Problem:
What volume of 0.10 M H2SO4 must be added to 50 mL of a 0.10 M NaOH Solution to make a solution in which the molarity of the H2SO4 is 0.050 M?

Solution:

To solve this problem, we need to use the concept of stoichiometry and the equation of neutralization reaction between H2SO4 and NaOH. The balanced equation is as follows:

H2SO4 + 2NaOH → Na2SO4 + 2H2O

We are given the initial volume and molarity of the NaOH solution (50 mL and 0.10 M, respectively). Let's assume we add V mL of the H2SO4 solution to achieve the desired molarity of 0.050 M.

Step 1: Calculate the number of moles of NaOH:

Using the formula:

Moles = Molarity × Volume (in liters)

Moles of NaOH = 0.10 M × 0.050 L (50 mL converted to liters)
Moles of NaOH = 0.005 moles

Step 2: Calculate the number of moles of H2SO4:

From the balanced equation, we can see that one mole of H2SO4 reacts with two moles of NaOH. Therefore, to neutralize the NaOH completely, we need twice the number of moles of H2SO4.

Moles of H2SO4 = 2 × Moles of NaOH
Moles of H2SO4 = 2 × 0.005 moles
Moles of H2SO4 = 0.010 moles

Step 3: Calculate the volume of 0.10 M H2SO4 needed:

Using the formula:

Volume (in liters) = Moles / Molarity

Volume of 0.10 M H2SO4 = 0.010 moles / 0.10 M
Volume of 0.10 M H2SO4 = 0.10 L (100 mL)

Therefore, we need to add 0.10 L (100 mL) of the 0.10 M H2SO4 solution to the 50 mL of 0.10 M NaOH solution to achieve a final solution with a molarity of 0.050 M H2SO4.

Conclusion:
To make a solution in which the molarity of H2SO4 is 0.050 M, we need to add 0.10 L (100 mL) of the 0.10 M H2SO4 solution to 50 mL of the 0.10 M NaOH solution. This will result in the neutralization of the NaOH and the formation of a solution containing Na2SO4 and 2H2O.

100ml is the final answer