilute NaOH solution from a 1.5 M stock solution. How many mL of stock solution is needed?

Answer: 40mL

Explanation: What is required for this question is to obtain the number of moles of NaOH solute in the required solution.

Number of moles of solute in solution = (Concentration of solution in mol/L) * (Volume of solution in L)

Number of moles of NaOH in the required solution = 0.2 * (300/1000) = 0.06 moles

This number of moles has to be in the volume of stock solution used to make the required solution.

Volume of stock solution needed = (Number of moles of NaOH in the stock solution that has to match that in the required solution in L) / (concentration of stock solution in mol/L)

Volume of stock solution required = 0.06/1.5 = 0.04L = 40mL

QED.