JEE Advanced · Chemistry · 18. Chemical Kinetics

Consider the following reversible reaction:
$A (g) + B (g) ⇌ AB (g)$
The activation energy of the backward reaction exceeds that of the forward reaction by $2 RT$ (in ${mol}^{- 1}$ ). If the pre-exponential factor of the forward reaction is $4$ times that of the reverse reaction, the absolute value of $∆ G^{⊝} (in J {mol}^{- 1})$ for the reaction at $300 K$ is ____.
(Given; $\ln (2) = 0 .7, = 2500 J {mol}^{- 1} at 300 K$ and $G$ is the Gibbs energy)

A 8500
B 8400
C 8300
D 8200

Verified Solution

Answer & Solution

Correct Answer

(A) 8500

Step-by-step Solution

Detailed explanation

A (g) + B (g) ⇌ AB (g)

$\text E _{\text{ab}}-\text E _{\text{ef}}=2 \text{RT} \Rightarrow \Delta\text H =-2 \text{RT}$ and $\frac{\text A _{\text f }}{\text A _{\text b }}=4$

K_{eq} = (\frac{K_{f}}{K_{b}}) = \frac{A_{f} e^{- E_{af} / RT}}{A_{b} e^{- E_{ab} / RT}} = 4 (e^{2})

$\Delta\text G ^{\text o }=- \text{RT} \ln\text K =-2500 \times \ln \left(4 \times\text e ^2\right)$ $=-8500\text{ J/mol}$
$\therefore$ Absolute value of $\Delta\text G ^{\text o}-8500\text{ J/mol}$

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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The capacitor of capacitance $C$ can be charged (with the help of a resistance $R$ ) by a voltage source $V$, by closing switch $S_1$ while keeping switch $S_2$ open. The capacitor can be connected in series with an inductor $L$ by closing switch $S_2$ and opening $S_1$.

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Initially, the capacitor was uncharged. Now, switch $S_1$ is closed and $S_2$ is kept open. If time constant of this circuit is $\tau$, then

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Consider the Bohr's model of a one-electron atom where the electron moves around the nucleus. In the following List-I contains some quantities for the

n^{t h}

orbit of the atom and List-II contains options showing how they depend on

n

List - I	List - II
(I) Radius of the $n^{t h}$ orbit	$(P)$ $\propto n^{- 2}$
(II) Angular momentum of the electron in the $n^{t h}$ orbit	$(Q)$ $\propto n^{- 1}$
(III) Kinetic energy of the electron in the $n^{t h}$ orbit	$(R)$ $\propto n^{0}$
(IV) Potential energy of the electron in the $n^{t h}$ orbit	$(S)$ $\propto n^{1}$
	$(T)$ $\propto n^{2}$
	$(U)$ $\propto n^{1 / 2}$

Which of the following options has the correct combination considering List-I and List-II?

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	List – I		List – II
A	Pathway P	P.
B.	Pathway Q	Q.
C.	Pathway R	R.
D.	Pathway S	S.