An elementary gas-phase reaction 2 A (g) + B (g) C (g) is carried out in a closed vessel. If the volume of the reaction vessel is suddenly reduced to one-third of its original volume at constant temperature, the rate of the reaction will

Step-by-step solution

For an elementary reaction, the rate law is written directly from the stoichiometry of the balanced equation. The rate law for the given reaction is: Rate = k[ A ]^2[ B ] When the volume of the closed vessel is reduced to 1 3 of its original volume, the concentration (moles/volume) of each gaseous reactant increases by a factor of 3. Let the new concentrations be [ A ]' = 3[ A ] and [ B ]' = 3[ B ] . The new rate of reaction is: Rate ' = k(3[ A ])^2(3[ B ]) Rate ' = k 9[ A ]^2 3[ B ] Rate ' = 27 k[ A ]^2[ B ] = 27