Given the following rate data for F2(g) + 2ClO2(g) -> 2ClO2F(g), determine the order of reaction with respect to each reactant, the overall order of the reaction, write the rate equation for the reaction, and calculate the rate constant of the reaction.

Using Experiment 1 and Experiment 2, $[ClO_2]$ is constant at 0.15 M.
$$
\frac{Rate_1}{Rate_2} = \frac{k[F_2]_1^x[ClO_2]_1^y}{k[F_2]_2^x[ClO_2]_2^y}
$$
$$
\frac{1.8 \times 10^{-5}}{1.8 \times 10^{-5}} = \left(\frac{0.105}{0.05}\right)^x \left(\frac{0.15}{0.15}\right)^y
$$
$$
1 = (2.1)^x \cdot 1^y
$$
For this equation to be true, $x$ must be 0.  
The order with respect to $F_2$ is $\boxed{0}$.

• Order with respect to $ClO_2$ ($y$):

Using Experiment 3 and Experiment 4, $[F_2]$ is constant at 0.052 M.
$$
\frac{Rate_3}{Rate_4} = \frac{k[F_2]_3^x[ClO_2]_3^y}{k[F_2]_4^x[ClO_2]_4^y}
$$
$$
\frac{7.1 \times 10^{-5}}{8.9 \times 10^{-6}} = \left(\frac{0.052}{0.052}\right)^x \left(\frac{0.30}{0.15}\right)^y
$$
$$
7.9775 \approx (1)^x (2)^y
$$
$$
7.9775 \approx 2^y
$$
Since $2^3 = 8$, $y$ is approximately 3.  
The order with respect to $ClO_2$ is $\boxed{3}$.

2. Determine the overall order of reaction.

3. Write the rate equation for the reaction.

Since $[F_2]^0 = 1$:

4. Calculate the rate constant of the reaction.

Note: There is an inconsistency in the provided data, as calculating $k$ from experiments 1 and 2 yields a different value than from experiments 3 and 4. We will use experiments 3 and 4, which were used to determine the order of $ClO_2$.

• Using Experiment 3:

  $$7.1 \times 10^{-5} \text{ M/s} = k(0.30 \text{ M})^3$$ $$7.1 \times 10^{-5} \text{ M/s} = k(0.027 \text{ M}^3)$$ $$k = \frac{7.1 \times 10^{-5} \text{ M/s}}{0.027 \text{ M}^3} = 0.0026296 \text{ M}^{-2}\text{s}^{-1}$$

• Using Experiment 4:

  $$8.9 \times 10^{-6} \text{ M/s} = k(0.15 \text{ M})^3$$ $$8.9 \times 10^{-6} \text{ M/s} = k(0.003375 \text{ M}^3)$$ $$k = \frac{8.9 \times 10^{-6} \text{ M/s}}{0.003375 \text{ M}^3} = 0.0026370 \text{ M}^{-2}\text{s}^{-1}$$

Averaging the values from experiments 3 and 4:

The rate constant is $\boxed{0.00263 \text{ M}^{-2}\text{s}^{-1}}$.