A 0.205 M NaOH solution is used to titrate 20.0 mL of a solution of H₂SO₄. If 45.6 mL of the NaOH solution is required to reach the endpoint, what is the molarity of the H₂SO₄ solution? (10.7) H₂SO₄(aq) + 2NaOH(aq) → 2H₂O(l) + Na₂SO₄

Verified step by step guidance

1. Identify the balanced chemical equation: ${\text{H}}_2{\text{SO}}_4(aq)+2\text{NaOH}(aq)\to 2{\text{H}}_2\text{O}(l)+{\text{Na}}_2{\text{SO}}_4(aq)$.
2. Determine the moles of NaOH used: Use the formula $\text{moles}=\text{molarity}\times \text{volume (L)}$ to calculate the moles of NaOH.
3. Use the stoichiometry of the reaction: From the balanced equation, 1 mole of ${\text{H}}_2{\text{SO}}_4$ reacts with 2 moles of $\text{NaOH}$. Use this ratio to find the moles of ${\text{H}}_2{\text{SO}}_4$.
4. Calculate the molarity of ${\text{H}}_2{\text{SO}}_4$: Use the formula $\text{molarity}=\frac{\text{moles of solute}}{\text{volume of solution in liters}}$ to find the molarity of the ${\text{H}}_2{\text{SO}}_4$ solution.
5. Convert the volume of ${\text{H}}_2{\text{SO}}_4$ solution from mL to L: Remember that 1 L = 1000 mL, so convert 20.0 mL to liters for the calculation.

Key Concepts

Titration

Titration is a quantitative analytical technique used to determine the concentration of a solute in a solution. It involves the gradual addition of a titrant (a solution of known concentration) to a sample solution until the reaction reaches its endpoint, indicated by a color change or a specific measurement. In this case, NaOH is the titrant used to neutralize H₂SO₄.

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions based on the balanced chemical equation. It allows us to determine the relationships between the amounts of substances involved. For the reaction between H₂SO₄ and NaOH, the stoichiometric ratio is 1:2, meaning one mole of H₂SO₄ reacts with two moles of NaOH, which is crucial for calculating the molarity of the H₂SO₄ solution.

Molarity

Molarity is a measure of concentration defined as the number of moles of solute per liter of solution. It is expressed in moles per liter (M). To find the molarity of the H₂SO₄ solution in this titration, we need to use the volume of NaOH used, its molarity, and the stoichiometric relationship from the balanced equation to calculate the moles of H₂SO₄ present in the original solution.