JEE Main 2025 Apr 3 Shift 1, Chemistry Q5: Reactions of Various Orders

JEE Main2025Apr 3, Shift 1Chemistry

In a reaction $A + B \to C$ , initial concentrations of A and B are related as $[A]_{0} = 8 [B]_{0}$ . The half lives of A and B are 10 min and 40 min. respectively. If they start to disappear at the same time, both following first order kinetics, after how much time will the concentration of both the reactants be same?

A
60 min
B
80 min
C
20 min
D
40 min

Solution

For first order kinetics, $[A]_{t} = [A]_{0} e^{- k_{A} t}$ and $[B]_{t} = [B]_{0} e^{- k_{B} t}$ with $k = \frac{ln 2}{t _{1/2}}$ .

So $k_{A} = \frac{ln 2}{10}$ per min and $k_{B} = \frac{ln 2}{40}$ per min, giving $k_{A} > k_{B}$ (A decays faster).

Setting $[A]_{t} = [B]_{t}$ with $[A]_{0} = 8 [B]_{0}$ :

$8 [B]_{0} e^{- k_{A} t} = [B]_{0} e^{- k_{B} t} \Rightarrow 8 = e^{(k_{A} - k_{B}) t}$

$\Rightarrow ln 8 = (k_{A} - k_{B}) t \Rightarrow 3 ln 2 = ln 2 (\frac{1}{10} - \frac{1}{40}) t$

$\Rightarrow 3 = \frac{3}{40} t \Rightarrow t = 40 min .$

Concept behind this question

Reactions of Various OrdersNotes, formulas and examples →

Practice more Chemistry

Concept-wise practice with instant solutions on Fundamenthol.

Start practicing →

JEE Main 2025 Apr 3 Shift 1, Chemistry Q5: Reactions of Various Orders

Concept behind this question

More previous year questions on Reactions of Various Orders

Practice more Chemistry