Rate of a reaction `A + B rarr` Product, is given as a function of different initial concentration of `A` and `B`.
`|{:([A] (mol L^(-1)),(B) (mol L^(-1)),"Initial rate" (mol L^(-1) min^(-1)),),(0.01,0.01,0.005,),(0.02,0.01,0.010,),(0.01,0.02,0.005,):}|`
Determine the order of the reaction with respect to `A` and with respect to `B`. What is the half life of `A` in the reaction ?

Explanation

To determine the order of the reaction with respect to A and B, and to find the half-life of A, we can follow these steps:

### Step 1: Write the Rate Law
The rate law for the reaction can be expressed as:
\[ \text{Rate} = k[A]^x[B]^y \]
where \( x \) is the order with respect to A and \( y \) is the order with respect to B.

### Step 2: Set Up the Experiments
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