1 mole of `OH^(-)` ions is obtained from 85 g of hydroxide of a metal. What is the equivalent weight of the metal ?

Answer

To find the equivalent weight of the metal from the given information, follow these steps:

### Step 1: Understand the composition of the metal hydroxide
The metal hydroxide can be represented as \( \text{MOH} \), where \( M \) is the metal. Given that 1 mole of \( \text{OH}^- \) ions is produced, we know that the metal hydroxide dissociates to release one hydroxide ion.

### Step 2: Calculate the mass of \( \text{OH}^- \)
The molar mass of \( \text{OH}^- \) is calculated as follows:
- The atomic mass of oxygen (O) is approximately 16 g/mol.
- The atomic mass of hydrogen (H) is approximately 1 g/mol.
- Therefore, the molar mass of \( \text{OH}^- \) = 16 g/mol + 1 g/mol = 17 g/mol.

Since 1 mole of \( \text{OH}^- \) corresponds to a mass of 17 grams, we can confirm that:

\[ \text{Mass of } \text{OH}^- = 1 \text{ mole} \times 17 \text{ g/mol} = 17 \text{ g} \]

### Step 3: Calculate the mass of the metal
The total mass of the metal hydroxide \( \text{MOH} \) is given as 85 g.

To find the mass of the metal \( M \):

\[ \text{Mass of metal} = \text{Mass of metal hydroxide} - \text{Mass of } \text{OH}^- \]

Substituting the values:

\[ \text{Mass of metal} = 85 \text{ g} - 17 \text{ g} = 68 \text{ g} \]

### Step 4: Determine the number of moles of the metal
Since we have 1 mole of \( \text{OH}^- \), it indicates that we also have 1 mole of the metal \( M \).

### Step 5: Calculate the molecular weight of the metal
Using the formula for molecular weight:

\[ \text{Molecular weight (M)} = \frac{\text{Mass (W)}}{\text{Number of moles (n)}} \]

Substituting the known values:

\[ \text{Molecular weight of metal} = \frac{68 \text{ g}}{1 \text{ mole}} = 68 \text{ g/mol} \]

### Step 6: Find the equivalent weight of the metal
The equivalent weight is calculated using the formula:

\[ \text{Equivalent weight} = \frac{\text{Molecular weight}}{n \text{ factor}} \]

For the metal \( M \), the n factor (valency) is 1 (since it forms one hydroxide ion). Therefore:

\[ \text{Equivalent weight} = \frac{68 \text{ g/mol}}{1} = 68 \text{ g/equiv} \]

### Final Answer
The equivalent weight of the metal is **68 g/equiv**.

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