JEE Advanced · Chemistry · 6. Thermodynamics (C)

Which is correct statement if $\mathrm{N}_2$ is added at equilibrium condition?

A The equilibrium will shift to forward direction because according to IInd law of thermodynamics the entropy must increases in the direction of spontaneous reaction.
B The condition for equilibrium is $G_{\mathrm{N}_2}+3 G_{\mathrm{H}_2}=2 G_{\mathrm{NH}_3}$ where $G$ is Gibbs free energy per mole of the gaseous species measured at the partial pressure. The condition of equilibrium is unaffected by the use of catalyst, which increases the rate of both the forward and backward reactions to the same extent.
C The catalyst will increase the rate of forward reaction by $\alpha$ and that of backward reaction by $\beta$.
D Catalyst will not alter the rate of either of the reaction.

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Correct Answer

(B) The condition for equilibrium is $G_{\mathrm{N}_2}+3 G_{\mathrm{H}_2}=2 G_{\mathrm{NH}_3}$ where $G$ is Gibbs free energy per mole of the gaseous species measured at the partial pressure. The condition of equilibrium is unaffected by the use of catalyst, which increases the rate of both the forward and backward reactions to the same extent.

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Detailed explanation

$K_p$ or $K_c$ remains constant for above reaction at constant temperature.
Although in presence of catalyst rate of forward and backward reaction is increased in same order (extent) due to decreasing the activation energy of both reaction. So the equilibrium is established in short time i.e., catalyst is able to increase the concentration of reactants and products in same order, so the value of $K_C$ or $K_p$ remains constant. Hence equilibrium state is not effected in presence of catalyst. Hence, at equilibrium $\Delta G=0$
$\because \Delta G=2 G \text { of } \mathrm{NH}_3-(\mathrm{G} \text { of } \mathrm{H}_2+3 \times G$ of $\mathrm{NH}_3)$
$\therefore G_{\mathrm{N}_2}+3 G_{\mathrm{H}_2}=2 G_{\mathrm{NH}_3}$

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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From JEE Advanced

Let

f (x) = \sin (π \cos x)

and

g (x) = \cos (2 π \sin x)

be two functions defined for

x > 0 .

Define the following sets whose elements are written in the increasing order:

X = \{x : f (x) = 0\}, Y = \{x : f^{'} (x) = 0\}

Z = \{x : g (x) = 0\}, W = \{x : g^{'} (x) = 0\}

List-

I

contains the sets

X, Y, Z

and

W .

List-

I I

contains some information regarding these sets.

	List- I		List- II
$(I)$	$X$	$(P)$	$\supseteq \{\frac{π}{2}, \frac{3 π}{2}, 4 π, 7 π\}$
$(I I)$	$Y$	$(Q)$	an arithmetic progression
$(I I I)$	$Z$	$(R)$	NOT an arithmetic progression
$(I V)$	$W$	$(S)$	$\supseteq \{\frac{π}{6}, \frac{7 π}{6}, \frac{13 π}{6}\}$
		$(T)$	$\supseteq \{\frac{π}{3}, \frac{2 π}{3}, π\}$
		$(U)$	$\supseteq \{\frac{π}{6}, \frac{3 π}{4}\}$

Which of the following is the only correct combination?

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Which is correct statement if \(\mathrm{N}_2\) is added at equilibrium condition?

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