A mixture of `SO_(2)` and `O_(2)` in the molar ratio `16:1` is diffused through a pin hole for successive effusion three times to give a molar ratio `1:1` of diffused mixture. Which one are not correct if diffusion is made at same `P` and `T` in each operation?
(`I`) Eight operation are needed to get `1:1` molar ratio.
(`II`) Rate of diffusion for `SO_(2):O_(3)` after eight operations in `0.707`.
(`III`) Six operations are needed to get `2:1` molar ratio for `SO_(2)` and `O_(2)` in diffusion mixture.
(`IV`) Rate of diffusion for `SO_(2)` and `O_(2)` after six operations is `2.41`.

Options

A. `I`, `II`, `III`
B. `II`, `III`
C. `I`, `III`
D. `IV`

Explanation

To solve the problem, we need to analyze the diffusion of a mixture of \( SO_2 \) and \( O_2 \) with an initial molar ratio of \( 16:1 \) through a pinhole for successive effusion. We will determine the validity of the four statements provided.

### Step 1: Understand the Initial Conditions
The initial molar ratio of \( SO_2 \) to \( O_2 \) is \( 16:1 \). This means for every 16 moles of \( SO_2 \), there is 1 mole of \( O_2 \).

### Step 2: Determine the Final Molar Ratio
The problem states that after successive effusion, the final molar ratio of the diffused mixture should be \( 1:1 \) (i.e., equal amounts of \( SO_2 \) and \( O_2 \)).

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