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 ______________.