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A kinetics question gives you a table of concentrations and times and asks for "the rate". Which rate, over which interval, and measured by which substance? Those three choices decide the answer, and mixing them up is where marks go. This post works through average rate, instantaneous rate and rates for different species, using NCERT's own data, with every number checked.
Where is this in the syllabus?
The NCERT Class 12 chapter on Chemical Kinetics (reprint 2026-27) opens with the rate of a chemical reaction, and lists among its aims to "define the average and instantaneous rate of a reaction". "Rate of a chemical reaction" is the first item in the chemical kinetics unit of the JEE (Main) 2026 syllabus and of the NEET (UG) 2026 syllabus. Check the documents for your own exam year.
What is the average rate of a reaction?
For a reaction R → P, NCERT defines the average rate as a change in concentration divided by the time taken:
Rate of disappearance of R = −Δ[R]/Δt
Rate of appearance of P = +Δ[P]/Δt
The minus sign is there because Δ[R] is negative while R is used up, and a rate is reported as a positive number. Units are concentration per time, usually mol L⁻¹ s⁻¹.
Worked example: average rates from a table
NCERT's Example 3.1 gives these concentrations of butyl chloride, C4H9Cl, during its hydrolysis (in mol L⁻¹):
t = 0 s: 0.100
t = 50 s: 0.0905
t = 100 s: 0.0820
t = 200 s: 0.0671
t = 300 s: 0.0549
t = 400 s: 0.0439
From 0 to 50 s: (0.100 − 0.0905)/50 = 0.0095/50 = 1.90 × 10⁻⁴ mol L⁻¹ s⁻¹.
From 0 to 200 s: (0.100 − 0.0671)/200 = 0.0329/200 = 1.645 × 10⁻⁴, about 1.65 × 10⁻⁴ mol L⁻¹ s⁻¹.
From 200 to 300 s: (0.0671 − 0.0549)/100 = 0.0122/100 = 1.22 × 10⁻⁴ mol L⁻¹ s⁻¹.
The rate falls as the reactant is used up. That is why "the rate" without an interval is not a complete answer: the 0 to 200 s figure is an average over a period in which the true rate kept dropping.
How do you find the instantaneous rate?
The instantaneous rate is the average rate over a vanishingly small interval: r = −d[R]/dt = d[P]/dt. NCERT finds it by drawing a tangent to the concentration-time curve and taking its slope. For the butyl chloride data it reports 1.22 × 10⁻⁴ mol L⁻¹ s⁻¹ at 250 s and 1.0 × 10⁻⁴ at 350 s.
With a table but no graph, a fair estimate is the average rate over a short interval centred on the time you want. The 200 to 300 s interval is centred on 250 s and gave 1.22 × 10⁻⁴, matching NCERT's tangent value. The 300 to 400 s interval, centred on 350 s, gives (0.0549 − 0.0439)/100 = 1.10 × 10⁻⁴, a little above the tangent value. The estimate is close but not exact, because the curve bends within the interval. Narrower intervals give better estimates.
This is the same idea as velocity from a position-time graph; our post on the calculus used in JEE physics makes that link.
How does stoichiometry change the rate?
When the coefficients are not all 1, species change at different speeds. NCERT divides each rate of change by its coefficient so the reaction has a single rate. For 2HI → H2 + I2, rate = −½ Δ[HI]/Δt = Δ[H2]/Δt = Δ[I2]/Δt.
Worked example (sample numbers). For N2 + 3H2 → 2NH3, suppose [H2] falls from 0.90 to 0.60 mol L⁻¹ in 15 min.
Rate of disappearance of H2 = 0.30/15 = 0.020 mol L⁻¹ min⁻¹.
Rate of reaction = 0.020/3 = 6.7 × 10⁻³ mol L⁻¹ min⁻¹.
Rate of disappearance of N2 = 1 × 6.7 × 10⁻³ = 6.7 × 10⁻³ mol L⁻¹ min⁻¹.
Rate of formation of NH3 = 2 × 6.7 × 10⁻³ = 1.3 × 10⁻² mol L⁻¹ min⁻¹.
In seconds, the rate of reaction is 6.7 × 10⁻³/60 = 1.1 × 10⁻⁴ mol L⁻¹ s⁻¹.
Check: the rates for H2, N2 and NH3 (0.020, 0.0067 and 0.013) are in the ratio 3 : 1 : 2, the same as the coefficients.
Which mistakes cost marks?
Dropping the minus sign for a reactant and reporting a negative rate.
Forgetting to divide by the coefficient when the question asks for the rate of reaction rather than the rate for one species.
Dividing when you should multiply. To go from the rate of reaction to one species, multiply by its coefficient.
Using a long interval for an instantaneous rate. The average from 0 to 200 s is not the rate at 100 s.
Unit slips: divide a per-minute rate by 60 to get a per-second rate.
Reading the order from the coefficients. Coefficients fix the ratios between species, not the rate law; our post on rate laws and orders explains why.
Misconceptions in kinetics tend to last. In a study of 191 secondary school and undergraduate students in Turkey, Cakmakci (2010) found that several alternative conceptions held by school students persisted among undergraduates, and linked them to weak understanding of thermodynamics and equilibrium.
A practice routine
Table drill (twice a week): from any concentration-time table, compute three average rates over different intervals and say why they differ.
Centred estimate: estimate an instantaneous rate from the narrowest centred interval, then compare it with a tangent drawn on graph paper.
Species conversion: for three balanced equations, write the full rate expression with every fraction, then convert one given rate into all the others.
Mix it up: a week later, put these into sets with rate law problems and the method of initial rates.
If you are not sure why a tangent gives the rate, the Fermi Concept Library covers every concept in physics, chemistry, biology, mathematics and computing, so you can revisit the idea of a rate of change.
Today, use NCERT's table to estimate the rate at 150 s from the 100 to 200 s interval, and check that it fits the falling trend.
