Example 10 A sodium hydroxide solution is used to titrate 25.00 mL of a sulfuric acid The titration requires 43.79 mL of the 0.1172 M NaOH solution to completely neutralize the acid. What is the concentration of the H_(2)SO_(4) solution? H_(2)SO_(4)+2NaOHarrow Na_(2)SO_(4)+2H_(2)O

To find the concentration of the sulfuric acid (H₂SO₄) solution, we can use the concept of stoichiometry and the balanced chemical equation provided:<br /><br />\[ H_{2}SO_{4} + 2NaOH \rightarrow Na_{2}SO_{4} + 2H_{2}O \]<br /><br />From the balanced equation, we see that one mole of sulfuric acid reacts with two moles of sodium hydroxide (NaOH).<br /><br />First, calculate the moles of NaOH used in the titration:<br /><br />\[ \text{Moles of NaOH} = \text{Volume (L)} \times \text{Concentration (M)} \]<br />\[ \text{Moles of NaOH} = 0.04379 \, \text{L} \times 0.1172 \, \text{M} \]<br />\[ \text{Moles of NaOH} = 0.00512376 \, \text{mol} \]<br /><br />Since it takes 2 moles of NaOH to neutralize 1 mole of H₂SO₄, the moles of H₂SO₄ can be calculated as:<br /><br />\[ \text{Moles of H₂SO₄} = \frac{\text{Moles of NaOH}}{2} \]<br />\[ \text{Moles of H₂SO₄} = \frac{0.00512376 \, \text{mol}}{2} \]<br />\[ \text{Moles of H₂SO₄} = 0.00256188 \, \text{mol} \]<br /><br />Next, calculate the concentration of the H₂SO₄ solution:<br /><br />\[ \text{Concentration (M)} = \frac{\text{Moles of solute}}{\text{Volume (L)}} \]<br />\[ \text{Concentration (M)} = \frac{0.00256188 \, \text{mol}}{0.02500 \, \text{L}} \]<br />\[ \text{Concentration (M)} = 0.1027392 \, \text{M} \]<br /><br />Therefore, the concentration of the H₂SO₄ solution is approximately 0.1027 M.