1. Understand the Concepts

* Molarity (M): Represents the moles of solute per liter of solution.

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

2. Key Formula

The principle behind dilution is that the moles of solute remain constant before and after dilution. We can use the following equation:

M₁V₁ = M₂V₂

Where:

* M₁ = Initial molarity

* V₁ = Initial volume

* M₂ = Final molarity (what we want to find)

* V₂ = Final volume

3. Convert Units

* Volume: We need to express the volumes in liters (L):

* 250 mL = 0.250 L

* 45.0 mL = 0.045 L

4. Calculate the Final Volume

* V₂ = V₁ + volume of water added

* V₂ = 0.045 L + 0.250 L = 0.295 L

5. Apply the Dilution Formula

* M₁ = 4.2 M

* V₁ = 0.045 L

* V₂ = 0.295 L

* M₂ = ?

(4.2 M)(0.045 L) = M₂ (0.295 L)

6. Solve for M₂

M₂ = (4.2 M * 0.045 L) / 0.295 L

M₂ ≈ 0.64 M

Answer: The concentration of the solution after adding 250 mL of water will be approximately 0.64 M.