JEE Main 2026 — Jan 22, Shift 2 — Chemistry solution

JEE Main2026Jan 22, Shift 2Chemistry

Consider $A k_{1} B$ and $C k_{2} D$ are two reactions. If the rate constant ( $k_{1}$ ) of the $A \to B$ reaction can be expressed by the following equation $lo g_{10} k = 14.34 - \frac{1.5 \times 1 0 ^{4}}{T / K}$ and activation energy of $C \to D$ reaction ( $E_{a_{2}}$ ) is $\frac{1}{5}$ th of the $A \to B$ reaction ( $E_{a_{1}}$ ), then the value of $E_{a_{2}}$ is ______ kJ mol $^{- 1}$ . (Nearest Integer)

Your answer

Solution

Comparing the given expression to the Arrhenius form $lo g_{10} k = lo g_{10} A - \frac{E _{a}}{2.303 R T}$ :

$\frac{E _{a_{1}}}{2.303 \times R} = 1.5 \times 1 0^{4} \Rightarrow E_{a_{1}} = 1.5 \times 1 0^{4} \times 2.303 \times 8.314 J mol^{- 1}$

$E_{a_{1}} \approx 2.872 \times 1 0^{5}$ J mol $^{- 1}$ $\approx 287.2$ kJ mol $^{- 1}$ .

$E_{a_{2}} = \frac{E _{a_{1}}}{5} \approx \frac{287.2}{5} \approx 57.4$ kJ mol $^{- 1}$ $\approx 57$ .

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