The figure shows the distribution of kinetic energy among the molecules of a reacting gas at a temperature t and at (t + 10), with the energy of activation marked on it.
The gas is now heated further, to (t + 20). For this reaction, the rate constant nearly doubles for every 10° rise in temperature. Which of the following describes the curve at (t + 20) compared with the curve at t?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → The maximum of the curve is lower than at t, and the fraction of molecules having energy equal to or greater than the activation energy is about four times that at t.
The curves plot the fraction of molecules against their kinetic energy. Only the molecules lying to the right of the Ea line can react, and the Ea line stays where it is when the gas is heated.
Height of the maximum — Lower than at t. In the figure, going from t to (t + 10), the peak becomes lower and moves to a higher kinetic energy, and the curve spreads to the right. The total area under the curve stays the same, so a curve that spreads out must become flatter. At (t + 20) the same change goes one step further: the maximum is lower still and lies at a still higher energy.
Fraction beyond Ea — About four times that at t. In the Arrhenius equation the factor e−Ea/RT is the fraction of molecules with energy greater than Ea, so this fraction rises in step with the rate constant. The figure shows it for one 10° rise: the shaded area at t plus the area of additional molecules at (t + 10) makes the fraction double. Each further 10° rise doubles it again:
t → (t + 10): 1 × 2 = 2 times
(t + 10) → (t + 20): 2 × 2 = 4 times the fraction at t
Why the other options are incorrect
Option (1) The maximum of the curve is taller than at t, and the fraction of molecules having energy equal to or greater than the activation energy is about three times that at t. — Incorrect. Both parts are wrong:
A taller peak would need a larger total area or a narrower curve, which is the opposite of what the figure shows.
Adding the same extra area once more gives 3 times; the change is a doubling of whatever fraction is present, not a fixed addition.
Option (2) The maximum of the curve is lower than at t, and the fraction of molecules having energy equal to or greater than the activation energy is about three times that at t. — Incorrect. The maximum is lower, but adding the same extra area once more gives 3 times; the change is a doubling of whatever fraction is present, not a fixed addition.
Option (4) The maximum of the curve is taller than at t, and the fraction of molecules having energy equal to or greater than the activation energy is about four times that at t. — Incorrect. The fraction is about four times, but a taller peak would need a larger total area or a narrower curve, which is the opposite of what the figure shows.
NCERT (2026-27 edition):
3.4 Temperature Dependence of the Rate of a Reaction – “It has been found that for a chemical reaction with rise in temperature by 10°, the rate constant is nearly doubled.”
“When the temperature is raised, the maximum of the curve moves to the higher energy value (Fig. 3.9) and the curve broadens out, i.e., spreads to the right such that there is a greater proportion of molecules with much higher energies. The area under the curve must be constant since total probability must be one at all times.”
“It is clear from the diagram that in the curve at (t + 10), the area showing the fraction of molecules having energy equal to or greater than activation energy gets doubled leading to doubling the rate of a reaction.”
“In the Arrhenius equation (3.18) the factor e–Ea/RT corresponds to the fraction of molecules that have kinetic energy greater than Ea.”
Fig. 3.9: Distribution curve showing temperature dependence of rate of a reaction