The oxide of a metal contains `40%` of oxygen. The valency of metal is 2. what is the atomic weight of the metal ?

Options

A. 12
B. 40
C. 36
D. 24

Explanation

To find the atomic weight of the metal in the oxide that contains 40% oxygen, we can follow these steps:

### Step 1: Determine the mass of oxygen and the metal
Assume we have 100 grams of the oxide. Since the oxide contains 40% oxygen, the mass of oxygen in the oxide is:
\[ \text{Mass of oxygen} = 40\% \text{ of } 100 \text{ grams} = 40 \text{ grams} \]
The remaining mass will be the metal:
\[ \text{Mass of metal} = 100 \text{ grams} - 40 \text{ grams} = 60 \text{ grams} \]

### Step 2: Calculate the number of moles of oxygen
The molar mass of oxygen (O) is approximately 16 grams/mole. Therefore, the number of moles of oxygen in the oxide is calculated as:
\[ \text{Number of moles of oxygen} = \frac{\text{Mass of oxygen}}{\text{Molar mass of oxygen}} = \frac{40 \text{ grams}}{16 \text{ grams/mole}} = 2.5 \text{ moles} \]

### Step 3: Determine the formula of the oxide
The valency of the metal is given as 2. Since oxygen has a valency of 2 (O²⁻), the formula of the oxide can be represented as:
\[ \text{Metal} (M) + \text{Oxygen} (O) \rightarrow \text{MO} \]
This indicates that one mole of the metal combines with one mole of oxygen, leading us to the formula \( \text{MO} \).

### Step 4: Relate moles of metal to moles of oxygen
Since we have 2.5 moles of oxygen, and the formula is \( \text{MO} \), we also have 2.5 moles of the metal.

### Step 5: Use the number of moles to find the molar mass of the metal
The molar mass (atomic weight) of the metal can be calculated using the formula:
\[ \text{Number of moles} = \frac{\text{Mass of metal}}{\text{Molar mass of metal}} \]
Rearranging this gives us:
\[ \text{Molar mass of metal} = \frac{\text{Mass of metal}}{\text{Number of moles of metal}} = \frac{60 \text{ grams}}{2.5 \text{ moles}} = 24 \text{ grams/mole} \]

### Conclusion
The atomic weight of the metal is **24 grams/mole**.

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