To calculate the volume of NaOH required to reach the first equivalence point, we need to determine the number of moles of H2SO4 in the 50.0 mL sample.
Number of moles of H2SO4 = concentration of H2SO4 * volume of H2SO4
= 0.1 M * 0.050 L
= 0.005 moles

At the first equivalence point, the number of moles of NaOH will be equal to the number of moles of H2SO4. Since the stoichiometric ratio between NaOH and H2SO4 is 2:1, the volume of NaOH required can be calculated as follows:
Volume of NaOH = Number of moles of NaOH / concentration of NaOH
= 0.005 moles / 0.2 M
= 0.025 L = 25.0 mL

To calculate the volume of NaOH required to reach the second equivalence point, we need to determine the number of moles of H2SO4 reacting with the first half of NaOH (NaOH required to reach the first equivalence point).
Number of moles of NaOH at the first equivalence point = 0.005 moles

Since the stoichiometric ratio between NaOH and H2SO4 is 2:1, the number of moles of H2SO4 reacting with the first half of NaOH will be half of the number of moles of NaOH at the first equivalence point.
Number of moles of H2SO4 reacting with the first half of NaOH = 0.005 moles / 2 = 0.0025 moles

Now, we can calculate the number of moles of NaOH required to reach the second equivalence point. Since the stoichiometric ratio between NaOH and H2SO4 is still 2:1, the number of moles of NaOH required will be twice the number of moles of H2SO4.
Number of moles of NaOH at the second equivalence point = 2 * 0.0025 moles = 0.005 moles

Finally, we can calculate the volume of NaOH required to reach the second equivalence point.
Volume of NaOH = Number of moles of NaOH / concentration of NaOH
= 0.005 moles / 0.2 M
= 0.025 L = 25.0 mL

Therefore, the volume of NaOH required to reach the first and second equivalence points in a 50.0 mL sample of H2SO4 is both 25.0 mL.

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