A 100% pure sample of a divalent metal carbonate weighing 2 g on complete thermal decomposition releases 448 cc of carbon dioxide at STP. The equivalent mass of the metal is

Options

A. 40
B. 20
C. 28
D. 12

Explanation

To find the equivalent mass of the divalent metal in the carbonate (MCO3) that decomposes to release carbon dioxide (CO2), we can follow these steps:

### Step 1: Calculate the volume of CO2 released in liters.
Given that 448 cc of CO2 is released, we convert this to liters:
\[ 448 \, \text{cc} = \frac{448}{1000} \, \text{L} = 0.448 \, \text{L} \]

### Step 2: Determine the number of moles of CO2 produced.
Using the ideal gas law, we know that 1 mole of gas at STP occupies 22.4 L. Thus, we can calculate the moles of CO2:
\[ \text{Moles of } CO2 = \frac{\text{Volume of } CO2}{\text{Molar volume at STP}} = \frac{0.448 \, \text{L}}{22.4 \, \text{L/mol}} = 0.02 \, \text{mol} \]

### Step 3: Relate moles of CO2 to moles of MCO3.
From the thermal decomposition of the carbonate (MCO3), we know that 1 mole of MCO3 produces 1 mole of CO2. Therefore, the moles of MCO3 that decomposed is also 0.02 mol.

### Step 4: Calculate the molar mass of MCO3.
The mass of the MCO3 sample is given as 2 g. Using the number of moles calculated:
\[ \text{Molar mass of } MCO3 = \frac{\text{Mass}}{\text{Moles}} = \frac{2 \, \text{g}}{0.02 \, \text{mol}} = 100 \, \text{g/mol} \]

### Step 5: Determine the atomic mass of the divalent metal (M).
The molar mass of MCO3 can be expressed as:
\[ \text{Molar mass of } MCO3 = \text{Atomic mass of } M + 12 \, (\text{C}) + 3 \times 16 \, (\text{O}) = 100 \, \text{g/mol} \]
Calculating the mass of oxygen and carbon:
\[ \text{Mass of O} = 3 \times 16 = 48 \, \text{g} \]
\[ \text{Mass of C} = 12 \, \text{g} \]
Thus,
\[ M + 48 + 12 = 100 \]
\[ M + 60 = 100 \]
\[ M = 100 - 60 = 40 \, \text{g/mol} \]

### Step 6: Calculate the equivalent mass of the metal.
The equivalent mass of a divalent metal is given by:
\[ \text{Equivalent mass} = \frac{\text{Atomic mass}}{\text{Valency}} = \frac{40}{2} = 20 \, \text{g/equiv} \]

### Final Answer:
The equivalent mass of the divalent metal is **20 g/equiv**.

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