Question 78: For a certain reaction, the rate =\mathrm{k}[\mathrm{A}]^{2}[\mathrm{~B}], when the initial concentration of A is tripled keeping concentration of B constant, the initial rate would
(1) increase by a factor of nine.
(2) increase by a factor of three.
(3) decrease by a factor of nine.
(4) increase by a factor of six.
Answer: Option (1)
Explanation:
The given rate law is \text{Rate} = k[\mathrm{A}]^{2}[\mathrm{B}].
The rate of the reaction is directly proportional to the square of the concentration of A
and directly proportional to the concentration of B.
If the initial concentration of A is tripled, then [\mathrm{A}] \rightarrow 3[\mathrm{A}]
while [\mathrm{B}] remains constant.
Substituting into the rate law, the new rate becomes
\text{Rate}' = k(3[\mathrm{A}])^{2}[\mathrm{B}].
This simplifies to \text{Rate}' = 9k[\mathrm{A}]^{2}[\mathrm{B}].
Thus, the rate increases by a factor of 9.
Therefore, the correct answer is option (1).