Mechanism of the reaction is:
`A underset(k_(1))overset(k_(2))hArr B` ...(i)
`B+A overset(k_(3))hArr C` ...(ii)
`ul(bar(2A rarr C))` ...(iii)
What is (a) `(-d[A])/(dt)`, (b) `(d[B])/(dt)` , (c ) `(d[C])/(dt)`

Explanation

(a) Rate of disappearance of `[A] = (-d[A])/(dt)`
form step (1) `= k_(1)[A] - k_(2)[B]`
form step (2) `= k_(3)[B][A]`.
`:. (-d[A])/(dt) = k_(1)[A] - k_(2)[B] + k_(3)[B][A]`
(b) `(d[B])/(dt) = k_(1)[A] - k_(2)[B] - k_(3)[A][B]`
( c) `(d[C])/(dt) = k_(3)[A][B]`