Most of the commercial hydrochloric acid is prepared by heating NaCI with conc. `H_2 SO_4` How much sulphuric acid containing 90% `H_2 SO_4` by mass is needed for the production of 103 kg of hydrochloric acid?

Options

A. 319.55 kg
B. 888.02 kg
C. 153.63 kg
D. 343.28 kg

Answer

To solve the problem of how much sulfuric acid (H₂SO₄) containing 90% H₂SO₄ by mass is needed for the production of 103 kg of hydrochloric acid (HCl), we will follow these steps:

### Step 1: Write the balanced chemical equation
The reaction between sodium chloride (NaCl) and sulfuric acid (H₂SO₄) is:
\[ 2 \text{NaCl} + \text{H}_2\text{SO}_4 \rightarrow 2 \text{HCl} + \text{Na}_2\text{SO}_4 \]

### Step 2: Calculate the number of moles of HCl produced
We need to convert the mass of HCl to moles. The molar mass of HCl is approximately 36.5 g/mol.

Given:
- Mass of HCl = 103 kg = 103,000 g

Now, calculate the number of moles of HCl:
\[ \text{Number of moles of HCl} = \frac{\text{mass of HCl}}{\text{molar mass of HCl}} = \frac{103000 \text{ g}}{36.5 \text{ g/mol}} \approx 2821.92 \text{ moles} \]

### Step 3: Determine the moles of H₂SO₄ required
From the balanced equation, we see that 2 moles of HCl require 1 mole of H₂SO₄. Therefore, the moles of H₂SO₄ required can be calculated as follows:
\[ \text{Moles of H}_2\text{SO}_4 = \frac{\text{Moles of HCl}}{2} = \frac{2821.92}{2} \approx 1410.96 \text{ moles} \]

### Step 4: Calculate the mass of H₂SO₄ required
The molar mass of H₂SO₄ is approximately 98 g/mol. Now, calculate the mass of H₂SO₄ needed:
\[ \text{Mass of H}_2\text{SO}_4 = \text{Moles of H}_2\text{SO}_4 \times \text{Molar mass of H}_2\text{SO}_4 = 1410.96 \text{ moles} \times 98 \text{ g/mol} \approx 138,877.08 \text{ g} \]

### Step 5: Convert the mass of H₂SO₄ to kg
\[ \text{Mass of H}_2\text{SO}_4 \text{ in kg} = \frac{138877.08 \text{ g}}{1000} \approx 138.88 \text{ kg} \]

### Step 6: Adjust for the concentration of H₂SO₄
Since the sulfuric acid is 90% by mass, we need to find the total mass of the 90% solution required to obtain the calculated mass of H₂SO₄:
\[ \text{Mass of 90% H}_2\text{SO}_4 = \frac{\text{Mass of H}_2\text{SO}_4}{0.90} = \frac{138877.08 \text{ g}}{0.90} \approx 154,308.98 \text{ g} \]

### Step 7: Convert the mass of the solution to kg
\[ \text{Mass of 90% H}_2\text{SO}_4 \text{ in kg} = \frac{154308.98 \text{ g}}{1000} \approx 154.31 \text{ kg} \]

### Final Answer
Approximately **154.31 kg** of sulfuric acid containing 90% H₂SO₄ by mass is needed for the production of 103 kg of hydrochloric acid.

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