One mole of \(N_2H_4\) loses 10 moles of electrons and form \(y\) which retain all nitrogen and hydrogen present in the original compound. Assuming that there is no change in the oxidation state of hydrogen, the change in oxidation state of nitrogen will be from

-2 to +3

The correct answer is option 2. -2 to +3.

 Let us analyze the problem in detail by considering the oxidation states and the number of electrons involved in the reaction.

Step-by-Step Analysis

Step 1: Determine the initial oxidation state of nitrogen in \(N_2H_4\)

The molecular formula of hydrazine is \(N_2H_4\).

Hydrogen (H) has an oxidation state of +1.

Let the oxidation state of nitrogen in \(N_2H_4\) be \(x\).

The sum of oxidation states in \(N_2H_4\) must be zero (since it's a neutral molecule):

\(2x + 4(+1) = 0\)

\(2x + 4 = 0\)

\(2x = -4\)

\(x = -2\)

So, the initial oxidation state of nitrogen in \(N_2H_4\) is -2.

Step 2: Determine the final oxidation state of nitrogen after losing 10 moles of electrons

One mole of \(N_2H_4\) loses 10 moles of electrons.

The loss of electrons increases the oxidation state of the atom (since oxidation is the loss of electrons).

There are 2 nitrogen atoms in \(N_2H_4\), and they collectively lose 10 electrons. Hence, each nitrogen atom loses:

\(\frac{10}{2} = 5 \text{ electrons per nitrogen atom}\)

Since losing electrons increases the oxidation state by the number of electrons lost:

\(\text{New oxidation state of nitrogen} = -2 + 5 = +3\)

Step 3: Verify that all nitrogen and hydrogen atoms are retained in the product

The problem states that the product \(y\) retains all nitrogen and hydrogen atoms present in the original compound \(N_2H_4\). This means the final product \(y\) has the same number of nitrogen and hydrogen atoms as \(N_2H_4\), ensuring the calculations are valid.

Step 4: Determine the change in oxidation state of nitrogen
The change in oxidation state of nitrogen is from -2 to +3.

Conclusion

The change in the oxidation state of nitrogen is from -2 to +3, which corresponds to: (2) -2 to +3

This means the initial oxidation state of nitrogen in \(N_2H_4\) was -2, and after losing 10 electrons (5 electrons per nitrogen atom), the oxidation state becomes +3. Therefore, the correct answer is: (2) -2 to +3