For the reaction $2P_{(g)} + Q_{(g)} \rightleftharpoons R_{(g)} + S_{(g)}$; $K_C = 10^{12}$. If the initial moles of $P, Q, R, S$ are $2, 1, 7$ and $3$ moles respectively in a $1 \ L$ vessel,find the equilibrium concentration of $P$.

Given the following equilibria:
$N_2 + 3H_2 \rightleftharpoons 2NH_3 : K_1$
$N_2 + O_2 \rightleftharpoons 2NO : K_2$
$H_2 + 1/2O_2 \rightleftharpoons H_2O : K_3$
Then the equilibrium constant for the reaction $2NH_3 + 5/2O_2 \rightleftharpoons 2NO + 3H_2O$ in terms of $K_1, K_2,$ and $K_3$ will be:

Fill in the blanks:
$a$. If a reaction is in equilibrium,then the rate of the forward reaction and the rate of the backward reaction will be ....... .
$b$. If $\Delta G$ is negative,then thermodynamically the reaction takes place in the ...... direction.
$c$. The equilibrium constant gives ........ information for a reaction.

At $1000 \ K$ in a $0.654 \ L$ vessel,$CaCO_{3(s)}$ is taken. For the reaction $CaCO_{3(s)} \rightleftharpoons CaO_{(s)} + CO_{2(g)}$,the equilibrium constant $K_p$ is $3.9 \times 10^{-2} \ bar$. Find the weight of $CaO$ produced at equilibrium. $(Ca=40, C=12, O=16)$

For the reaction $N_2 + O_2 \rightleftharpoons 2NO$,the equilibrium concentrations of $N_2$,$O_2$,and $NO$ are $0.25 \ mol/L$,$0.05 \ mol/L$,and $1.0 \ mol/L$ respectively. What are the initial concentrations of $N_2$ and $O_2$?

For the reaction,$N_2O_{4(g)} \rightleftharpoons 2NO_{2(g)}$,if dinitrogen tetroxide is $50\%$ dissociated at $60^\circ C$,the standard free energy change at this temperature and $1 \ atm$ pressure is: