For the reaction R → P, the rate of disappearance of R is written as \( -\frac{\Delta[\text{R}]}{\Delta t} \). Why is a minus sign used in this expression?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Δ[R] is a negative quantity, and multiplying it by −1 makes the rate a positive quantity.
As the reaction goes on, the concentration of the reactant falls, so [R]2 at the later time t2 is smaller than [R]1 at t1. Hence Δ[R] = [R]2 − [R]1 is negative.
The rate of a reaction is always given as a positive quantity, so Δ[R] is multiplied by −1.
For a product, Δ[P] is already positive, and the rate of appearance of P is written with a plus sign.
Why the other options are incorrect
Option (1) The rate of a reaction decreases with the passage of time as the reactant is used up. — Incorrect. The rate does usually fall with time, but that is not why the sign is used; the sign comes from Δ[R] being negative.
Option (2) The rate of a reaction is a negative quantity when it is expressed in terms of a reactant. — Incorrect. The minus sign is used so that the rate in terms of a reactant comes out positive, the same as the rate in terms of a product.
Option (4) Δt is a negative quantity, and multiplying it by −1 makes the time interval positive. — Incorrect. Δt = t2 − t1 is positive, because t2 is the later time; the negative quantity is Δ[R].
NCERT (2026-27 edition):
3.1 Rate of a Chemical Reaction – “Since, Δ[R] is a negative quantity (as concentration of reactants is decreasing), it is multiplied with –1 to make the rate of the reaction a positive quantity.”