Given:
Molarity of H2SO4 solution (initial) = 0.1 M
Volume of H2SO4 solution (initial) = unknown
Molarity of NaOH solution = 0.1 M
Volume of NaOH solution = 50 mL

To Find:
Volume of 0.1 M H2SO4 solution required to make a solution with a molarity of 0.05 M

Explanation:
To find the volume of 0.1 M H2SO4 solution required, we can use the concept of stoichiometry and the equation of neutralization between H2SO4 and NaOH:

H2SO4 + 2NaOH → Na2SO4 + 2H2O

The equation shows that 1 mole of H2SO4 reacts with 2 moles of NaOH in a 1:2 ratio. Therefore, if we know the moles of NaOH, we can determine the moles of H2SO4 required to react completely.

Step 1: Calculate the moles of NaOH:
Molarity of NaOH = 0.1 M
Volume of NaOH = 50 mL = 0.05 L (convert mL to L)
Moles of NaOH = Molarity × Volume
= 0.1 M × 0.05 L
= 0.005 moles

Step 2: Determine the moles of H2SO4 required:
Since the stoichiometry ratio is 1:2 (H2SO4:NaOH), the moles of H2SO4 required will be half of the moles of NaOH.
Moles of H2SO4 required = 0.005 moles ÷ 2
= 0.0025 moles

Step 3: Calculate the volume of 0.1 M H2SO4 solution required:
Moles of H2SO4 solution (final) = 0.0025 moles
Molarity of H2SO4 solution (final) = 0.05 M

Volume of H2SO4 solution (final) = Moles of H2SO4 solution (final) ÷ Molarity of H2SO4 solution (final)
= 0.0025 moles ÷ 0.05 M
= 0.05 L = 50 mL

Therefore, 50 mL of 0.1 M H2SO4 solution must be added to 50 mL of 0.1 M NaOH solution to obtain a solution with a molarity of 0.05 M H2SO4.