Question

How much water must be added to 500 mL of 2 M $ \mathrm{H_2SO_4} $ solution to make it 0.5 M?

• A. 1.5 L
• B. 2.0 L
• C. 1.0 L
• D. 0.75 L

Hint:

Use the dilution formula \( M_1 V_1 = M_2 V_2 \) for problems involving changing concentrations by adding solvent. Always convert volumes to consistent units.

Answer 1

The Correct Option is A

Step 1: Apply the dilution equation \[ M_1 V_1 = M_2 V_2 \] with the following values:
\( M_1 = 2 \, \mathrm{M} \),
\( V_1 = 500 \, \mathrm{mL} = 0.5 \, \mathrm{L} \),
\( M_2 = 0.5 \, \mathrm{M} \),
\( V_2 = \) the final diluted volume in liters.
Step 2: Determine the final volume \( V_2 \) \[ 2 \times 0.5 = 0.5 \times V_2 \implies 1 = 0.5 V_2 \implies V_2 = \frac{1}{0.5} = 2 \, \mathrm{L} \] Step 3: Calculate the volume of water required \[ V_{\text{water}} = V_2 - V_1 = 2 - 0.5 = 1.5 \, \mathrm{L} \]