The reaction $$2A + B_2 \to 2AB$$ is an elementary reaction. For a certain quantity of reactants, if the volume of the reaction vessel is reduced by a factor of 3, the rate of the reaction increases by a factor of ________. (Round off to the Nearest Integer).

The reaction $$2A + B_2 \to 2AB$$ is given to be an elementary reaction. For an elementary reaction, the rate law can be written directly from the stoichiometry. The rate is:

$$\text{Rate} = k[A]^2[B_2]$$

When the volume of the reaction vessel is reduced by a factor of 3 (i.e., the new volume is $$V/3$$), the concentrations of all species increase by a factor of 3 (since concentration = moles/volume, and the moles remain unchanged).

The new concentrations are $$[A]' = 3[A]$$ and $$[B_2]' = 3[B_2]$$. The new rate becomes:

$$\text{Rate}' = k(3[A])^2(3[B_2]) = k \times 9[A]^2 \times 3[B_2] = 27 \times k[A]^2[B_2] = 27 \times \text{Rate}$$

Therefore, the rate of the reaction increases by a factor of 27.

The answer is 27.