# In which of the following reactions, standard entropy change $\left ( \Delta S^{o} \right )$ is positive and standard Gibb's energy change $\left ( \Delta G^{o} \right )$ decreases sharply with increasing temperature? Option 1) $C\ graphite+\frac{1}{2}O_{2}\left ( g \right )\rightarrow CO\left ( g \right )$ Option 2) $CO\left ( g \right )+\frac{1}{2}O_{2}\left ( g \right )\rightarrow CO_2\left ( g \right )$ Option 3) $Mg\left (s \right )+\frac{1}{2}O_{2}\left ( g \right )\rightarrow MgO\left ( s \right )$ Option 4) $\frac{1}{2}C\ graphite+\frac{1}{2}O_{2}\left ( g \right )\rightarrow \frac{1}{2}CO_2\left ( g \right )$

V Vakul

Gibb's free energy (? G) -

$\Delta G= \Delta H-T \Delta S$

- wherein

$\Delta G=$ Gibb's free energy

$\Delta H=$ enthalpy of reaction

$\Delta S=$ entropy

$T=$ temperature

C graphite + $\frac{1}{2}O_{2}\left ( g \right )\rightarrow CO\left ( g \right )$

$\Delta ng=1-\frac{1}{2}=\frac{1}{2}$

As amount of geseous substancance is increasing in product, thus $\Delta S$ is positive for this reaction, and we know that $\Delta G=\Delta H-T\Delta S$. As $\Delta S$  is positive thus increase in tempreature will make $T\Delta S$ more negative and $\Delta G$ will decrease.

Option 1)

$C\ graphite+\frac{1}{2}O_{2}\left ( g \right )\rightarrow CO\left ( g \right )$

Correct Option

Option 2)

$CO\left ( g \right )+\frac{1}{2}O_{2}\left ( g \right )\rightarrow CO_2\left ( g \right )$

Incorrect Option

Option 3)

$Mg\left (s \right )+\frac{1}{2}O_{2}\left ( g \right )\rightarrow MgO\left ( s \right )$

Incorrect Option

Option 4)

$\frac{1}{2}C\ graphite+\frac{1}{2}O_{2}\left ( g \right )\rightarrow \frac{1}{2}CO_2\left ( g \right )$

Incorrect Option

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