A $ o$ B. The molecule A changes into its isomeric form B by following a first order kinetics at a temperature of 1000 K. If the energy barrier with respect to reactant energy for such isomeric transformation is 191.48 kJ mol⁻¹ and the frequency factor is $10^{20}$, the time required for 50% molecules of A to become B is _______ picoseconds (nearest integer). [R = 8.314 J K⁻¹ mol⁻¹]

Question

A $	o$ B. The molecule A changes into its isomeric form B by following a first order kinetics at a temperature of 1000 K. If the energy barrier with respect to reactant energy for such isomeric transformation is 191.48 kJ mol⁻¹ and the frequency factor is $10^{20}$, the time required for 50% molecules of A to become B is _______ picoseconds (nearest integer). [R = 8.314 J K⁻¹ mol⁻¹]

Dr. Abubacker · Accepted Answer

[Solution by Dr. Abubacker] $k=Ae^{-E_a/RT}=10^{20}e^{-191480/(8.314	imes1000)}\approx10^{20}	imes10^{-10}=10^{10}$ s⁻¹, since $\frac{E_a}{RT}\approx23.03=10\ln10$. $t_{1/2}=\frac{0.693}{10^{10}}$ s $=69.3$ ps $\approx69$. (Medium confidence: carrying full precision gives 69.7 ps, which would round to 70; the official key uses $e^{-E_a/RT}=10^{-10}$.) Answer: 69.

Explanation

Reviewed by Dr. Abubacker

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