An element forms an oxide, in which the oxygen is `20%` of the oxide by weight, the equivalent weight of the given element will be

Options

A. `32`
B. `40`
C. `60`
D. `128`

Explanation

To find the equivalent weight of the given element that forms an oxide with oxygen constituting 20% of the oxide by weight, we can follow these steps:

### Step 1: Determine the composition of the oxide
Given that oxygen is 20% of the oxide by weight, we can conclude that the remaining 80% must be the metal (M).

### Step 2: Set up the mass relationship
If we assume the total mass of the oxide (MO) is 100 grams, then:
- Mass of oxygen (O) = 20 grams
- Mass of metal (M) = 100 grams - 20 grams = 80 grams

### Step 3: Calculate the equivalent weight of oxygen
The equivalent weight of an element is calculated using the formula:
\[ \text{Equivalent weight} = \frac{\text{Molar mass}}{\text{Valence factor}} \]
For oxygen (O), the molar mass is 16 g/mol, and since it typically has a valence of -2 in oxides, the valence factor is 2. Therefore, the equivalent weight of oxygen is:
\[ \text{Equivalent weight of O} = \frac{16 \text{ g/mol}}{2} = 8 \text{ g/equiv} \]

### Step 4: Relate the equivalent weights of metal and oxygen
From the mass relationship established earlier:
- 20 grams of oxygen corresponds to 80 grams of metal (M).
- The equivalent weight of oxygen is 8 g/equiv, so we can find how many equivalents of oxygen are in 20 grams:
\[ \text{Equivalents of O} = \frac{20 \text{ g}}{8 \text{ g/equiv}} = 2.5 \text{ equiv} \]

### Step 5: Calculate the equivalent weight of the metal
Since the ratio of equivalents of metal to equivalents of oxygen must be the same as their masses, we can set up the following relationship:
\[ \text{Mass of M} : \text{Mass of O} = \text{Equivalents of M} : \text{Equivalents of O} \]
Let the equivalent weight of metal be \( E_M \):
\[ 80 \text{ g} : 20 \text{ g} = \frac{80}{E_M} : 2.5 \]
Cross-multiplying gives:
\[ 80 \times 2.5 = 20 \times E_M \]
\[ 200 = 20 \times E_M \]
\[ E_M = \frac{200}{20} = 10 \text{ g/equiv} \]

### Conclusion
The equivalent weight of the given element (metal M) is **10 g/equiv**.

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