Understanding the Concepts

* Molarity (M): Represents the concentration of a solution, expressed as moles of solute per liter of solution.

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

* The Dilution Equation: M₁V₁ = M₂V₂

* M₁ = Initial molarity of the concentrated solution

* V₁ = Initial volume of the concentrated solution

* M₂ = Final molarity of the diluted solution

* V₂ = Final volume of the diluted solution

Solving the Problem

1. Identify the knowns:

* M₁ = 1.75 M (initial molarity of HCl)

* M₂ = 0.250 M (final molarity of HCl)

* V₂ = 0.500 L (final volume of the diluted solution)

2. Identify the unknown:

* V₁ = ? (initial volume of the concentrated HCl solution)

3. Apply the dilution equation:

* M₁V₁ = M₂V₂

* (1.75 M) * V₁ = (0.250 M) * (0.500 L)

4. Solve for V₁:

* V₁ = (0.250 M * 0.500 L) / 1.75 M

* V₁ = 0.0714 L

Answer: You would need to dilute 0.0714 L (or 71.4 mL) of 1.75 M hydrochloric acid with water to prepare 0.500 L of 0.250 M hydrochloric acid.