Question

For $I_2+2e^{-}\to 2I^{-},\text{standard reduction potential}=+0.54\text{Volt}.$
For $2B{r}^{-}\to B{r}_2+2e^{-},\text{standard oxidation potential}=-1.09\text{Volt}.$
For $Fe\to F{e}^{2+}+2e^{-},\text{standard oxidation potential}=+0.44\text{Volt}.$
Out of the below given reactions, how many reactions are spontaneous in nature (predict from the above data) ?
$B{r}_2+2I^{-}\to 2B{r}^{-}+I_2$
$Fe+B{r}_2\to F{e}^{2+}+2B{r}^{-}$
$Fe+I_2\to F{e}^{2+}+2I^{-}$
$I_2+2B{r}^{-}\to 2I^{-}+B{r}_2$

Answer 1

We know that,
$\Delta G^o=-nF{E}_{cell}^o$
For a spontanesous reaction, $\Delta G<0$ which is when $E_{cell}^o>0$

(a) $B{r}_2+2e^{-}\to 2B{r}^{-}{E}_{B{r}_2/B{r}^{-}}^o=1.09V$
$2I^{-}\to I_2+2e^{-}{E}_{I^{-}/I_2}^o=-0.54V$
$\therefore \text{for}B{r}_2+2I^{-}\to I_2+2B{r}^{-}{E}^o=(1.09-0.54)V=0.55V$
Hence, this is a spontaneous reaction.

(b)
$Fe\to F{e}^{2+}+2e^{-}{E}_{Fe/F{e}^{2+}}^o=0.44V$
$B{r}_2+2e^{-}\to 2B{r}^{-}{E}_{B{r}_2/B{r}^{-}}^o=1.09V$
$\therefore B{r}_2+Fe\to F{e}^{2+}+2B{r}^{-}{E}^o=(0.44+1.09)V=1.53V$
So, this reaction is also spontaneous.

(c)
$Fe\to F{e}^{2+}+2e^{-}{E}_{Fe/F{e}^{2+}}^o=0.44V$
$I_2+2e^{-}\to 2I^{-}{E}_{I_2/I^{-}}^o=0.54V$
$\therefore I_2+Fe\to F{e}^{2+}+2I^{-}{E}^o=(0.44+0.54)V=0.98V$
Hence, this is also a spontaneous reaction.

(d)
$I_2+2e^{-}\to 2I^{-}{E}_{I_2/I^{-}}^o=0.54V$
$2B{r}^{-}\to B{r}_2+2e^{-}{E}_{B{r}^{-}/B{r}_2}^o=-1.09V$
$\therefore I_2+2B{r}^{-}\to B{r}_2+2I^{-}{E}^o=(0.54-1.09)V=-0.55V$
This reaction is non-spontaneous.