For the reaction : `2A +B rarr C +D`, measurement of the rate of the reaction at varying concentrations are given below
`{:("Trial No.","[A]","[B]","rate"("m mole L"^(-1)"s"^(-1))),(1,0.010,0.010,2.5),(2,0.010,0.020,5.0),(3,0.030,0.020,45.0):}`
The rate law is therefore

Options

A. rate`= k[A]^(2)[B]`
B. rate `=k[A][B]^(2)`
C. rate `= k[A][B]`
D. rate `=k[A]^(2)[B]^(2)`

Answer

A

Explanation

Let rate, `r = k[A]^(m)[B]^(n)`
`2.5 = k[0.01]^(m) [0.01]^(n)` …..(i)
`5.0 = k[0.01]^(m) [0.02]^(n)`….(ii)
From (i) and (ii)
`:. n=1`
`45 =k[0.03]^(m)[0.02]^(n)` ….(iii)
From (ii) and (iii) `m=2`
`:.` Rate `= k[A]^(2)[B]`.