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 to produce 103 kg of hydrochloric acid (HCl), we will follow these steps:

### Step 1: Calculate the moles of HCl produced
Given that 103 kg of HCl is produced, we first convert this mass into grams:
\[ 103 \text{ kg} = 103 \times 1000 \text{ g} = 103000 \text{ g} \]

Next, we need to find the molar mass of HCl:
- Atomic weight of Hydrogen (H) = 1 g/mol
- Atomic weight of Chlorine (Cl) = 35.5 g/mol
- Molar mass of HCl = 1 + 35.5 = 36.5 g/mol

Now, we calculate the number of moles of HCl:
\[ \text{Moles of HCl} = \frac{\text{mass of HCl}}{\text{molar mass of HCl}} = \frac{103000 \text{ g}}{36.5 \text{ g/mol}} \approx 2821.917 \text{ moles} \]

### Step 2: Determine the moles of H₂SO₄ required
From the balanced reaction:
\[ 2 \text{NaCl} + \text{H}_2\text{SO}_4 \rightarrow 2 \text{HCl} + \text{Na}_2\text{SO}_4 \]
This indicates that 1 mole of H₂SO₄ produces 2 moles of HCl. Therefore, to find the moles of H₂SO₄ needed for 2821.917 moles of HCl, we use the stoichiometric ratio:
\[ \text{Moles of H₂SO₄} = \frac{1}{2} \times \text{Moles of HCl} = \frac{1}{2} \times 2821.917 \approx 1410.9585 \text{ moles} \]

### Step 3: Calculate the mass of H₂SO₄ required
Next, we calculate the mass of H₂SO₄ needed. The molar mass of H₂SO₄ is:
- Atomic weight of Hydrogen (H) = 1 g/mol (2 H atoms)
- Atomic weight of Sulfur (S) = 32 g/mol
- Atomic weight of Oxygen (O) = 16 g/mol (4 O atoms)

Calculating the molar mass:
\[ \text{Molar mass of H₂SO₄} = (2 \times 1) + 32 + (4 \times 16) = 98 \text{ g/mol} \]

Now, we can find the mass of H₂SO₄:
\[ \text{Mass of H₂SO₄} = \text{Moles of H₂SO₄} \times \text{Molar mass of H₂SO₄} = 1410.9585 \text{ moles} \times 98 \text{ g/mol} \approx 138273.933 \text{ g} \]

### Step 4: Calculate the mass of the 90% H₂SO₄ solution required
Since the solution is 90% H₂SO₄ by mass, we can set up the equation:
\[ \text{Mass of 90% H₂SO₄ solution} = \frac{\text{Mass of H₂SO₄}}{0.90} = \frac{138273.933 \text{ g}}{0.90} \approx 153085.48 \text{ g} \]

Now, converting grams to kilograms:
\[ \text{Mass in kg} = \frac{153085.48 \text{ g}}{1000} \approx 153.085 \text{ kg} \]

### Final Answer
Thus, the mass of sulfuric acid solution containing 90% H₂SO₄ by mass needed for the production of 103 kg of hydrochloric acid is approximately:
\[ \text{Mass of 90% H₂SO₄ solution} \approx 153.09 \text{ kg} \]