Question

At $300K$ , a concentration cell is formed by coupling two $Cu$ electrodes immersed in $CuS{O}_4$ solution .
Given, the concentration of $C{u}^{2+}$ in one electrode is 100 times than that of the other. Which of the following is/are true for the given concentration cell?

• A. Spontaneous cell reaction is,
  $C{u}^{2+}(aq,xM)\to C{u}^{2+}(aq,100xM)$
• B. Spontaneous cell reaction is,
  $C{u}^{2+}(aq,100xM)\to C{u}^{2+}(aq,xM)$
• C. At $300K,E_{cell}=0.06V$
• D. At $300K,E_{cell}=0.24V$

Answer 1

Answer: (B), (C)

At $300K,E_{cell}=0.06V$

Let us consider the concentration of $C{u}^{2+}$ to be $xM$

Then, concentration of $C{u}^{2+}$ of another electrolyte is $100xM$

In concentration cell, for a spontaneous process, the electrode with higher concentration of electrolyte will act as cathode and lower concentration electrolyte half cell will act as anode.

$Cu|C{u}^{2+}(aq,xM)||C{u}^{2+}(aq,100xM)|Cu$

The electrode half cell reaction will be
$C{u}^{2+}(aq,100xM)+2e^{-}\to Cu\left(s\right)$
$Cu\left(s\right)\to C{u}^{2+}(aq,xM)+2e^{-}$

The cell reaction will be
$C{u}^{2+}(aq,100xM)\to C{u}^{2+}(aq,xM)$

By nernst equation,

$E=E^0-2.303\frac{RT}{nF}log\frac{\left[Anode\right]}{\left[cathode\right]}$

For concentration cells,
$E^0=0$

$E=2.303\times \frac{8.314\times 300}{2\times 96500}log\frac{\left[100x\right]}{\left[1x\right]}$

$E=2.303\times \frac{8.314\times 300}{96500}$

$E=0.0595V$

$E\approx 0.06$