The carbonate of a metal is isomorphous with `MgCO_(3)` and contains 10.34 percent of carbon. Atomic mass of metal will be:

Options

A. 56
B. 98
C. 40
D. 23

Answer

To solve the problem, we will follow these steps:

### Step 1: Understand the problem
The carbonate of a metal is isomorphous with MgCO₃ and contains 10.34% carbon. We need to find the atomic mass of the metal.

### Step 2: Write the formula for the metal carbonate
Since the metal carbonate is isomorphous with MgCO₃, we can represent the metal carbonate as MCO₃, where M is the metal.

### Step 3: Calculate the molar mass of MCO₃
The molar mass of MCO₃ can be calculated as follows:
- Atomic mass of carbon (C) = 12 g/mol
- Atomic mass of oxygen (O) = 16 g/mol (and there are 3 oxygen atoms, so 3 × 16 = 48 g/mol)
- Therefore, the molar mass of MCO₃ = M + 12 + 48 = M + 60 g/mol

### Step 4: Set up the equation using the percentage of carbon
We know that the percentage of carbon in MCO₃ is given as 10.34%. This can be expressed mathematically as:
\[ \frac{\text{mass of carbon}}{\text{molar mass of MCO}_3} \times 100 = 10.34 \]
Substituting the values we have:
\[ \frac{12}{M + 60} \times 100 = 10.34 \]

### Step 5: Solve for M
Rearranging the equation gives:
\[ 12 \times 100 = 10.34 \times (M + 60) \]
\[ 1200 = 10.34M + 620.4 \]
Subtracting 620.4 from both sides:
\[ 579.6 = 10.34M \]
Now, dividing both sides by 10.34:
\[ M = \frac{579.6}{10.34} \approx 56 \]

### Step 6: Conclusion
The atomic mass of the metal is approximately 56 g/mol. This corresponds to iron (Fe), which means the metal carbonate is FeCO₃ (ferrous carbonate).

### Final Answer:
The atomic mass of the metal is 56 g/mol.

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