Answer: The final rate will become 9 times of the initial rate.
Explanation: Rate law says that rate of a reaction is directly proportional to the concentration of the reactants each raised to a stoichiometric coefficient determined experimentally called as order.
[tex]Rate=k[A]^x[B]^y[/tex]
k= rate constant
x = order with respect to A
y = order with respect to B
n = x+y = Total order
[tex]2A+B\rightarrow B+3C[/tex]
Rate law :[tex]Rate=k[A]^0[B]^2[/tex], order with respect to A is 0, order with respect to B is 2 and total order is 2.
Given: doubling the concentration of A and increasing the concentration of B by a factor of three.
[tex]Rate'=[tex]k[2A]^0[3B]^2[/tex]
[tex]Rate'=k[2]^0[A]^0[3]^2[B]^2[/tex]
[tex]Rate'=k\times 1\times [A]^0\times 9\times [B]^2[/tex]
[tex]Rate'=Rate\times 9[/tex]
Thus the final rate will become 9 times of the initial rate.