In the conversion `NH_(2)OH rarr N_(2)O`, the equivalent weight of `NH_(2)OH` will be:

Options

A. M
B. M/2
C. M/4
D. M/5

Answer

To find the equivalent weight of NH₂OH (hydroxylamine) in the conversion to N₂O (nitrous oxide), we can follow these steps:

### Step 1: Determine the oxidation states of nitrogen in both compounds.
- In NH₂OH, let the oxidation state of nitrogen be \( x \).
- The oxidation state of hydrogen is +1, and that of oxygen is -2.
- The equation for the oxidation state in NH₂OH can be set up as:
\[ x + 2(+1) + (-2) = 0 \]
Simplifying this gives:
\[ x + 2 - 2 = 0 \implies x = -1 \]

- In N₂O, let the oxidation state of nitrogen be \( y \).
- There are two nitrogen atoms and one oxygen atom, so the equation is:
\[ 2y + (-2) = 0 \]
Simplifying this gives:
\[ 2y - 2 = 0 \implies 2y = 2 \implies y = +1 \]

### Step 2: Calculate the change in oxidation state.
- The change in oxidation state from NH₂OH to N₂O is:
\[ \Delta = y - x = 1 - (-1) = 1 + 1 = 2 \]

### Step 3: Calculate the equivalent weight.
- The equivalent weight is given by the formula:
\[ \text{Equivalent weight} = \frac{\text{Molecular weight}}{\text{n}} \]
where \( n \) is the change in oxidation state (which we found to be 2).

### Step 4: Substitute the values into the formula.
- Let the molecular weight of NH₂OH be \( m \). Then:
\[ \text{Equivalent weight} = \frac{m}{2} \]

### Conclusion
Thus, the equivalent weight of NH₂OH in the conversion to N₂O is \( \frac{m}{2} \).