A 0.6gm sample consisting of only `CaC_(2)O_(4)` and `MgC_(2)O_(4)` is heated at `500^(@)C`gets converted into `CaCO_(3)` and `MgCO_(3)`. The sample then weighed 0.465gm. If the sample had been heated to `900^(@)C` where the products are CaO and MgO, then what would the mixture of oxides weigh?

Options

A. 0.12 g
B. 0.21 g
C. 0.252 g
D. 0.3 g

Answer

To solve the problem step by step, we will break down the process of heating the sample and the subsequent reactions that occur.

### Step 1: Understand the Initial Reaction
When the sample consisting of calcium oxalate (CaC₂O₄) and magnesium oxalate (MgC₂O₄) is heated at 500°C, it converts into calcium carbonate (CaCO₃) and magnesium carbonate (MgCO₃). The reactions can be represented as:

1. CaC₂O₄ → CaCO₃ + CO
2. MgC₂O₄ → MgCO₃ + CO

### Step 2: Calculate the Weight Loss Due to CO
The initial weight of the sample is 0.6 g, and after heating, the weight of the remaining sample is 0.465 g. The weight loss due to the formation of carbon monoxide (CO) can be calculated as:

Weight loss = Initial weight - Final weight
Weight loss = 0.6 g - 0.465 g = 0.135 g

### Step 3: Calculate Moles of CO Produced
The molecular weight of CO is 28 g/mol. To find the moles of CO produced, we use the formula:

Moles of CO = Weight of CO / Molecular weight of CO
Moles of CO = 0.135 g / 28 g/mol = 0.00482 mol

### Step 4: Relate Moles of CO to Moles of Carbonates
Since 1 mole of CaC₂O₄ produces 1 mole of CO and 1 mole of MgC₂O₄ also produces 1 mole of CO, we can denote the moles of calcium carbonate formed as X and the moles of magnesium carbonate formed as Y. Thus, we have:

X + Y = 0.00482 mol

### Step 5: Reaction at 900°C
When the carbonates are heated to 900°C, they decompose into their respective oxides:

1. CaCO₃ → CaO + CO₂
2. MgCO₃ → MgO + CO₂

### Step 6: Calculate Weight Loss Due to CO₂
The loss of weight during this reaction is due to the carbon dioxide (CO₂) released. The molecular weight of CO₂ is 44 g/mol. The total moles of carbonates (X + Y) will also give the moles of CO₂ produced.

Weight loss due to CO₂ = (X + Y) * 44 g/mol

Substituting the value of (X + Y) from Step 4:

Weight loss due to CO₂ = 0.00482 mol * 44 g/mol = 0.21208 g

### Step 7: Calculate the Final Weight of the Oxides
The weight of the mixture of oxides (CaO and MgO) after heating to 900°C can be calculated as follows:

Final weight of oxides = Weight of carbonates - Weight loss due to CO₂
Final weight of oxides = 0.465 g - 0.21208 g = 0.25292 g

### Conclusion
The weight of the mixture of oxides (CaO and MgO) after heating to 900°C is approximately **0.252 g**.

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