Which of the following is correct for the equilibrium shown below?
$2CH_3COOH \rightleftharpoons (CH_3COOH)_2$
(Equilibrium constants for the reaction in water and benzene are $K_{Water}$ and $K_{Benzene}$ respectively.)

$3.00 \ mol$ of $PCl_5$ kept in $1 \ L$ closed reaction vessel was allowed to attain equilibrium at $380 \ K$. If $1.59 \ mol$ of reactant was converted into the product at equilibrium,then $K_c$ is:

$PCl_{5}$ dissociates as $PCl_{5(g)} \rightleftharpoons PCl_{3(g)} + Cl_{2(g)}$. $5 \, \text{moles}$ of $PCl_{5}$ are placed in a $200 \, L$ vessel which contains $2 \, \text{moles}$ of $N_{2}$ and is maintained at $600 \, K$. The equilibrium pressure is $2.46 \, atm$. The equilibrium constant $K_{p}$ for the dissociation of $PCl_{5}$ is $...... \times 10^{-3}$. (nearest integer) (Given: $R = 0.082 \, L \, atm \, K^{-1} \, mol^{-1}$: Assume ideal gas behaviour)

Calculate:
$(a)$ $\Delta G^{\circ}$ and
$(b)$ the equilibrium constant for the formation of $NO_2$ from $NO$ and $O_2$ at $298 \, K$
$NO_{(g)} + 1/2 O_{2(g)} \longleftrightarrow NO_{2(g)}$
Given:
$\Delta G^{\circ}_f(NO_2) = 52.0 \, kJ/mol$
$\Delta G^{\circ}_f(NO) = 87.0 \, kJ/mol$
$\Delta G^{\circ}_f(O_2) = 0 \, kJ/mol$

In a $10 \ L$ vessel,$SO_3, SO_2$,and $O_2$ gases are present at a definite temperature with $K_c = 100$. For the reaction $2SO_{2(g)} + O_{2(g)} \rightleftharpoons 2SO_{3(g)}$,if $SO_3$ and $SO_2$ are present in the same number of moles at equilibrium,find the moles of $O_2$. If $SO_3$ is double the moles of $SO_2$,what is the number of moles of $O_2$?

For the reaction $PCl_{5(g)} \rightleftharpoons PCl_{3(g)} + Cl_{2(g)}$,at equilibrium,the mole fraction of $PCl_5$ is $0.4$ and the mole fraction of $Cl_2$ is $0.3$. What will be the mole fraction of $PCl_3$?