For the reaction `:`
`2A+B rarr A_(2)B`
the rate `=k[A][B]^(2)` with `k=2.0xx10^(-6)mol^(-2)L^(2)s^(-1)`. Calculate the initial rate of the reaction when `[A]=0.1 mol L^(-),[B]=0.2 mol L^(-1)`. Calculate the rate of reaction after `[A]` is reduced to `0.06 mol L^(-1)`.

Explanation

To solve the problem, we need to calculate the initial rate of the reaction and then the rate after the concentration of A is reduced.

### Step 1: Write the rate law expression
The rate law for the reaction \(2A + B \rightarrow A_2B\) is given as:
\[ \text{Rate} = k[A][B]^2 \]
where \(k = 2.0 \times 10^{-6} \, \text{mol}^{-2} \, \text{L}^2 \, \text{s}^{-1}\).
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