${C_2}{H_5}\,\boxed{Br + 2Na + Br} - {C_2}{H_5} \to \mathop {{C_2}{H_5} - {C_2}{H_5}}\limits_{{\text{Butane}}} + 2NaBr$
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If $T_1=2 T_2$ and $\left(\Delta G_2^{\Theta}-\Delta G_1^{\varphi}\right)=R T_2 \ln x$, then the value of $x$ is. . . . .
$\left[\Delta G_1^\theta\right.$ and $\Delta G_2^\theta$ are standard Gibb's free energy change for the reaction at temperatures $T_1$ and $T_2$, respectively.]
| $LIST-I$ | $LIST-II$ |
| $(I)$ Aniline | $(P)$ Sodium fusion extract of the compound on boiling with $FeSO _4$, followed by acidification with conc. $H _2 SO _4$, gives Prussian blue color. |
| $(II)$ o-Cresol | $(Q)$ Sodium fusion extract of the compound on treatment with sodium nitroprusside gives blood red color. |
| $(III)$ Cysteine | $(R)$ Addition of the compound to a saturated solution of $NaHCO _3$ results in effervescence. |
| $(IV)$ Coprolactam | $(S)$ The compound reacts with bromine water to give a white precipitate. |
| $(T)$ Treating the compound with neutral $FeCl _3$ solution produces violet color. |