In conversion of limestone 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 limestone to lime will be spontaneous is

  • Option 1)

    1118 K

  • Option 2)

    1008 K

  • Option 3)

    1200 K

  • Option 4)

    845 K

 

Answers (1)

As we learnt in

Entropy for phase transition at constant pressure -

\Delta S= \frac{\Delta H_{Transition}}{T}

- wherein

Transition \RightarrowFusion, Vaporisition, Sublimation

\Delta H\RightarrowEnthalpy

\Delta E\RightarrowInternal Energy

T\RightarrowTransitional temperature

 

 \Delta S\:=\:\frac{\Delta H}{T}\\ \Rightarrow \:T=\frac{\Delta S}{\Delta H}\:=\:\frac{179.1\times10^{3}}{160.2}\:=\:1117.97K=1118K


Option 1)

1118 K

This option is correct.

Option 2)

1008 K

This option is incorrect.

Option 3)

1200 K

This option is incorrect.

Option 4)

845 K

This option is incorrect.

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