4 g of a metal oxide contains 1.6 g-oxygen, then equivalent mass of the metal is

Options

A. 3.2
B. 24
C. 12
D. 20

Answer

To find the equivalent mass of the metal in the metal oxide, we can follow these steps:

### Step 1: Identify the given data
- Mass of metal oxide = 4 g
- Mass of oxygen in the metal oxide = 1.6 g

### Step 2: Calculate the mass of the metal
To find the mass of the metal, we subtract the mass of oxygen from the mass of the metal oxide:
\[ \text{Mass of metal} = \text{Mass of metal oxide} - \text{Mass of oxygen} \]
\[ \text{Mass of metal} = 4 \, \text{g} - 1.6 \, \text{g} = 2.4 \, \text{g} \]

### Step 3: Determine the equivalent weight of oxygen
The equivalent weight of an element can be calculated using the formula:
\[ \text{Equivalent weight} = \frac{\text{Atomic weight}}{\text{Valency}} \]
For oxygen:
- Atomic weight of oxygen = 16 g/mol
- Valency of oxygen = 2

Thus, the equivalent weight of oxygen is:
\[ \text{Equivalent weight of oxygen} = \frac{16}{2} = 8 \, \text{g} \]

### Step 4: Set up the equation for equivalent weights
Using the relationship between the equivalent weights of the metal and oxygen, we can write:
\[ \frac{\text{Mass of metal}}{\text{Mass of oxygen}} = \frac{\text{Equivalent weight of metal}}{\text{Equivalent weight of oxygen}} \]
Substituting the known values:
\[ \frac{2.4 \, \text{g}}{1.6 \, \text{g}} = \frac{X}{8} \]
Where \(X\) is the equivalent weight of the metal.

### Step 5: Solve for \(X\)
Cross-multiplying gives:
\[ 2.4 \times 8 = 1.6 \times X \]
\[ 19.2 = 1.6X \]
Now, divide both sides by 1.6 to solve for \(X\):
\[ X = \frac{19.2}{1.6} = 12 \, \text{g} \]

### Conclusion
The equivalent mass of the metal is \(12 \, \text{g}\).

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