JEE Advanced 2025 Paper 2 · Q12 · Integrated Rate Equations

Question

Consider a reaction $A + R 	o$ Product. The rate is measured to be $k[A][R]$. At the start of the reaction, $[R]_0 = 10 [A]_0$. The reaction can be considered pseudo first order with $k[R] = k' = $ constant. Due to this assumption, the relative error (in %) in the rate when the reaction is 40% complete is __________. ($k$ and $k'$ represent corresponding rate constants.)

SolveKar AI · Accepted Answer

True rate at fractional conversion $x = 0.40$ of A: 
  $rate_{true} = k \cdot [A] \cdot [R] = k \cdot [A]_0 (1 - x) \cdot ([R]_0 - x [A]_0)$. 
Pseudo-first-order rate (assuming $[R] = [R]_0$ throughout): 
  $rate_{pseudo} = k \cdot [A]_0 (1 - x) \cdot [R]_0$. 
Relative error = $(rate_{pseudo} - rate_{true})/rate_{true}$ 
  = $[[R]_0 - ([R]_0 - x [A]_0)] / ([R]_0 - x [A]_0)$ 
  = $x [A]_0 / ([R]_0 - x [A]_0)$. 
Substitute $[R]_0 = 10 [A]_0$, $x = 0.4$: 
  = $0.4 [A]_0 / (10 [A]_0 - 0.4 [A]_0) = 0.4 / 9.6 \approx 0.0417 = 4.17\%$. 
Reported as 4 (to 1 sf / nearest integer per the official accepted-range key).

JEE Advanced 2025 Paper 2 · Q12 · Integrated Rate Equations

Solution