The amount of Mg in gms to be dissovled in dilute `H_(2)SO_(4)` to liberate `H_(2)` which is just sufficient to reduce 160 g of ferric oxide is

Options

A. 24
B. 48
C. 72
D. 96

Answer

To solve the problem of how much magnesium (Mg) is needed to be dissolved in dilute sulfuric acid (H₂SO₄) to liberate hydrogen (H₂) sufficient to reduce 160 g of ferric oxide (Fe₂O₃), we can follow these steps:

### Step 1: Understand the reactions involved
1. **Reaction of magnesium with sulfuric acid**:
\[ \text{Mg} + \text{H}_2\text{SO}_4 \rightarrow \text{MgSO}_4 + \text{H}_2 \]
Here, magnesium reacts with sulfuric acid to produce magnesium sulfate and hydrogen gas.

2. **Reduction of ferric oxide by hydrogen**:
\[ \text{Fe}_2\text{O}_3 + 3\text{H}_2 \rightarrow 2\text{FeO} + 3\text{H}_2\text{O} \]
In this reaction, ferric oxide is reduced to ferrous oxide using hydrogen.

### Step 2: Calculate the molar mass of Fe₂O₃
- The molar mass of Fe₂O₃ can be calculated as follows:
- Iron (Fe) has an atomic mass of 56 g/mol.
- Oxygen (O) has an atomic mass of 16 g/mol.

Therefore, the molar mass of Fe₂O₃ is:
\[ 2 \times 56 + 3 \times 16 = 112 + 48 = 160 \text{ g/mol} \]

### Step 3: Determine the amount of hydrogen needed
From the balanced equation for the reduction of ferric oxide, we see that 3 moles of H₂ are required to reduce 1 mole of Fe₂O₃.

Given that 160 g of Fe₂O₃ corresponds to 1 mole (since its molar mass is 160 g/mol), we need 3 moles of H₂ to reduce it.

### Step 4: Calculate the mass of hydrogen required
The molar mass of hydrogen (H₂) is:
\[ 2 \times 1 = 2 \text{ g/mol} \]
Thus, the mass of hydrogen needed for 3 moles is:
\[ 3 \times 2 = 6 \text{ g} \]

### Step 5: Relate the amount of magnesium to the amount of hydrogen produced
From the reaction of magnesium with sulfuric acid, we know that:
- 24 g of magnesium produces 2 g of hydrogen.

To find out how much magnesium is required to produce 6 g of hydrogen, we set up a proportion:
\[ \frac{24 \text{ g Mg}}{2 \text{ g H}_2} = \frac{x \text{ g Mg}}{6 \text{ g H}_2} \]

Cross-multiplying gives:
\[ 2x = 24 \times 6 \]
\[ 2x = 144 \]
\[ x = \frac{144}{2} = 72 \text{ g} \]

### Conclusion
The amount of magnesium that needs to be dissolved in dilute H₂SO₄ to liberate enough hydrogen to reduce 160 g of ferric oxide is **72 g**.

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