COMEDK 2024 Shift 2 Paper

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]n
where:
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]n
Now, the concentration of X is tripled and the concentration of Y is decreased to one-third, so the new concentrations are 3[X] and ‌

1

3

[Y] respectively.
The new rate of the reaction is:
New Rate =k(3[X])m(‌

1

3

[Y])n
Simplifying this expression:
New Rate =k⋅3m([X])m⋅(‌

1

3

)n([Y])n
New Rate =k⋅3m⋅[X]m⋅‌

1

3n

⋅[Y]n
New Rate =k⋅[X]m⋅[Y]n⋅‌

3m

3n

New Rate = Initial Rate ⋅‌

3‌m ‌

3‌n ‌

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)