`1.82` g of a metal requires `32.5` ml of `1` N `HCl` to dissolve it. What is the equivalent weight of metal ?

Options

A. 46
B. 65
C. 56
D. 42

Answer

To find the equivalent weight of the metal, we can follow these steps:

### Step 1: Understand the Concept of Normality
Normality (N) is defined as the number of gram equivalents of solute per liter of solution. In this case, we have a 1 N HCl solution.

### Step 2: Convert Volume from mL to L
Given that the volume of HCl used is 32.5 mL, we need to convert this to liters:
\[ \text{Volume in liters} = \frac{32.5 \, \text{mL}}{1000} = 0.0325 \, \text{L} \]

### Step 3: Calculate the Number of Gram Equivalents of HCl
Since we have a 1 N solution, the number of gram equivalents of HCl in 0.0325 L is:
\[ \text{Number of gram equivalents} = \text{Normality} \times \text{Volume in L} = 1 \, \text{N} \times 0.0325 \, \text{L} = 0.0325 \, \text{equivalents} \]

### Step 4: Relate the Number of Gram Equivalents to the Metal
The number of gram equivalents of the metal will be equal to the number of gram equivalents of HCl used, as they react in a 1:1 ratio:
\[ \text{Number of gram equivalents of metal} = 0.0325 \, \text{equivalents} \]

### Step 5: Use the Formula for Equivalent Weight
The equivalent weight of the metal can be calculated using the formula:
\[ \text{Equivalent weight} = \frac{\text{Weight of metal}}{\text{Number of gram equivalents of metal}} \]
Substituting the values we have:
\[ \text{Equivalent weight} = \frac{1.82 \, \text{g}}{0.0325 \, \text{equivalents}} = 56 \, \text{g/equiv} \]

### Conclusion
The equivalent weight of the metal is **56 g/equiv**.