The equilibrium constant of a reaction at $298 \ K$ is $5 \times 10^{-3}$ and at $1000 \ K$ is $2 \times 10^{-5}$. What is the sign of $\Delta H$ for the reaction?

For the reaction $2A_{(g)} + B_{(g)} \rightleftharpoons 3C_{(g)} + D_{(g)}$,two moles each of $A$ and $B$ were taken into a $1 \ L$ flask. Which of the following must always be true when the system attains equilibrium?

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:
$\Delta G^{\circ}_f(NO_2) = 52.0 \, kJ/mol$
$\Delta G^{\circ}_f(NO) = 87.0 \, kJ/mol$
$\Delta G^{\circ}_f(O_2) = 0 \, kJ/mol$

At high temperature,$2 \, \text{mol}$ of $NH_3$ is placed in a $500 \, \text{mL}$ vessel. For the decomposition reaction $2NH_{3(g)} \rightleftharpoons N_{2(g)} + 3H_{2(g)}$,if $1 \, \text{mol}$ of $NH_3$ remains at equilibrium,then $K_c$ is equal to:

When $5 \ mol$ of $SO_2$ and $5 \ mol$ of $O_2$ are reacted,$60\%$ of $SO_2$ is consumed at equilibrium. If the total pressure of the equilibrium mixture is $1 \ atm$,then the partial pressure of $O_2$ will be ...... $atm$.

In the reaction $2P_{(g)} + Q_{(g)} \rightleftharpoons 3R_{(g)} + S_{(g)}$,if $2 \text{ moles}$ of each $P$ and $Q$ are taken initially in a $1 \text{ L}$ flask,which of the following is true at equilibrium?