The rate constant for the reaction in gaseous phase
`O+O_(3) rarr 2O_(2)` is `8.0xx10^(-15)" cm"^(3)" molecule"^(-1) s^(-1)` at 298 K. Corresponding value in `dm^(3)" mol"^(-1) s^(-1)` is :

Options

A. `4.8xx10^(6)" dm"^(3)" mol"^(-1)s^(-1)`
B. `1.33xx10^(-6)" dm"^(3)" mol"^(-1) s^(-1)`
C. `4.8xx10^(8)" dm"^(3)" mol"^(-1) s^(-1)`
D. `1.33xx10^(6)" dm"^(3)" mol"^(-1) s^(-1)`

Explanation

To convert the rate constant from \( \text{cm}^3 \text{molecule}^{-1} \text{s}^{-1} \) to \( \text{dm}^3 \text{mol}^{-1} \text{s}^{-1} \), we will follow these steps:

### Step 1: Understand the conversion factors
1. **Volume Conversion**:
- \( 1 \text{ dm} = 10 \text{ cm} \)
- Therefore, \( 1 \text{ dm}^3 = (10 \text{ cm})^3 = 1000 \text{ cm}^3 \)
- This means \( 1 \text{ cm}^3 = 0.001 \text{ dm}^3 \) or \( 1 \text{ cm}^3 = 10^{-3} \text{ dm}^3 \).

2. **Molecule to Mole Conversion**:
- We know that \( 1 \text{ mole} = 6.02 \times 10^{23} \text{ molecules} \).
- Therefore, \( 1 \text{ molecule} = \frac{1}{6.02 \times 10^{23}} \text{ moles} \).

### Step 2: Write the given rate constant
The given rate constant is:
\[ k = 8.0 \times 10^{-15} \text{ cm}^3 \text{ molecule}^{-1} \text{s}^{-1} \]

### Step 3: Convert the volume from cm³ to dm³
Using the conversion factor:
\[ k = 8.0 \times 10^{-15} \text{ cm}^3 \text{ molecule}^{-1} \text{s}^{-1} \times \left(10^{-3} \text{ dm}^3/\text{cm}^3\right) \]
\[ k = 8.0 \times 10^{-15} \times 10^{-3} \text{ dm}^3 \text{ molecule}^{-1} \text{s}^{-1} \]
\[ k = 8.0 \times 10^{-18} \text{ dm}^3 \text{ molecule}^{-1} \text{s}^{-1} \]

### Step 4: Convert molecules to moles
Now, we convert from molecules to moles:
\[ k = 8.0 \times 10^{-18} \text{ dm}^3 \text{ molecule}^{-1} \text{s}^{-1} \times \left(6.02 \times 10^{23} \text{ molecules/mole}\right) \]
\[ k = 8.0 \times 10^{-18} \times 6.02 \times 10^{23} \text{ dm}^3 \text{ mol}^{-1} \text{s}^{-1} \]

### Step 5: Calculate the final value
Calculating the above expression:
\[ k = 8.0 \times 6.02 \times 10^{5} \text{ dm}^3 \text{ mol}^{-1} \text{s}^{-1} \]
\[ k = 48.16 \times 10^{5} \text{ dm}^3 \text{ mol}^{-1} \text{s}^{-1} \]
\[ k \approx 4.8 \times 10^{6} \text{ dm}^3 \text{ mol}^{-1} \text{s}^{-1} \]

### Final Answer
Thus, the corresponding value of the rate constant in \( \text{dm}^3 \text{mol}^{-1} \text{s}^{-1} \) is:
\[ \boxed{4.8 \times 10^{6} \text{ dm}^3 \text{ mol}^{-1} \text{s}^{-1}} \]