in a titration, a sample of H2SO4 solution with a volume of 15.00 mL required 36.42 mL of 0.147 M NaOH for complete reaction. What is the molarity of the H2SO4 solution?

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.

In a titration, a sample of H2SO4 solution with a volume of 15.00 mL required 36.42 mL of 0.147 M NaOH for complete reaction. What is the molarity of the H2SO4 solution?

Find the molarity of an H2SO4 solution using titration data. A sample of H2SO4 (15.00 mL) reacts with 36.42 mL of 0.147 M NaOH. Learn about molarity calculations and stoichiometry, essential for high school chemistry students (Grades 11-12).

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