Question

A cell is to be constructed to show a redox change: $Cr+2C{r}^{3+}\rightleftharpoons 3C{r}^{2+}$. The number of cells with different $E^{\ominus }$ and n but same value of $\Delta G^{\ominus }$ can be made:

(Given: $E_{C{r}^{3+}|C{r}^{2+}}^{\ominus }=-0.40V,E_{C{r}^{3+}|Cr}^{\ominus }=-0.74V,and{E}_{C{r}^{2+}|Cr}^{\ominus }=-0.91V$

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

Answer: (C)

3

$Cr|C{r}^{3+}||C{r}^{3+},C{r}^{2+}|Pt\left(I\right);$
$Cr|C{r}^{2+}||C{r}^{3+}|Cr\left(II\right);$
$Cr|C{r}^{2+}||C{r}^{3+},C{r}^{2+}|Pt\left(III\right);$
(I) $Cr\to C{r}^{3+}+3e^{-};E^{\ominus }=+0.74V$
$3C{r}^{3+}+3e^{-}\to 3C{r}^{2+};E^{\ominus }=-0.40V$
$Cr+2C{r}^{3+}\to 3C{r}^{2+}(n=3)$
$E^{\ominus }=0.74-0.4=0.34V$
$\Delta G^{\ominus }=3\times 0.34\times F$
= 1.02 F
(II) $3Cr\to 3C{r}^{2+}+6e^{-};E^{\ominus }=+0.91V$
$2C{r}^{3+}+6e^{-}\to 2Cr;E^{\ominus }=-0.74V$
$Cr+2C{r}^{3+}\to 3C{r}^{2+}(n=6)$
$E^{\ominus }=0.91-0.74=0.17V$
$\Delta G^{\ominus }=0.17\times 6\times F$
= 1.02 F
(III) $Cr\to C{r}^{2+}+2e^{-};E^{\ominus }=+0.91V$
$2C{r}^{3+}+2e^{-}\to 2C{r}^{2+};E^{\ominus }=-0.40V$
$Cr+2C{r}^{3+}\to 3C{r}^{2+}(n=2)$
$E^{\ominus }=0.91-0.40=0.51V$
$\Delta G^{\ominus }=2\times 0.51\times F$
= $1.02F$
So total 3 cells can be made.