Why Can't Rate of Reaction Equal Rate of Disappearance of H2?

[subhradeep mahata]

Homework Statement

Suppose there is a chemical reaction : N₂ + 3H₂ = 2NH₃
The following things are written in my book :
rate of disappearance of H₂ = - Δ

/ Δt
rate of reaction wrt H₂ = - 1/3 * Δ

/ Δt
My question is that why can't we write rate of reaction = rate of disappearance of H2 ? In other words, can I write rate of disappearance of H2 = -1/3 * Δ

/ Δt and vice versa?

Homework Equations

The Attempt at a Solution

 

[haruspex]

why can't we write rate of reaction = rate of disappearance of H2 ?

They are defining one reaction as one occurrence of N₂+3H₂→2NH₃. Each such takes 3 instances of H₂, so the rate of loss of H₂ is three times the reaction rate.

 

[mjc123]

You cannot write "rate of disappearance of H₂ = -1/3 Δ[H₂]/Δt" because that simply isn't true. By definition, the rate of disappearance of H₂ is -Δ[H₂]/Δt.
(Strictly, that should be the rate of change of [H₂]. The rate of disappearance would be positive, and equal to minus the rate of change.)
It is the "rate of reaction" that is subject to ambiguous definition. You could define the "reaction" as:
N₂ + 3H₂ → 2NH₃ in which case rate of reaction = rate of consumption of N₂ = 1/3 rate of consumption of H₂
1/2N₂ + 3/2H₂ → NH₃ in which case rate of reaction = rate of production of NH₃ = 2/3 rate of consumption of H₂
1/3N₂ + H₂ → 2/3NH₃ in which case rate of reaction = rate of consumption of H₂ = 3* rate of consumption of N₂
That is why I don't like "rate of reaction", and always like to do kinetics in terms of the rate of change of a specified reagent. But you need to know this stuff to do exams these days.