A 25.00-mL sample of an H2SO4 (2 and 4 are subscripted) solution of unknown concentration is titrated with a .1328 M KOH solution. A volume of 38.33 mL of KOH was required to reach the endpoint. What is the concentration of the unknown H2SO4 (again, the 2 and 4 are subscripted) solution?

my work:
38.33 mL KOH* (1L/1000mL)*(.1328 M KOH/L KOH)*(1 mol H2SO4/1mol KOH)=.005090 mol H2SO4

M= mol solution/L= .005090mol/.025L
=.2036M

However, the answer in the book says it should equal .1018M. I'm confused.

I'm sorry... I accidently reposted this--it is not answered yet though.

look at you last ( ). If you balance the reaction, you will find it takes 2mol KOH to neutralize one mole of H2SO4

Your calculations are correct. The concentration of the unknown H2SO4 solution is indeed 0.2036 M. It seems there may be a mistake in the book.

To determine the concentration of the unknown H2SO4 solution, we can use the concept of stoichiometry and the balanced chemical equation for the reaction between H2SO4 and KOH.

The balanced chemical equation is:
H2SO4 + 2 KOH → K2SO4 + 2 H2O

From the equation, we can see that the stoichiometric ratio between H2SO4 and KOH is 1:2. This means that for every 1 mole of H2SO4, we need 2 moles of KOH to react completely.

Let's go through the steps again to calculate the concentration:

1. Convert the volume of KOH used in the titration to moles:
38.33 mL KOH * (1 L / 1000 mL) * (0.1328 mol KOH / 1 L KOH) = 0.00508624 mol KOH

2. Since the stoichiometric ratio between H2SO4 and KOH is 1:2, we need to divide the number of moles of KOH by 2 to find the number of moles of H2SO4:
0.00508624 mol KOH / 2 = 0.00254312 mol H2SO4

3. Now, we can calculate the concentration of the H2SO4 solution:
Concentration (M) = mol H2SO4 / Volume (L)
Concentration = 0.00254312 mol / 0.025 L = 0.1017248 M

Based on the calculations, the concentration of the unknown H2SO4 solution is approximately 0.1017 M. It seems that the answer in the book is correct, and there might have been a mistake in your calculations. Double-checking your steps should help you find the error.