The following rate data were obtained at `303 K` for the following reaction:
`2A + B rarr C + D`

What is the rate law? What is the order with respect to each reactant and the overall order? Also calculate the rate constant and wriye its units.

Explanation

form experiment I and IV, it may be noted that `[B]` is same but `[A]` has been four times. The rate of reaction also has become four times. This means that order w.r.t. `A`,
Rate `prop [A]` …(i)
form experiment II and III, it may be noted that `[A]` is kept same and `[B]` has been doubled, the rate of reaction has become four times. This means that order w.r.t. `B`,
Rate `prop [B]^(2)` ...(ii)
Combining (i) and (ii), we get the rate law for the given reaction as:
Rate `= k[A][B]^(2)`
Thus, order w.r.t. `A = 1`, order w.r.t. `B = 2`, and overall order of the reaction `= + 2 = 3`.
The rate constant and its units can be calculated form the data of each experiment uisng the expresison
`k = ("Rate")/([A][B]^(2)) = (mol L^(-1) min^(-1))/((mol L^(-1))(mol L^(-1))^(2)) = mol^(-2) L^(2) min^(-1)`

`:.` Rate constant, `k = 6.0 mol^(-2) L^(2) min^(-1)`