Question

The reaction $2\mathrm{A}+{\mathrm{B}}_2\to 2\mathrm{AB}$ 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 $.......$

Answer 1

An explanation for the answer:

For an elementary reaction:

Rate of reaction $=\mathrm{K}{\left[\mathrm{A}\right]}^2\left[{\mathrm{B}}_2\right]$

Initial Reaction $=\mathrm{K}{\left(\frac{{\mathrm{n}}_{\mathrm{A}}}{{\mathrm{v}}_{\mathrm{o}}}\right)}^2\left(\frac{{\mathrm{n}}_{\mathrm{B}}}{{\mathrm{v}}_{\mathrm{o}}}\right)$

$\begin{array}{rcl}\mathrm{Final}\mathrm{rate}& =& \mathrm{K}{\left(\frac{{\mathrm{n}}_{\mathrm{A}}}{\raisebox{1ex}{${\mathrm{v}}_{\mathrm{o}}$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}\right)}^2\left(\frac{{\mathrm{n}}_{\mathrm{B}}}{\raisebox{1ex}{${\mathrm{v}}_{\mathrm{o}}$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}\right)\\ & =& 27\mathrm{K}\left(\frac{{\mathrm{n}}_{\mathrm{A}}}{{\mathrm{v}}_{\mathrm{o}}}\right)\left(\frac{{\mathrm{n}}_{\mathrm{B}}}{{\mathrm{v}}_{\mathrm{o}}}\right)\\ \mathrm{Final}\mathrm{Rate}& =& 27\times \mathrm{Inital}\mathrm{Rate}\end{array}$

Final Answer: Therefore, the correct answer for the blank is $27$.