Question

The molar mass of the water insoluble product formed from the fusion of chromite ore \(FeCr_2\text{O}_4\) with \(Na_2\text{CO}_3\) in presence of \(O_2\) is ....... g mol\(^{-1}\):

Answer 1

Correct Answer: 160

To solve this problem, we need to identify the insoluble product formed in the reaction and then calculate its molar mass.

1. Identifying the Reaction:
Chromite ore ($FeCr_2O_4$) reacts with sodium carbonate ($Na_2CO_3$) and oxygen ($O_2$) to form sodium chromate ($Na_2CrO_4$), iron(III) oxide ($Fe_2O_3$), and carbon dioxide ($CO_2$).
The balanced chemical equation is: $4FeCr_2O_4(s) + 8Na_2CO_3(s) + O_2(g) \rightarrow 8Na_2CrO_4(aq) + 2Fe_2O_3(s) + 8CO_2(g)$

2. Identifying the Insoluble Product:
From the reaction, sodium chromate is soluble, while iron(III) oxide ($Fe_2O_3$) is insoluble.

3. Calculating the Molar Mass of $Fe_2O_3$:
Given: Molar mass of Fe = 56 g/mol
Molar mass of O = 16 g/mol
Molar mass of $Fe_2O_3$ = (2 × Molar mass of Fe) + (3 × Molar mass of O) = (2 × 56 g/mol) + (3 × 16 g/mol) = 112 g/mol + 48 g/mol = 160 g/mol

Final Answer:
The molar mass of the insoluble product $Fe_2O_3$ is 160 g/mol.

Answer 2

Step 1: Understand Chromite Ore and the Reaction

Chromite ore, with the formula FeCr₂O₄, contains iron (Fe) and chromium (Cr). When it’s heated (fused) with sodium carbonate (Na₂CO₃) and oxygen (O₂), a chemical reaction occurs. This is a common process to extract chromium from its ore.

The balanced chemical equation for the reaction is:

4FeCr₂O₄ + 8Na₂CO₃ + 7O₂ → 2Fe₂O₃ + 8NaCrO₂ + 8CO₂

Reactants: FeCr₂O₄ (chromite ore), Na₂CO₃ (sodium carbonate), O₂ (oxygen).

Products:

• Fe₂O₃ (iron(III) oxide, insoluble in water).
• NaCrO₂ (sodium chromite, soluble in water; may further oxidize to Na₂CrO₄).
• CO₂ (carbon dioxide, a gas).

Step 2: Identify the Water-Insoluble Product

The question asks for the water-insoluble product. Let’s analyze the products:

• Fe₂O₃: Iron(III) Oxide is a solid and insoluble in water.
• NaCrO₂: Sodium chromite (or Na₂CrO₄ if further oxidized) is soluble in water.
• CO₂: A gas, so not relevant here.

Therefore, the water-insoluble product is Fe₂O₃.

Step 3: Calculate the Molar Mass of Fe₂O₃

The molar mass of a compound is the sum of the atomic masses of its atoms. Let’s calculate for Fe₂O₃:

Atomic masses:

• Iron (Fe): 55.85 g/mol
• Oxygen (O): 16.00 g/mol

Fe₂O₃ has 2 iron atoms and 3 oxygen atoms:

• Mass of 2 Fe atoms: 2 × 55.85 = 111.70 g/mol
• Mass of 3 O atoms: 3 × 16.00 = 48.00 g/mol

Total molar mass of Fe₂O₃ = 111.70 + 48.00 = 159.70 g/mol

Final Answer

The molar mass of the water-insoluble product (Fe₂O₃) is 159.70 g/mol.