A mineral consists of an equimolar mixture of the carbonates of two bivalent metals. One metal is present to the extent of 15.0% by weight, `3.0 g` of the mineral on heating lost `1.10 g` of `CO_(2)`. The percent by weight of other metal is

Options

A. 65
B. 25
C. 75
D. 35

Explanation

To solve the problem step by step, we will analyze the information given and apply stoichiometric principles to find the percentage by weight of the other metal in the mineral.

### Step 1: Understand the composition of the mineral
The mineral consists of an equimolar mixture of the carbonates of two bivalent metals. We can denote the carbonates as:
- Metal 1: \( M_1CO_3 \)
- Metal 2: \( M_2CO_3 \)

### Step 2: Determine the mass loss due to CO2
When the mineral is heated, it loses \( 1.10 \, g \) of \( CO_2 \). This loss corresponds to the decomposition of the carbonates into their respective metal oxides and carbon dioxide:
\[ MCO_3 \rightarrow MO + CO_2 \]

### Step 3: Calculate the moles of CO2 lost
The molar mass of \( CO_2 \) is \( 44 \, g/mol \). We can calculate the moles of \( CO_2 \) lost:
\[ \text{Moles of } CO_2 = \frac{1.10 \, g}{44 \, g/mol} = 0.025 \, mol \]

### Step 4: Relate moles of CO2 to moles of carbonates
Since the decomposition of one mole of carbonate produces one mole of \( CO_2 \), the moles of carbonates that decomposed is also \( 0.025 \, mol \).

### Step 5: Calculate the mass of carbonates
The molar mass of \( CO_3^{2-} \) is \( 60 \, g/mol \). The mass of carbonates that decomposed can be calculated as:
\[ \text{Mass of } CO_3^{2-} = \text{Moles} \times \text{Molar Mass} = 0.025 \, mol \times 60 \, g/mol = 1.5 \, g \]

### Step 6: Calculate the percentage of \( CO_3^{2-} \) in the mineral
The total mass of the mineral is \( 3.0 \, g \). The percentage of \( CO_3^{2-} \) in the mineral is:
\[ \text{Percentage of } CO_3^{2-} = \left( \frac{1.5 \, g}{3.0 \, g} \right) \times 100 = 50\% \]

### Step 7: Determine the percentage of the metals
From the problem, we know that one metal is present at \( 15\% \) by weight. Therefore, the percentage of the other metal can be calculated as:
\[ \text{Percentage of other metal} = 100\% - \text{Percentage of } CO_3^{2-} - \text{Percentage of first metal} \]
\[ = 100\% - 50\% - 15\% = 35\% \]

### Final Answer
The percent by weight of the other metal is \( 35\% \).

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