70 gms of a metal oxide on reduction produced 54 gms of metal. The atomic weight of the metal is 81. What is its valency?

Answer

To find the valency of the metal from the given data, we can follow these steps:

### Step 1: Determine the weight of oxygen in the metal oxide
The total weight of the metal oxide is given as 70 grams, and the weight of the metal produced is 54 grams. Therefore, the weight of oxygen can be calculated as follows:

\[ \text{Weight of Oxygen} = \text{Weight of Metal Oxide} - \text{Weight of Metal} \]
\[ \text{Weight of Oxygen} = 70 \, \text{g} - 54 \, \text{g} = 16 \, \text{g} \]

### Step 2: Calculate the equivalent mass of oxygen
The equivalent mass of oxygen is a known value, which is:

\[ \text{Equivalent Mass of Oxygen} = 16 \, \text{g/mol} \div 2 = 8 \, \text{g/equiv} \]

### Step 3: Use the weight of metal and oxygen to find the equivalent mass of the metal
According to the law of equivalent weights, we can set up the following relationship:

\[ \frac{\text{Weight of Metal}}{\text{Equivalent Mass of Metal}} = \frac{\text{Weight of Oxygen}}{\text{Equivalent Mass of Oxygen}} \]

Let the equivalent mass of the metal be \( E_m \). Therefore, we can write:

\[ \frac{54 \, \text{g}}{E_m} = \frac{16 \, \text{g}}{8 \, \text{g/equiv}} \]

Cross-multiplying gives:

\[ 54 \, \text{g} \cdot 8 \, \text{g/equiv} = 16 \, \text{g} \cdot E_m \]

Calculating the left side:

\[ 432 = 16 \cdot E_m \]

Now, solving for \( E_m \):

\[ E_m = \frac{432}{16} = 27 \, \text{g/equiv} \]

### Step 4: Calculate the valency of the metal
The valency can be calculated using the formula:

\[ \text{Valency} = \frac{\text{Molar Mass}}{\text{Equivalent Mass}} \]

Given that the atomic weight (molar mass) of the metal is 81 g/mol, we can substitute the values:

\[ \text{Valency} = \frac{81 \, \text{g/mol}}{27 \, \text{g/equiv}} = 3 \]

### Final Answer
The valency of the metal is **3**.

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