For the reaction, 2HI(g) → H2 (g) + I2 (g), the rate of reaction can be represented as:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( -\frac{\Delta[HI]}{\Delta t}=2\frac{\Delta[H_2]}{\Delta t}=2\frac{\Delta[I_2]}{\Delta t} \)
When the coefficients in a balanced equation are not all equal, the reactants and products change concentration at different speeds. To get one rate for the whole reaction, each rate of change is divided by the coefficient of that species, and reactants take a minus sign (their concentration falls). For a general reaction:
\( \displaystyle a\mathrm{A}+b\mathrm{B}\rightarrow c\mathrm{C}+d\mathrm{D} \)
\( \displaystyle \text{Rate}=-\frac{1}{a}\frac{\Delta[\mathrm{A}]}{\Delta t}=-\frac{1}{b}\frac{\Delta[\mathrm{B}]}{\Delta t}=+\frac{1}{c}\frac{\Delta[\mathrm{C}]}{\Delta t}=+\frac{1}{d}\frac{\Delta[\mathrm{D}]}{\Delta t} \)
For 2HI(g) → H2(g) + I2(g), the coefficients are 2 for HI and 1 each for \( \ce{H2} \) and \( \ce{I2} \):
\( \displaystyle \text{Rate}=-\frac{1}{2}\frac{\Delta[HI]}{\Delta t}=\frac{\Delta[H_2]}{\Delta t}=\frac{\Delta[I_2]}{\Delta t} \)
Multiplying every term by 2:
\( \displaystyle -\frac{\Delta[HI]}{\Delta t}=2\frac{\Delta[H_2]}{\Delta t}=2\frac{\Delta[I_2]}{\Delta t} \)
This says that HI is used up twice as fast as \( \ce{H2} \) or \( \ce{I2} \) is formed, which is what the equation shows. So the correct expression is Option (4).
Why the other options are incorrect
Option (1) \( \frac{\Delta[HI]}{\Delta t}=\frac{\Delta[H_2]}{\Delta t}=\frac{\Delta[I_2]}{\Delta t} \) — Incorrect. It has no minus sign for the reactant, which would make the rate negative, and it ignores the coefficient 2 of HI.
Option (2) \( -\frac{\Delta[HI]}{\Delta t}=\frac{1}{2}\frac{\Delta[H_2]}{\Delta t}=\frac{\Delta[I_2]}{\Delta t} \) — Incorrect. The factor 1/2 is on the wrong side. It would mean \( \ce{H2} \) forms twice as fast as HI disappears.
Option (3) \( -\frac{\Delta[HI]}{\Delta t}=2\frac{\Delta[H_2]}{\Delta t}=\frac{\Delta[I_2]}{\Delta t} \) — Incorrect. \( \ce{H2} \) and \( \ce{I2} \) are formed in equal amounts, so they must carry the same factor; here only \( \ce{H2} \) has the factor 2.
NCERT (2026-27 edition):
Rate of a Chemical Reaction – …
Note: The same/similar question has been asked in different years by NTA as per the details given below:
| 2026 | 2025 | 2024 | 2023 | 2022 |
|---|---|---|---|---|
| 26-05 S1 24-05 S2 | – | – | – | – |