To determine the ratio between the new rate and the original rate of the reaction given the changes in concentrations of X and Y , we need to start by writing the rate law for the reaction:
Rate =k[X]m[Y]nwhere:
k is the rate constant
[X] is the concentration of X
[Y] is the concentration of Y
m is the order of the reaction with respect to X
n is the order of the reaction with respect to Y
Let the initial concentrations of X and Y be
[X] and
[Y] respectively. The initial rate of reaction is:
Initial Rate
=k[X]m[Y]nNow, the concentration of X is tripled and the concentration of Y is decreased to one-third, so the new concentrations are
3[X] and
[Y] respectively.
The new rate of the reaction is:
New Rate
=k(3[X])m([Y])nSimplifying this expression:
New Rate
=k⋅3m([X])m⋅()n([Y])nNew Rate
=k⋅3m⋅[X]m⋅⋅[Y]nNew Rate
=k⋅[X]m⋅[Y]n⋅New Rate
= Initial Rate
⋅New Rate
= Initial Rate
⋅3(m−n) Thus, the ratio between the new rate and the original rate of the reaction is:
| New Rate |
| Initial Rate |
=3(m−n)So, the correct answer is:
Option A:
3(m−n)