Chemical Equilibrium · Chemistry · JEE Advanced

The plot of $\log k_f$ versus $1 / T$ for a reversible reaction $\mathrm{A}(\mathrm{g}) \rightleftharpoons \mathrm{P}(\mathrm{g})$ is shown.


Pre-exponential factors for the forward and backward reactions are $10^{15} \mathrm{~s}^{-1}$ and $10^{11} \mathrm{~s}^{-1}$, respectively. If the value of $\log K$ for the reaction at $500 \mathrm{~K}$ is 6 , the value of $\left|\log k_b\right|$ at $250 \mathrm{~K}$ is ______.

$$ \begin{aligned} & {[K=\text { equilibrium constant of the reaction }} \\\\ & k_f=\text { rate constant of forward reaction } \\\\ & \left.k_b=\text { rate constant of backward reaction }\right] \end{aligned} $$

Consider the reaction,

A $$\rightleftharpoons $$ B

at 1000 K. At time t', the temperature of the system was increased to 2000 K and the system was allowed to reach equilibrium. Throughout this experiment the partial pressure of A was maintained at 1 bar. Given, below is the plot of the partial pressure of B with time. What is the ratio of the standard Gibbs energy of the reaction at 1000 K to that at 2000 K?

For the following reaction, the equilibrium constant K_c at 298 K is 1.6 $$ \times $$ 10¹⁷.

Fe²⁺(aq) + S^2-(aq) ⇌ FeS(s)

When equal volumes of

0.06 M Fe²⁺(aq) and 0.2 M S^{2$$ - $$}(aq)

solutions are mixed, the equilibrium concentration of Fe²⁺(aq) is found by Y $$ \times $$ 10^{$$ - $$17} M. The value of Y is .................

A closed tank has two compartments $$A$$ and $$B,$$ both filled with oxygen (assumed to be ideal gas). The partition separating the two compartments is fixed and is a perfect heat insulator (Figure $$1.$$). If the old partition is replaced by a new partition which can slide and conduct heat but does NOT allow the gas to leak across (Figure $$2$$), the volume (in $${m^3}$$) of the compartment A after the system attains equilibrium is ______________.

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Thermal decomposition of gaseous X₂ to gaseous X at 298 K takes place according to the following equations:
X₂ (g) $$\leftrightharpoons$$ 2X (g)
The standard reaction Gibbs energy, $$\Delta _rG^o$$, of this reaction is positive. At the start of the reaction, there is one mole of X₂ and no X. As the reaction proceeds, the number of moles of X formed is given by $$\beta$$. Thus, $$\beta _{equilibrium}$$ is the number of moles of X formed at equilibrium. The reaction is carried out at a constant total pressure of 2 bar. Consider the gases to behave ideally. (Given R = 0.083 L bar K^-1 mol^-1)
Question
The INCORRECT statement among the following for this reaction, is

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Thermal decomposition of gaseous X₂ to gaseous X at 298 K takes place according to the following equations:
X₂ (g) $$\leftrightharpoons$$ 2X (g)
The standard reaction Gibbs energy, $$\Delta _rG^o$$, of this reaction is positive. At the start of the reaction, there is one mole of X₂ and no X. As the reaction proceeds, the number of moles of X formed is given by $$\beta$$. Thus, $$\beta _{equilibrium}$$ is the number of moles of X formed at equilibrium. The reaction is carried out at a constant total pressure of 2 bar. Consider the gases to behave ideally. (Given R = 0.083 L bar K^-1 mol^-1)
Question
The equilibrium constant K_p for this reaction at 298 K, in terms of $$\beta _{equilibrium}$$, is

Statement 1 : For every chemical reaction at equilibrium, standard Gibbs energy of reaction is zero.

and

Statement 2 : At constant temperature and pressure, chemical reactions are spontaneous in the direction of decreasing Gibbs energy.

$$ \begin{aligned} & \mathrm{Ag}^{+}+\mathrm{NH}_3 \quad\left[\mathrm{Ag}\left(\mathrm{NH}_3\right)\right]^{+} \\ & k_1=3.5 \times 10^{-3} \\ & {\left[\mathrm{Ag}\left(\mathrm{NH}_3\right]^{+}+\mathrm{NH}_3 \quad\left[\mathrm{Ag}\left(\mathrm{NH}_3\right)_2\right]^{+}\right.} \end{aligned} $$

$k_2=1.7 \times 10^{-3}$, then the formation constant of $\left[\mathrm{Ag}\left(\mathrm{NH}_3\right)_2\right]^{+}$ is :

$$ \mathrm{N}_2+3 \mathrm{H}_2 \to 2 \mathrm{NH}_3 $$

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

The thermal dissociation equilibrium of CaCO₃(s) is studied under different conditions

CaCO₃(s) $$\leftrightharpoons$$ CaO(s) + CO₂(g).

For this equilibrium, the correct statement(s) is (are)

The equilibrium

$$2C{u^+} \to Cu^\circ + C{u^{2+}}$$

In aqueous medium at 25$$^\circ$$C shifts towards the left in the presence of

When 3.06 g of solid NH₄HS is introduced into a two litre evacuated flask at 27^o C, 30% of the solid decomposes into gaseous ammonia and hydrogen sulphide. (i) K_c and K_p for the reaction at 27^o C (ii) What would happen to the equilibrium when more solid NH₄HS is introduced into the flask?