To solve this problem, let's start by writing the balanced chemical equation for the reaction between sulfuric acid (H₂SO₄) and sodium hydroxide (NaOH):

$\text{H}_2\text{SO}_4 + 2\text{NaOH} \rightarrow \text{Na}_2\text{SO}_4 + 2\text{H}_2\text{O}$

This equation tells us that one mole of sulfuric acid reacts with two moles of sodium hydroxide.

Step 1: Calculate the moles of NaOH used in the titration

The molarity (M) formula is: $\text{Molarity} = \frac{\text{moles of solute}}{\text{volume of solution in liters}}$

Rearranging it to find the number of moles: $\text{moles of NaOH} = \text{Molarity} \times \text{Volume (L)}$

Given:

• Molarity of NaOH = 0.147 M
• Volume of NaOH = 36.42 mL = 0.03642 L

$\text{moles of NaOH} = 0.147 \, \text{M} \times 0.03642 \, \text{L} = 0.00535374 \, \text{moles}$

Step 2: Determine the moles of H₂SO₄ reacted

From the balanced equation, 1 mole of H₂SO₄ reacts with 2 moles of NaOH, so we can use the stoichiometric ratio to find the moles of H₂SO₄:

$\text{moles of H}_2\text{SO}_4 = \frac{\text{moles of NaOH}}{2} = \frac{0.00535374}{2} = 0.00267687 \, \text{moles}$

Step 3: Calculate the molarity of the H₂SO₄ solution

Using the molarity formula again: $\text{Molarity of H}_2\text{SO}_4 = \frac{\text{moles of H}_2\text{SO}_4}{\text{volume of solution in liters}}$

Given:

• Volume of H₂SO₄ = 15.00 mL = 0.01500 L

$\text{Molarity of H}_2\text{SO}_4 = \frac{0.00267687 \, \text{moles}}{0.01500 \, \text{L}} = 0.178 \, \text{M}$

Answer

The molarity of the H₂SO₄ solution is: $\boxed{0.178 \, \text{M}}$

Would you like more details or have any questions on this calculation?

Here are five related questions to further explore this topic:

1. What is the importance of using a balanced chemical equation in titration calculations?
2. How do you determine the endpoint of a titration experimentally?
3. What would happen if the NaOH concentration was incorrectly measured in a titration?
4. How does a diprotic acid like H₂SO₄ affect the stoichiometry of a reaction?
5. What is the role of an indicator in acid-base titrations?

Tip: Always make sure to convert volumes to liters when using the molarity formula to ensure consistency in units.