For a chemical reaction,
Here,[A] is the concentration of reactant A,[B] is the concentration of reactant B,k is the rate constant of the reaction,x and y are the reaction orders which is an experimentally determined quantity.
The reaction is:
An expression for initial rate is obtained using the rate law by substituting the value of initial rate.
When the initial concentrations of the reactants are changed by any factor, then the first step is to write the new concentrations in terms of the initial concentrations.
Then, write the new rate law in terms of the initial concentrations. And then calculate the new rate law by substituting the values accordingly.