$CH_3COCH_{3(g)} \rightleftharpoons C_2H_{6(g)} + CO_{(g)}$. The initial pressure of $CH_3COCH_3$ is $100 \ mm$. When equilibrium is set up,the mole fraction of $CO_{(g)}$ is $\frac{1}{4}$. Hence,the partial pressure of $CO$ is:

  • A
    $\frac{50}{3} \ mm$
  • B
    $\frac{50}{12} \ mm$
  • C
    $\frac{25}{3} \ mm$
  • D
    $\frac{100}{3} \ mm$

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Which of the following statements is correct?

$\Delta _f G^o$ at $500 \, K$ for substance '$S$' in liquid state and gaseous state are $+100.7 \, kcal \, mol^{-1}$ and $+103 \, kcal \, mol^{-1}$,respectively. The vapour pressure of liquid '$S$' at $500 \, K$ is approximately equal to $(R = 2 \, cal \, K^{-1} \, mol^{-1}) \dots \dots \text{atm}$.

At $1 \ bar$ pressure and $310 \ K$ temperature,$25\%$ of $N_2O_4$ decomposes. The reaction is: $N_2O_{4(g)} \rightleftharpoons 2NO_{2(g)}$.
$(i)$ Find $K_p$.
$(ii)$ At $0.1 \ bar$ pressure and $310 \ K$,what is the percentage of $N_2O_4$ decomposed?

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In a closed vessel at $448^{\circ} C$,$0.5 \ mol$ of $H_2$ and $0.5 \ mol$ of $I_2$ react to form hydrogen iodide.
Reaction: $H_{2(g)} + I_{2(g)} \rightleftharpoons 2HI_{(g)}$,$K_c = 50$.
$(i)$ Calculate the moles of $I_2$ that remain unreacted at equilibrium.
$(ii)$ Calculate $K_p$.

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For the equilibrium reaction $A + B \rightleftharpoons C + D$,if we start with equal concentrations of $A$ and $B$,at equilibrium,the concentration of $C$ is $2$ times that of $A$. Find the value of $K_c$.

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