1. The problem is to explain why there is a factor of 2 in front of the term $k_c[OF]^2$ in equation (1) and why the rate term for $k_a$ is $k_a[F_2O]^2$ without an extra factor. 2. The factor 2 in front of $k_c[OF]^2$ appears because the reaction involves two identical reactive events contributing to the rate. This factor accounts for the number of ways two $OF$ molecules can react together, reflecting the stoichiometry and symmetry of the reaction. 3. For the reaction with rate constant $k_a$, the reaction consumes two $F_2O$ molecules to produce $OF$. The rate term is $k_a[F_2O]^2$ because the rate depends on the concentration of $F_2O$ squared, reflecting the stoichiometric consumption of two $F_2O$ molecules. 4. There is no extra factor in front of $k_a[F_2O]^2$ because the rate expression already incorporates the stoichiometry of the reaction. The squared concentration term naturally accounts for the involvement of two $F_2O$ molecules. 5. In summary, the factor 2 in front of $k_c[OF]^2$ is a combinatorial factor due to identical reactants, while the $k_a[F_2O]^2$ term inherently includes the stoichiometry without an additional factor. Final answer: The factor 2 in $k_c[OF]^2$ accounts for the number of identical reactant pairs, while $k_a[F_2O]^2$ includes stoichiometry in the concentration term without an extra factor.