Sulfuric was titrated with NaOH solution. 208 mL of .250 M NaOH solution was needed to completely neutralize 65.0 mL of H2SO4. What is the concentration of the sulfuric acid solution?

2NaOH + H2SO4 ==> Na2SO4 + 2H2O

Moles NaOH used = M x L = ??
Moles H2SO4 needed = 1/2 moles NaOH (from the equation).
M H2SO4 = moles H2SO4/L H2SO4.

0.4 mol/L or 0.4M

To find the concentration of the sulfuric acid (H2SO4) solution, we can use the concept of stoichiometry. The balanced chemical equation for the reaction between sulfuric acid and sodium hydroxide (NaOH) is:

H2SO4 + 2NaOH -> Na2SO4 + 2H2O

From the balanced equation, we can see that 1 mole of sulfuric acid (H2SO4) reacts with 2 moles of sodium hydroxide (NaOH).

Step 1: Calculate the number of moles of NaOH used.
Given the volume and molar concentration of NaOH used in the titration, we can calculate the number of moles of NaOH as follows:

Moles of NaOH = Volume of NaOH solution (in L) × Molar concentration of NaOH (in mol/L)

Since the volume is given in mL, we need to convert it to L by dividing it by 1000 (1 L = 1000 mL).

Volume of NaOH solution = 208 mL = 208/1000 L = 0.208 L
Molar concentration of NaOH = 0.250 mol/L

Moles of NaOH = 0.208 L × 0.250 mol/L = 0.052 mol

Step 2: Use the balanced equation to determine the moles of H2SO4.
According to the stoichiometry of the balanced equation, 1 mole of H2SO4 reacts with 2 moles of NaOH. Therefore, the number of moles of H2SO4 can be calculated as:

Moles of H2SO4 = (Moles of NaOH) / 2 = 0.052 mol / 2 = 0.026 mol

Step 3: Calculate the concentration of H2SO4.
Now that we know the number of moles of H2SO4 and the volume of the H2SO4 solution, we can calculate its concentration using the formula:

Concentration (in mol/L) = Moles / Volume (in L)

Volume of H2SO4 solution = 65.0 mL = 65.0/1000 L = 0.065 L
Concentration of H2SO4 = Moles H2SO4 / Volume of H2SO4 solution

Concentration of H2SO4 = 0.026 mol / 0.065 L = 0.4 mol/L

Therefore, the concentration of the sulfuric acid solution is 0.4 mol/L.