On reduction 1.644 g of hot iron oxide give 1.15g of iron. Evaluate the equivalent weight of iron.

Options

A. 18.62
B. 19.13
C. 18.95
D. 12.95

Explanation

To evaluate the equivalent weight of iron based on the reduction of iron oxide, we can follow these steps:

### Step 1: Understand the Concept of Equivalent Weight
The equivalent weight of an element is defined as the mass of that element that combines with or displaces 1 mole of hydrogen or 8 grams of oxygen. In the case of iron, we will determine how much iron is produced from the reduction of iron oxide.

### Step 2: Calculate the Mass of Iron Displaced
From the problem, we know that 1.644 g of iron oxide gives 1.15 g of iron. Therefore, the mass of iron displaced is 1.15 g.

### Step 3: Calculate the Mass of Iron Oxide Reduced
The mass of iron oxide that was reduced is given as 1.644 g.

### Step 4: Calculate the Equivalent Weight of Iron
The equivalent weight of iron can be calculated using the formula:
\[ \text{Equivalent Weight} = \frac{\text{Mass of Iron Oxide}}{\text{Mass of Iron Produced}} \times \text{Molar Mass of Iron} \]
However, we can simplify this to finding the equivalent weight directly using the mass of iron produced and the number of moles of iron produced.

### Step 5: Calculate the Molar Mass of Iron
The molar mass of iron (Fe) is approximately 56 g/mol.

### Step 6: Calculate the Number of Moles of Iron Produced
Using the mass of iron produced:
\[ \text{Number of Moles of Iron} = \frac{\text{Mass of Iron}}{\text{Molar Mass of Iron}} = \frac{1.15 \, \text{g}}{56 \, \text{g/mol}} \approx 0.0205 \, \text{mol} \]

### Step 7: Calculate the Equivalent Weight of Iron
The equivalent weight of iron can be calculated as follows:
\[ \text{Equivalent Weight of Iron} = \frac{\text{Mass of Iron}}{\text{Number of Moles of Iron}} = \frac{1.15 \, \text{g}}{0.0205 \, \text{mol}} \approx 56.1 \, \text{g/mol} \]

### Step 8: Adjust for the Reaction
Since iron typically has a valency of 2 in reactions, we divide the molar mass by the valency:
\[ \text{Equivalent Weight of Iron} = \frac{56.1 \, \text{g/mol}}{2} \approx 28.05 \, \text{g/equiv} \]

### Final Answer
The equivalent weight of iron is approximately 28.05 g/equiv.

---