Consider the following liquid-vapour equilibrium.
$Liquid \rightleftharpoons Vapour$
Which of the following relations is correct?

  • A
    $\frac{d \ln P}{d T^2} = \frac{-\Delta H_v}{T^2}$
  • B
    $\frac{d \ln P}{d T} = \frac{\Delta H_v}{R T^2}$
  • C
    $\frac{d \ln G}{d T^2} = \frac{\Delta H_v}{R T^2}$
  • D
    $\frac{d \ln P}{d T} = \frac{-\Delta H_v}{R T}$

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$A$ gaseous reaction $A_{2(g)} \to B_{(g)} + \frac{1}{2} C_{(g)}$ shows an increase in pressure from $100 \ mm$ of $Hg$ to $120 \ mm$ of $Hg$ in $5 \ min$. What will be the rate of disappearance of $A_2$ in $mm$ of $Hg/min$?

Which of the following statements is/are true about equilibrium?
$(a)$ Equilibrium is possible only in a closed system at a given temperature.
$(b)$ All the measurable properties of the system remain constant at equilibrium.
$(c)$ Equilibrium constant for the reverse reaction is the inverse of the equilibrium constant for the reaction in the forward direction.

In a $1 \, L$ container,the reaction of $2 \, mol$ $N_2$ and $5 \, mol$ $H_2$ occurs. If the equilibrium concentration of $NH_3$ is half the equilibrium concentration of $N_2$,what is the equilibrium constant $(K_c)$?

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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:

$N_{2(g)} + 3H_{2(g)} \rightleftharpoons 2NH_{3(g)}$
$56 \ g$ of nitrogen and $8 \ g$ of hydrogen gas are heated in a closed vessel. At equilibrium,$34 \ g$ of ammonia are present. The equilibrium number of moles of nitrogen,hydrogen and ammonia are respectively:

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