`SO_(2)` reacts with `O_(2)` as follows `2SO_(2) +O_(2)to2SO_(3)`, the rate of disappearance of `SO_(2)` is `2.4xx10^(-4)` mole `"lit"^(-1)"min"^(-1)`. Then

Options

A. Rate of reaction is `1.2xx10^(-4)"mol lit"^(-1)"min"^(-1)`
B. Rate of appearance of `SO_(3)` is`2.4xx10^(-4)"mole lit"^(-1)"min"^(-1)`
C. Rate of disappearance of `O_(2)` is `1.2xx10^(-4)` mole `'lit"^(-1)min^(-1)`
D. Rate of reaction is twice the rate of disappeanrance of `SO_(3)`

Explanation

To solve the problem, we need to analyze the reaction and the rates of disappearance and appearance of the species involved. The reaction given is:

\[ 2 \text{SO}_2 + \text{O}_2 \rightarrow 2 \text{SO}_3 \]

### Step 1: Write the Rate of Reaction

The rate of reaction can be expressed in terms of the rates of disappearance of the reactants and the rate of appearance of the products. The general form is:

\[ \text{Rate} = -\frac{1}{2} \frac{d[\text{SO}_2]}{dt} = -\frac{1}{1} \frac{d[\text{O}_2]}{dt} = +\frac{1}{2} \frac{d[\text{SO}_3]}{dt} \]

### Step 2: Given Rate of Disappearance of SO₂

We are given that the rate of disappearance of SO₂ is:

\[ -\frac{d[\text{SO}_2]}{dt} = 2.4 \times 10^{-4} \text{ mol L}^{-1} \text{ min}^{-1} \]

### Step 3: Calculate the Rate of Reaction

From the rate equation, we can express the rate of reaction:

\[ \text{Rate} = -\frac{1}{2} \frac{d[\text{SO}_2]}{dt} \]

Substituting the value of the rate of disappearance of SO₂:

\[ \text{Rate} = -\frac{1}{2} \times (-2.4 \times 10^{-4}) = 1.2 \times 10^{-4} \text{ mol L}^{-1} \text{ min}^{-1} \]

### Step 4: Calculate the Rate of Appearance of SO₃

Using the rate expression for SO₃:

\[ \text{Rate} = +\frac{1}{2} \frac{d[\text{SO}_3]}{dt} \]

We can find the rate of appearance of SO₃:

\[ \frac{d[\text{SO}_3]}{dt} = 2 \times \text{Rate} = 2 \times (1.2 \times 10^{-4}) = 2.4 \times 10^{-4} \text{ mol L}^{-1} \text{ min}^{-1} \]

### Step 5: Calculate the Rate of Disappearance of O₂

From the rate expression for O₂:

\[ \text{Rate} = -\frac{1}{1} \frac{d[\text{O}_2]}{dt} \]

Thus, the rate of disappearance of O₂ is:

\[ \frac{d[\text{O}_2]}{dt} = -\text{Rate} = -1.2 \times 10^{-4} \text{ mol L}^{-1} \text{ min}^{-1} \]

### Summary of Results

1. Rate of reaction: \( 1.2 \times 10^{-4} \text{ mol L}^{-1} \text{ min}^{-1} \) (Correct)
2. Rate of appearance of SO₃: \( 2.4 \times 10^{-4} \text{ mol L}^{-1} \text{ min}^{-1} \) (Correct)
3. Rate of disappearance of O₂: \( 1.2 \times 10^{-4} \text{ mol L}^{-1} \text{ min}^{-1} \) (Correct)

### Final Conclusion

The correct statements are A, B, and C. The statement regarding the rate of reaction being twice the rate of disappearance of SO₃ is incorrect, as SO₃ is a product and is being formed, not disappearing.

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