One mole of $O_{2(g)}$ and two moles of $SO_{2(g)}$ were heated in a closed vessel of $1 \, L$ capacity at $1098 \, K$. At equilibrium,$1.6 \, moles$ of $SO_{3(g)}$ were found. The equilibrium constant $K_c$ of the reaction would be

From the given data of equilibrium constants for the following reactions:
$(1) \ CO_{2(g)} + H_{2(g)} \rightleftharpoons CO_{(g)} + H_2O_{(g)} \ ; \ K_1$
$(2) \ CO_{(g)} + H_2O_{(g)} \rightleftharpoons CO_{2(g)} + H_{2(g)} \ ; \ K_2$
Wait,the provided question text has a typo in the reaction equations. Assuming the standard problem format where we relate equilibrium constants for reverse or combined reactions,if the target reaction is the same as reaction $(1)$,the answer is $K_1$. However,based on the options provided,this is likely a question asking for the relationship between $K_1$ and $K_2$ where reaction $(2)$ is the reverse of reaction $(1)$. If reaction $(2)$ is the reverse of reaction $(1)$,then $K_2 = \frac{1}{K_1}$. Given the options,please re-verify the input. Assuming the question asks for the equilibrium constant of a reaction derived from these,if the target reaction is $CO_{(g)} + H_2O_{(g)} \rightleftharpoons CO_{2(g)} + H_{2(g)}$,the answer is $K_1^{-1}$. Given the options,if we assume the target reaction is the reverse of reaction $(1)$,then $K = \frac{1}{K_1}$.

For the equilibrium $2SO_{2(g)} + O_{2(g)} \rightleftharpoons 2SO_{3(g)}$,the partial pressures of $SO_2$,$O_2$,and $SO_3$ are $0.662 \ atm$,$0.101 \ atm$,and $0.331 \ atm$ respectively. If the equilibrium concentrations of $SO_2$ and $SO_3$ are made equal,the partial pressure of $O_2$ will be ..... $atm$.

Write a relation between $\Delta G$ and $Q$ and define the meaning of each term and answer the following:
$(a)$ Why a reaction proceeds forward when $Q < K$ and no net reaction occurs when $Q = K$.
$(b)$ Explain the effect of increase in pressure in terms of reaction quotient $Q$.
For the reaction: $CO_{(g)} + 3H_{2(g)} \rightleftharpoons CH_{4(g)} + H_{2}O_{(g)}$

Identify the incorrect statement.

In a reaction,$A + B \rightleftharpoons C + D$,$40 \%$ of $B$ has reacted at equilibrium,when $1 \ mol$ of $A$ was heated with $1 \ mol$ of $B$ in a $10 \ L$ closed vessel. The value of $K_C$ is