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  • For oxidation of iron: <img alt="\mathrm{4Fe\left ( s \right )+3O_{2}\left ( g \right )\rightarrow 2Fe_{2}O_{3}\left ( s \right )}" src="https://entrancecorner.oncodecogs.com

For oxidation of iron: \mathrm{4Fe\left ( s \right )+3O_{2}\left ( g \right )\rightarrow 2Fe_{2}O_{3}\left ( s \right )} 

the entropy change is \mathrm{-550\; J/mol.K} at \mathrm{300\; K}. What could be said for the spontaneity of the reaction ?(Given,  \mathrm{\Delta H_r^0=-1650 kJ/mol} )


 

Option: 1

Reaction is non spontaneous at all temperatures

 


Option: 2

Reaction is non spontaneous at all temperatures


Option: 3

Reaction is spontaneous at temperatures less than 3000 K.


Option: 4

Reaction is spontaneous at temperatures greater than 3000 K.


Answers (1)

As we have learnt,

The spontaneity of the reaction is decided by the total entropy change of the process or it can also be related to the Gibb's free energy.

\mathrm{\Delta G= \Delta H-T \times \Delta S }

Given

\mathrm{\Delta S=-550\; J/mol.K}

\mathrm{\Delta H=-1650\; kJ/mol}

\therefore \mathrm{\Delta G=-1650-T \times (-550) \times 10^{-3}}

For Spontaneity, the value for Gibb's energy change should be negative

\therefore \mathrm{-1650-T \times (-550) \times 10^{-3}<0}

\Rightarrow \mathrm{T < \frac{1650 \times 10^3}{550}< 3000\ K}

Therefore, the reaction is spontaneous at all temperatures below 3000K

Hence, option number (3) is correct

Posted by

Kshitij

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