A substance `''A''` decomposes in solution following the first order kinetics. Flask `I` contains `1L` of `1 M` solution of `A` and falsk `II` constains `100 mL` of `0.6 M` solution. After `8 hr`, the concentration, of `A` in flask `I` becomes `0.25 M`. What will be the time for concentration of `A` in flask `II` to become `0.3 M` ?

Options

A. `0.4 hr`
B. `2.4 hr`
C. `4.0 hr`
D. Unpredictable as rate constant is not given

Explanation

To solve the problem step by step, we need to analyze the data provided and apply the principles of first-order kinetics.

### Step 1: Understand the initial conditions
- Flask I contains 1 L of 1 M solution of A.
- Flask II contains 100 mL of 0.6 M solution of A.

### Step 2: Determine the concentration change in Flask I
After 8 hours, the concentration of A in Flask I decreases from 1 M to 0.25 M.

### Step 3: Calculate the half-life for Flask I
In first-order kinetics, the half-life (t₁/₂) is constant and independent of the initial concentration.

- Initial concentration in Flask I = 1 M
- Final concentration after 8 hours = 0.25 M

We can assume that the concentration first reaches half (0.5 M) and then decreases to 0.25 M.

- Time to go from 1 M to 0.5 M = t₁/₂
- Time to go from 0.5 M to 0.25 M = t₁/₂

Thus, the total time for both halves is:
\[ t_{\text{total}} = t_{1/2} + t_{1/2} = 2 \times t_{1/2} \]

Given that the total time is 8 hours:
\[ 2 \times t_{1/2} = 8 \text{ hours} \]
\[ t_{1/2} = 4 \text{ hours} \]

### Step 4: Analyze Flask II
In Flask II, the initial concentration is 0.6 M, and we want to find out how long it takes for the concentration to decrease to 0.3 M.

### Step 5: Determine the change in concentration in Flask II
- Initial concentration in Flask II = 0.6 M
- Final concentration in Flask II = 0.3 M

The concentration decreases from 0.6 M to 0.3 M, which is exactly half of the initial concentration (0.6 M to 0.3 M).

### Step 6: Calculate the time for Flask II
Since the concentration in Flask II decreases from 0.6 M to 0.3 M, which is a half-life change:
- Time required = t₁/₂ = 4 hours (as calculated from Flask I).

### Conclusion
The time required for the concentration of A in Flask II to become 0.3 M is **4 hours**.

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