When $2 \ L$ of $CO_2$ is heated with graphite,the volume of gases collected is $3 \ L$. Calculate the number of moles of $CO$ produced at $STP$.

At $600 \ K$,$2 \ mol$ of $NO$ are mixed with $1 \ mol$ of $O_2$.
$2 \ NO_{(g)} + O_{2(g)} \rightleftarrows 2 \ NO_{2(g)}$
The reaction occurring as above comes to equilibrium under a total pressure of $1 \ atm$. Analysis of the system shows that $0.6 \ mol$ of oxygen are present at equilibrium. The equilibrium constant for the reaction is $.........$ (Nearest integer).

Thermal decomposition of gaseous $X_2$ to gaseous $X$ at $298 \ K$ takes place according to the following equation :
$X_{2(g)} \rightleftharpoons 2 X_{(g)}$
The standard reaction Gibbs energy,$\Delta_r G^{\circ}$,of this reaction is positive. At the start of the reaction,there is one mole of $X_2$ and no $X$. As the reaction proceeds,the number of moles of $X$ formed is given by $\beta$. Thus,$\beta_{\text{equilibrium}}$ 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 : $R=0.083 \ L \ bar \ K^{-1} \ mol^{-1}$)
$(1)$ The equilibrium constant $K_P$ for this reaction at $298 \ K$,in terms of $\beta_{\text{equilibrium}}$,is
$(A)$ $\frac{8 \beta_{\text{equilibrium}}^2}{2-\beta_{\text{equilibrium}}}$ $(B)$ $\frac{8 \beta_{\text{equilibrium}}^2}{4-\beta_{\text{equilibrium}}^2}$ $(C)$ $\frac{4 \beta_{\text{equilibrium}}^2}{2-\beta_{\text{equilibrium}}}$ $(D)$ $\frac{4 \beta_{\text{equilibrium}}^2}{4-\beta_{\text{equilibrium}}^2}$
$(2)$ The $INCORRECT$ statement among the following,for this reaction,is
$(A)$ Decrease in the total pressure will result in formation of more moles of gaseous $X$
$(B)$ At the start of the reaction,dissociation of gaseous $X_2$ takes place spontaneously
$(C)$ $\beta_{\text{equilibrium}}=0.7$
$(D)$ $K_c < 1$

$A$ $1 \, M$ solution of glucose reaches dissociation equilibrium according to the equation $C_6H_{12}O_6 \rightleftharpoons 6HCHO$. What is the concentration of $HCHO$ at equilibrium if the equilibrium constant $K_c$ for the formation of glucose from formaldehyde is $6 \times 10^{22}$?

At $T$ $(K)$,the equilibrium constant for the reaction $H_{2(g)} + Br_{2(g)} \rightleftharpoons 2 HBr_{(g)}$ is $1.6 \times 10^5$. If $10 \ bar$ of $HBr$ is introduced into a sealed vessel at $T$ $(K)$,the equilibrium pressure of $HBr$ (in $bar$) is approximately

For the reaction $SO_{2(g)} + NO_{2(g)} \rightleftharpoons SO_{3(g)} + NO_{(g)}$,the equilibrium constant $K_c$ is $16$. If $1 \ mol$ of each gas is taken in a $1 \ dm^3$ vessel,the equilibrium concentration of $NO$ will be ....