Question

The rate of the reaction, \[\ce{A + B + C -> Products}\], is given by \[\ce{- \frac{d[A]}{dt} = k [A]^{1/2} [B]^{1/3} [C]^{1/4}}\].

The order of reaction is ______.

Options

• `1/2`

• `13/12`

• 1

• 2

Answer 1

The rate of the reaction, \[\ce{A + B + C -> Products}\], is given by \[\ce{- \frac{d[A]}{dt} = k [A]^{1/2} [B]^{1/3} [C]^{1/4}}\].

The order of reaction is `bbunderline(13/12)`.

Explanation:

The order of a reaction is obtained by adding the exponents of the concentration terms in the rate law. Here, the rate law is given as \[\ce{- \frac{d[A]}{dt} = k [A]^{1/2} [B]^{1/3} [C]^{1/4}}\]

∴ Order = `1/2 + 1/3 + 1/4`

Take LCM (12):

`1/2 = (1 xx 6)/(2 xx 6) = 6/12`    ...(i)

`1/3 = (1 xx 4)/(3 xx 4) = 4/12`    ...(ii)

`1/4 = (1 xx 3)/(4 xx 3) = 3/12`    ...(iii)

∴ Order = `6/12 + 4/12 + 3/12`    ...[From (i), (ii) and (iii)]

∴ Order = `13/12`