Q25 / 75 · JEE Main 2026 (23 January Shift 1) · Chemistry
For the thermal decomposition of reactant $\mathrm{AB}(\mathrm{g})$, the following plot is constructed.
The half life of the reaction is ' $x^{\prime} \min$. $x=$ $\_\_\_\_$ min. (Nearest integer)
The half life of the reaction is ' $x^{\prime} \min$. $x=$ $\_\_\_\_$ min. (Nearest integer)
Correct answer: 10
Solution
From the concentration vs. time graph, the thermal decomposition of AB(g) shows a linear decrease in concentration, indicating zeroth-order kinetics.
Initial concentration: [AB]₀ = 0.6 M at t = 0 s.
Reading from the graph: [AB] = 0.5 M at t = 200 s.
Rate of decomposition: Δ[AB]/Δt = (0.6 - 0.5) M / 200 s = 0.0005 M/s.
For zeroth-order kinetics: [AB] = [AB]₀ - kt.
Half-life occurs when [AB] = [AB]₀/2 = 0.3 M.
0.3 = 0.6 - 0.0005 × t₁/₂.
t₁/₂ = 0.3 / 0.0005 = 600 s = 10 min.
Initial concentration: [AB]₀ = 0.6 M at t = 0 s.
Reading from the graph: [AB] = 0.5 M at t = 200 s.
Rate of decomposition: Δ[AB]/Δt = (0.6 - 0.5) M / 200 s = 0.0005 M/s.
For zeroth-order kinetics: [AB] = [AB]₀ - kt.
Half-life occurs when [AB] = [AB]₀/2 = 0.3 M.
0.3 = 0.6 - 0.0005 × t₁/₂.
t₁/₂ = 0.3 / 0.0005 = 600 s = 10 min.
Hence, the correct answer is 10.