MCQ
In conversion of lime-stone to lime,

$CaCO _{3}( s ) \rightarrow CaO ( s )+ CO _{2}( g )$ the values of $\Delta H ^{\circ}$ and $\Delta S^{\circ}$ are $+179.1 kJ mol ^{-1}$ and $160.2\,J / K$ respectively at $298 \,K$ and $1 \,bar$. Assuming that $\Delta H ^{\circ}$ and $\Delta S ^{\circ}$ do not change with temperature, temperature above which conversion of lime-stone to lime will be spontaneous is ........... $K$

  • $1118$
  • B
    $1008$
  • C
    $1200$
  • D
    $845$

Answer

Correct option: A.
$1118$
a
From the Gibbs free energy,

$\Delta G^{\circ}=\Delta H^{\circ}-T \Delta S^{\circ}$

For spontaneous reaction, $\Delta G^{\circ}=0$

Now,

$\Delta H^{\circ}-T \Delta S^{\circ}<0$

$T=\frac{\Delta H^{\circ}}{\Delta S^{\circ}}$

Substitute the given value in the above expression.

$T > \frac{179.1 \times 10^{3}}{160.2}$

$> 1118\,K$

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