1. Understand the Concepts

* Stock Solution: A concentrated solution that is diluted to make working solutions.

* Dilution: The process of reducing the concentration of a solution by adding more solvent.

* Molarity (M): Moles of solute per liter of solution.

2. Use the Dilution Equation

The dilution equation helps us relate the volumes and concentrations of a stock solution and its dilution:

M₁V₁ = M₂V₂

Where:

* M₁ = Molarity of the stock solution

* V₁ = Volume of the stock solution (what we need to find)

* M₂ = Molarity of the diluted solution

* V₂ = Volume of the diluted solution

3. Plug in the Values

* M₁ = 2.00 M (stock solution)

* V₁ = Unknown (what we're solving for)

* M₂ = 0.50 M (diluted solution)

* V₂ = 150 mL (diluted solution)

4. Solve for V₁

(2.00 M) * V₁ = (0.50 M) * (150 mL)

V₁ = (0.50 M * 150 mL) / 2.00 M

V₁ = 37.5 mL

Answer: You would need 37.5 mL of the 2.00 M HCl stock solution to make 150 mL of a 0.50 M HCl solution.