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The problem involves a reaction between sulfuric acid \((\text{H}_2\text{SO}_4)\) and sodium hydroxide \((\text{NaOH})\) to produce sodium sulfate \((\text{Na}_2\text{SO}_4)\) and water \((\text{H}_2\text{O})\). The goal is to calculate the maximum mass of water produced when 57.0 g of sulfuric acid reacts with 86.3 g of sodium hydroxide.

### Step 1: Balanced Chemical Equation

The balanced chemical equation for this reaction is:

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

From this equation, we see that:
- 1 mole of sulfuric acid reacts with 2 moles of sodium hydroxide to produce 2 moles of water.

### Step 2: Molar Masses
- Molar mass of \(\text{H}_2\text{SO}_4\) = \(2(1.01) + 32.07 + 4(16.00) = 98.09 \, \text{g/mol}\)
- Molar mass of \(\text{NaOH}\) = \(22.99 + 15.999 + 1.008 = 40.00 \, \text{g/mol}\)
- Molar mass of \(\text{H}_2\text{O}\) = \(2(1.008) + 16.00 = 18.016 \, \text{g/mol}\)

### Step 3: Moles of Reactants
- Moles of \(\text{H}_2\text{SO}_4\): 
\[
\frac{57.0 \, \text{g}}{98.09 \, \text{g/mol}} = 0.5813 \, \text{mol}
\]
- Moles of \(\text{NaOH}\): 
\[
\frac{86.3 \, \text{g}}{40.00 \, \text{g/mol}} = 2.1575 \, \text{mol}
\]

### Step 4: Limiting Reactant
From the balanced equation, 1 mole of \(\text{H}_2\text{SO}_4\) reacts with 2 moles of \(\text{NaOH}\). Therefore, 0.5813 moles of \(\text{H}_2\text{SO}_4\) would require \(2 \times 0.5813 = 1.1626\) moles of \(\text{NaOH}\).

Since there are 2.1575 moles of \(\text{NaOH}\), sulfuric acid is the limiting reactant.

### Step 5: Calculating Maximum Water Produced
According to the balanced equation, 1 mole of \(\text{H}_2\text{SO}_4\) produces 2 moles of \(\text{H}_2\text{O}\). So, 0.5813 moles of \(\text{H}_2\text{SO}_4\) will produce:
\[
0.5813 \times 2 = 1.1626 \, \text{moles of} \, \text{H}_2\text{O}
\]

The mass of water produced is:
\[
1.1626 \, \text{mol} \times 18.016 \, \text{g/mol} = 20.95 \, \text{g}
\]

### Final Answer
The maximum mass of water that can be produced is **20.95 g**.

Would you like a more detailed explanation or have any other questions?

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Here are 5 related questions for deeper understanding:
1. What is the role of the limiting reactant in a chemical reaction?
2. How do you identify the limiting reactant in a reaction?
3. What happens to the excess reactant in this reaction?
4. How does the molar mass of a compound affect the mass of products?
5. Why is it important to balance a chemical equation?

**Tip:** Always ensure your calculations align with significant figures in the given data for accuracy.

Aqueous sulfuric acid (H2SO4) will react with solid sodium hydroxide (NaOH) to produce aqueous sodium sulfate (Na2SO4) and liquid water (H2O). Suppose 57.0 g of sulfuric acid is mixed with 86.3 g of sodium hydroxide. Calculate the maximum mass of water that could be produced by the chemical reaction.

Solve a stoichiometric problem where sulfuric acid reacts with sodium hydroxide. Learn to calculate the maximum mass of water produced using key chemical principles like the limiting reactant and molar mass. Suitable for high school students in Grades 10-12.

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