A trivalent metal has mass % of metal in its superoxide equal to 36%. Calcualte approximate specific heat capacity of metal.

Options

A. `(6.4/18) Cal//gm ^(@)C`
B. `6.4/18 Cal//gm ^(@)C`
C. `(18/6.4) Cal//gm ^(@)C`
D. `(54/6.4) Cal//gm ^(@)C`

Answer

To solve the problem, we need to calculate the specific heat capacity of a trivalent metal in its superoxide form, given that the mass percentage of the metal in the superoxide is 36%. Here is a step-by-step solution:

### Step 1: Understanding the Composition of Superoxide
Superoxide is a compound containing the superoxide ion (O₂⁻). For a trivalent metal (M), the formula for the superoxide can be written as \( M O_2 \).

### Step 2: Setting Up the Mass Percent Equation
The mass percent of the metal in the superoxide is given as 36%. This means that in 100 g of the superoxide, the mass of the metal (M) is 36 g, and the mass of the oxygen (O) is 64 g.

### Step 3: Determine the Mass of Oxygen
Since the superoxide contains two oxygen atoms, we can calculate the mass of oxygen:
- The atomic mass of oxygen (O) = 16 g/mol.
- Therefore, the mass of 2 oxygen atoms = \( 2 \times 16 = 32 \) g.

### Step 4: Setting Up the Equation
From the mass percent, we can set up the following equation:
\[ \text{Mass of Metal (M)} + \text{Mass of Oxygen (O)} = 100 \text{ g} \]
Substituting the values we have:
\[ M + 32 = 100 \]
This simplifies to:
\[ M = 100 - 32 = 68 \text{ g} \]

### Step 5: Calculate the Molar Mass of the Metal
Since the metal is trivalent, we can express the molar mass (M) in terms of the mass percent:
\[ \frac{36}{100} = \frac{M}{M + 32} \]
Cross-multiplying gives:
\[ 36(M + 32) = 100M \]
Expanding and rearranging:
\[ 36M + 1152 = 100M \]
\[ 100M - 36M = 1152 \]
\[ 64M = 1152 \]
\[ M = \frac{1152}{64} = 18 \text{ g/mol} \]

### Step 6: Calculate the Specific Heat Capacity
The specific heat capacity (C) of the metal can be calculated using the formula:
\[ C = \frac{6.4}{\text{Atomic Weight}} \]
Substituting the atomic weight we found:
\[ C = \frac{6.4}{18} \approx 0.3556 \text{ J/g°C} \]

### Conclusion
The approximate specific heat capacity of the trivalent metal is **0.36 J/g°C**.