The mass of `83.4%` pure salt cake `(Na_(2)SO_(4))` that can be produced from 250 kg of `94.5%` pure salt in the reaction `2NaCl+H_(2)SO_(4)rarr Na_(2)SO_(4)+2HCl` is :

Options

A. 344 kg
B. 244 kg
C. 444 kg
D. 222 kg

Explanation

To solve the problem of how much mass of 83.4% pure salt cake (Na₂SO₄) can be produced from 250 kg of 94.5% pure salt (NaCl), we will follow these steps:

### Step 1: Calculate the mass of pure NaCl
First, we need to find the mass of pure NaCl in the 250 kg of 94.5% NaCl.

\[ \text{Mass of pure NaCl} = \text{Total mass} \times \left(\frac{\text{Purity}}{100}\right) \]

\[ \text{Mass of pure NaCl} = 250 \, \text{kg} \times \left(\frac{94.5}{100}\right) = 236.25 \, \text{kg} \]

### Step 2: Use the stoichiometry of the reaction
The balanced chemical equation for the reaction is:

\[ 2 \, \text{NaCl} + \text{H}_2\text{SO}_4 \rightarrow \text{Na}_2\text{SO}_4 + 2 \, \text{HCl} \]

From the equation, we see that 2 moles of NaCl produce 1 mole of Na₂SO₄.

### Step 3: Calculate the molar masses
Next, we need to calculate the molar masses of NaCl and Na₂SO₄:

- Molar mass of NaCl = 23 (Na) + 35.5 (Cl) = 58.5 g/mol
- Molar mass of Na₂SO₄ = 2 × 23 (Na) + 32 (S) + 4 × 16 (O) = 142 g/mol

### Step 4: Calculate the amount of Na₂SO₄ produced
Using the stoichiometry, we can find out how much Na₂SO₄ can be produced from the mass of NaCl we have:

\[ \text{Moles of NaCl} = \frac{\text{Mass of NaCl}}{\text{Molar mass of NaCl}} = \frac{236250 \, \text{g}}{58.5 \, \text{g/mol}} \approx 4037.4 \, \text{mol} \]

From the balanced equation, 2 moles of NaCl produce 1 mole of Na₂SO₄, so:

\[ \text{Moles of Na₂SO₄} = \frac{4037.4 \, \text{mol}}{2} \approx 2018.7 \, \text{mol} \]

Now, we can find the mass of Na₂SO₄ produced:

\[ \text{Mass of Na₂SO₄} = \text{Moles of Na₂SO₄} \times \text{Molar mass of Na₂SO₄} = 2018.7 \, \text{mol} \times 142 \, \text{g/mol} \approx 286,673.4 \, \text{g} \approx 286.67 \, \text{kg} \]

### Step 5: Adjust for purity of Na₂SO₄
Since the Na₂SO₄ produced is only 83.4% pure, we need to calculate the total mass of the salt cake that corresponds to this purity:

Let \( x \) be the total mass of the salt cake. Then:

\[ \frac{x \times 83.4}{100} = 286.67 \, \text{kg} \]

Solving for \( x \):

\[ x = \frac{286.67 \, \text{kg} \times 100}{83.4} \approx 344.0 \, \text{kg} \]

### Final Answer
The mass of 83.4% pure salt cake (Na₂SO₄) that can be produced is approximately **344 kg**.

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