In the following reaction, `O_(3)+6I^(-)+6H^(+)rarr 3I_(2)+3H_(2)O` equivalent mass of `O_(3)` (with molecular mass M) is :

Options

A. `(M)/(2)`
B. `(M)/(4)`
C. `(M)/(24)`
D. `(M)/(6)`

Answer

To find the equivalent mass of \( O_3 \) in the reaction:

\[ O_3 + 6I^- + 6H^+ \rightarrow 3I_2 + 3H_2O \]

we need to follow these steps:

### Step 1: Identify the change in oxidation state of oxygen in \( O_3 \)

In \( O_3 \), the oxidation state of oxygen is 0. In water (\( H_2O \)), the oxidation state of oxygen is -2. Thus, the change in oxidation state for one oxygen atom is:

\[ 0 \rightarrow -2 \]

### Step 2: Calculate the total change in oxidation state

Since there are three oxygen atoms in \( O_3 \), the total change in oxidation state when \( O_3 \) is converted to \( H_2O \) is:

\[ 3 \times (0 \rightarrow -2) = 3 \times 2 = 6 \]

This means that \( O_3 \) gains a total of 6 electrons.

### Step 3: Define equivalent mass

The equivalent mass of a substance is defined as the molecular mass divided by the total change in oxidation state (in terms of electrons gained or lost). The formula for equivalent mass (\( E \)) is given by:

\[ E = \frac{M}{n} \]

where \( M \) is the molecular mass and \( n \) is the total change in oxidation state.

### Step 4: Calculate the equivalent mass of \( O_3 \)

From the previous steps, we have:

- Molecular mass of \( O_3 \) = \( M \)
- Total change in oxidation state = 6

Thus, the equivalent mass of \( O_3 \) is:

\[ E = \frac{M}{6} \]

### Conclusion

The equivalent mass of \( O_3 \) is \( \frac{M}{6} \).

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