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To solve this problem, we need to calculate the mass balance for the production of sodium sulfate and hydrochloric acid from sodium chloride (NaCl) and sulfuric acid (H₂SO₄), taking into account the given composition and conversion efficiency.

### Given:
1. **Product**: 1 ton of sodium sulfate (Na₂SO₄).
2. **Reactants**:
   - Table salt (NaCl) contains 95% NaCl.
   - Vitriol oil (H₂SO₄) contains 92.5% H₂SO₄.
3. **Conversion efficiency**: The decomposition of NaCl is 92%.

### Chemical Reaction:
The chemical reaction for the production of sodium sulfate and hydrochloric acid is as follows:
\[
2 \text{NaCl} + \text{H}_2\text{SO}_4 \rightarrow \text{Na}_2\text{SO}_4 + 2 \text{HCl}
\]

### Step 1: Calculate the molar masses
- Molar mass of NaCl = 58.44 g/mol
- Molar mass of H₂SO₄ = 98.08 g/mol
- Molar mass of Na₂SO₄ = 142.04 g/mol

### Step 2: Calculate the moles of Na₂SO₄ produced
1 ton of Na₂SO₄ = 1,000,000 grams.

\[
\text{Moles of Na}_2\text{SO}_4 = \frac{1,000,000 \text{g}}{142.04 \text{g/mol}} \approx 7041 \text{mol}
\]

### Step 3: Determine the moles of NaCl needed
From the balanced equation, 2 moles of NaCl produce 1 mole of Na₂SO₄, so:

\[
\text{Moles of NaCl required} = 2 \times 7041 = 14082 \text{mol}
\]

### Step 4: Convert moles of NaCl to mass
Mass of NaCl required = \(14082 \text{mol} \times 58.44 \text{g/mol} \approx 823,080 \text{g}\) or 823.08 kg.

Since the NaCl used is 95% pure, the actual mass of the table salt needed is:

\[
\frac{823.08 \text{kg}}{0.95} \approx 866.4 \text{kg}
\]

Considering a 92% decomposition rate:

\[
\frac{866.4 \text{kg}}{0.92} \approx 941.7 \text{kg}
\]

### Step 5: Determine the mass of H₂SO₄ needed
The reaction requires 1 mole of H₂SO₄ per mole of Na₂SO₄ produced. Thus, the moles of H₂SO₄ needed are 7041.

Mass of H₂SO₄ required = \(7041 \text{mol} \times 98.08 \text{g/mol} \approx 690,705 \text{g}\) or 690.7 kg.

Given that the vitriol oil is 92.5% pure:

\[
\frac{690.7 \text{kg}}{0.925} \approx 746.7 \text{kg}
\]

### Summary:
- **Table salt (95% NaCl)**: 941.7 kg
- **Vitriol oil (92.5% H₂SO₄)**: 746.7 kg

Let me know if you need further details or have questions. Here are some related questions for further exploration:

1. How would the required mass change if the purity of NaCl was different?
2. What would be the effect of increasing the decomposition degree of NaCl to 95%?
3. How much HCl would be produced as a by-product in this reaction?
4. Can this method be applied if using impure sulfuric acid with a different concentration?
5. How would a 5% loss of sodium sulfate during the process affect the input quantities?

**Tip:** Always account for impurities in reactants to ensure you have enough material for the desired reaction yield.

Calculate mass balance of hydrochloric-sulfate production for 1 ton sodium sulfate. Table salt, containing 95% NaCl, and vitriol oil, containing 92.5% H2SO4, are used in production. The NaCl decomposition degree is 92%.

Learn how to calculate the mass balance for producing 1 ton of sodium sulfate using table salt (95% NaCl) and vitriol oil (92.5% H2SO4) with a 92% NaCl decomposition rate. This stoichiometry problem covers mass balance and percentage purity calculations. Suitable for Grades 9-12.

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