Step-by-step explanation:
To determine the new initial rate, we need to consider the effect of changing the concentrations of reactants on the rate of the reaction.
According to the given rate law, the rate of the reaction is directly proportional to the concentrations of reactants A and B raised to their respective powers.
If [A] is halved, it means that the concentration of A is reduced by a factor of 1/2.
If [B] is tripled, it means that the concentration of B is increased by a factor of 3.
Let's assume the initial rate is denoted as R.
New initial rate = k * [A'] * [B']^2
Where [A'] represents the new concentration of A and [B'] represents the new concentration of B.
Since [A'] = 1/2 * [A] and [B'] = 3 * [B], we can substitute these values into the equation:
New initial rate = k * (1/2 * [A]) * (3 * [B])^2
= k * (1/2 * [A]) * 9 * [B]^2
= 9/2 * k * [A] * [B]^2
Since the initial rate is given as 0.0220 M/s, we can substitute this value into the equation:
0.0220 M/s = 9/2 * k * [A] * [B]^2
Now, we can solve for the new initial rate:
New initial rate = (0.0220 M/s) / [(9/2 * [A] * [B]^2)]
= (0.0220 M/s) / [(9/2 * 1/2 * [A] * 3^2 * [B]^2)]
= (0.0220 M/s) / [(9/2 * 1/2 * [A] * 9 * [B]^2)]
= (0.0220 M/s) / [(9/4 * [A] * [B]^2)]
= (0.0220 M/s) * (4/9) * (1/([A] * [B]^2))
Therefore, the new initial rate will be (0.0220 M/s) * (4/9) * (1/([A] * [B]^2)) M/s.