JEE Advanced · 2025 · 18 May 2025 · Paper 2 · Chemical Kinetics

Consider a reaction

A + R \to

Product. The rate of this reaction is measured to be

k [A] [R]

. At the start of the reaction, the concentration of

R, [R]_{0}

, is 10-times the concentration of

A, [A]_{0}

. The reaction can be considered to be a pseudo first order reaction with assumption that

k [R] = k^{'}

is constant. Due to this assumption, the relative error (in %) in the rate when this reaction is 40% complete, is ____.

[

k

and

k^{'}

represent corresponding rate constants]

Answer: 4.17

Solution

Actual reaction (second order):

At t = 0: [A] = A₀, [R] = 10A₀

When 40% complete: [A] = 0.6A₀, [R] = 10A₀ - 0.4A₀ = 9.6A₀

Actual rate₁ = k × (0.6A₀) × (9.6A₀) = 5.76kA₀²

Pseudo first-order assumption:

Assuming [R] remains constant at 10A₀:

Rate₂ = k′[A] = k(10A₀) × (0.6A₀) = 6kA₀²

Relative error:

Relative error = \frac{Rate _{2} - Rate _{1}}{Rate _{1}} \times 100

= \frac{6 k A _{0}^{2} - 5.76 k A _{0}^{2}}{5.76 k A _{0}^{2}} \times 100 = \frac{0.24}{5.76} \times 100 = 4.166... \approx 4.17%

JEE Advanced · 2025 · 18 May 2025 · Paper 2 · Numerical answer

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JEE Advanced · 2025 · 18 May 2025 · Paper 2 · Chemical Kinetics

Solution

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