The following lists contain reactions and their corresponding equilibrium constants at different temperatures:
List-$I$ (Reaction) List-$II$ $(K_p)$
$2 SO_{2(g)} + O_{2(g)} \rightleftharpoons 2 SO_{3(g)}$ at $298 \ K$ $4.0 \times 10^{24}$
$2 SO_{2(g)} + O_{2(g)} \rightleftharpoons 2 SO_{3(g)}$ at $700 \ K$ $3.0 \times 10^{4}$
$N_2O_{4(g)} \rightleftharpoons 2 NO_{2(g)}$ at $298 \ K$ $0.98$
$N_2O_{4(g)} \rightleftharpoons 2 NO_{2(g)}$ at $500 \ K$ $1700$

If $\Delta H_1^0$ and $\Delta H_2^0$ are the standard enthalpies for the reactions $2 SO_{2(g)} + O_{2(g)} \rightleftharpoons 2 SO_{3(g)}$ and $N_2O_{4(g)} \rightleftharpoons 2 NO_{2(g)}$ respectively, then:

  • A
    Both $\Delta H_1^0$ and $\Delta H_2^0$ are negative
  • B
    Both $\Delta H_1^0$ and $\Delta H_2^0$ are positive
  • C
    $\Delta H_1^0$ is negative and $\Delta H_2^0$ is positive
  • D
    $\Delta H_1^0$ is positive and $\Delta H_2^0$ is negative

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For the reaction $C_{(s)} + CO_{2(g)} \rightleftharpoons 2CO_{(g)}$,if $25\%$ of $CO_2$ is converted to $CO$ at equilibrium and the total equilibrium pressure is $12 \ atm$,then the partial pressure of $CO_2$ at equilibrium will be............$atm$.

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The reaction $2 NO_{2(g)} \rightleftharpoons N_2O_{4(g)}$ is at equilibrium in a closed $15 \ L$ vessel at $300 \ K$. The total weight of the mixture of $NO_2$ and $N_2O_4$ in the vessel is $64.4 \ g$. The equilibrium constant for the reaction is $K_p = 6.67$. Assuming ideal gas behavior,the total pressure in the vessel (in $atm$) is: [Given: Gas constant $R = 0.082 \ atm \ L \ K^{-1} \ mol^{-1}$]

The equilibrium constants for the following three reactions $(i)$,$(ii)$,and $(iii)$ are given as:
$(i)$ $CO_{(g)} + H_2O_{(g)} \rightleftharpoons CO_{2(g)} + H_{2(g)} \quad K_1$
$(ii)$ $CH_{4(g)} + H_2O_{(g)} \rightleftharpoons CO_{(g)} + 3H_{2(g)} \quad K_2$
$(iii)$ $CH_{4(g)} + 2H_2O_{(g)} \rightleftharpoons CO_{2(g)} + 4H_{2(g)} \quad K_3$
Which of the following relations is correct?

When $20 \ g$ of $CaCO_3$ are subjected to decomposition at $227 \ ^oC$ in a closed container of $10 \ L$ capacity,$50 \%$ of $CaCO_3$ remained unreacted at equilibrium. Calculate $K_P$ for $CaCO_{3(s)} \rightleftharpoons CaO_{(s)} + CO_{2(g)}$ in $atm$.

Ethyl acetate is formed by the reaction between ethanol and acetic acid and the equilibrium is represented as:
$CH_3COOH_{(l)} + C_2H_5OH_{(l)} \longleftrightarrow CH_3COOC_2H_{5(l)} + H_2O_{(l)}$
$(i)$ Write the concentration ratio (reaction quotient),$Q_c$,for this reaction (note: water is not in excess and is not a solvent in this reaction).
$(ii)$ At $293 \ K$,if one starts with $1.00 \ mol$ of acetic acid and $0.18 \ mol$ of ethanol,there is $0.171 \ mol$ of ethyl acetate in the final equilibrium mixture. Calculate the equilibrium constant.
$(iii)$ Starting with $0.5 \ mol$ of ethanol and $1.0 \ mol$ of acetic acid and maintaining it at $293 \ K$,$0.214 \ mol$ of ethyl acetate is found after sometime. Has equilibrium been reached?

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