`A` mineral consists of an equimolar mixture of the carbonates of two bivalent metals. One metal is present to the extent of `13.2%` by weight. `2.58g` of the mineral on heating lost `1.232g` of `CO_(2)`. Calculate the `%` by weight of the other metal.

Explanation

To solve the problem step by step, we will follow these calculations:

### Step 1: Determine the mass of carbonate lost
Given that 2.58 g of the mineral lost 1.232 g of CO₂ upon heating, we can find the mass of the carbonate that decomposed to produce this CO₂.

**Calculation:**
The molar mass of CO₂ is 44 g/mol. The molar mass of carbonate (CO₃) is 60 g/mol (C = 12 g/mol, O = 16 g/mol × 3 = 48 g/mol, thus 12 + 48 = 60 g/mol).

Using the ratio of the molar masses:
\[ \text{Mass of carbonate} = \left(\frac{60 \text{ g of carbonate}}{44 \text{ g of CO₂}}\right) \times 1.232 \text{ g of CO₂ \]
\[ = \frac{60}{44} \times 1.232 \approx 1.678 \text{ g of carbonate} \]

### Step 2: Calculate the percentage of carbonate in the mineral
Now, we can find the percentage of carbonate in the original mineral sample.

**Calculation:**
\[ \text{Percentage of carbonate} = \left(\frac{\text{mass of carbonate}}{\text{mass of mineral}}\right) \times 100 \]
\[ = \left(\frac{1.678 \text{ g}}{2.58 \text{ g}}\right) \times 100 \approx 65.11\% \]

### Step 3: Find the percentage of the first metal
We know that one metal constitutes 13.2% of the mineral.

### Step 4: Calculate the percentage of the second metal
Since the mineral consists of an equimolar mixture of the carbonates of two bivalent metals, we can find the percentage of the second metal by subtracting the known percentages from 100%.

**Calculation:**
\[ \text{Percentage of second metal} = 100\% - (\text{Percentage of first metal} + \text{Percentage of carbonate}) \]
\[ = 100\% - (13.2\% + 65.11\%) = 100\% - 78.31\% \approx 21.69\% \]

### Final Answer
The percentage by weight of the other metal is approximately **21.69%**.

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