Write Nernst's equation for the following cell and find out the emf (electro motive force) of the cell at $298\,{}^\circ K$. ($E^0_{cell} = 2.71\,V$)

$Mg(s)\,|\,Mg^{+2}(0.001M)\,||\,Cu^{+2}(0.0001M)\,|\,Cu(s)$

OR

Describe the Lead Accumulator Cell with labelled diagram and wri

Question

Write Nernst's equation for the following cell and find out the emf (electro motive force) of the cell at $298\,{}^\circ K$. ($E^0_{cell} = 2.71\,V$)

$Mg(s)\,|\,Mg^{+2}(0.001M)\,||\,Cu^{+2}(0.0001M)\,|\,Cu(s)$

OR

Describe the Lead Accumulator Cell with labelled diagram and write the equation of chemical reactions taking place in it.

Accepted Answer

![Figure — The OR alternative asks to 'Describe the Lead Accumulator Cell with labelled diagram' and the answer supplies](/figures/electrochemistry/lead-storage-battery-fig-2-10.svg)

>

> [!TLDR]
> Applying the Nernst equation with $n=2$ gives $E_{cell} \approx 2.68\ V$.
>
> For the cell $Mg(s)\,|\,Mg^{2+}(0.001M)\,||\,Cu^{2+}(0.0001M)\,|\,Cu(s)$, the overall cell reaction is:
> $$Mg(s) + Cu^{2+}(aq) ightarrow Mg^{2+}(aq) + Cu(s)$$
> with $n = 2$ electrons transferred.
>
> The Nernst equation at 298 K is:
> $$E_{cell} = E^0_{cell} - \frac{0.0591}{n}\log\frac{[Mg^{2+}]}{[Cu^{2+}]}$$
> Substituting the given values ($E^0_{cell}=2.71\,V$, $[Mg^{2+}]=0.001\,M$, $[Cu^{2+}]=0.0001\,M$):
> $$E_{cell} = 2.71 - \frac{0.0591}{2}\log\left(\frac{0.001}{0.0001}ight) = 2.71 - 0.02955 	imes \log(10)$$
> $$E_{cell} = 2.71 - 0.02955 	imes 1 = 2.71 - 0.02955 = 2.68045\ V$$
>
>
> …

Concept	Physical Meaning
$E^\circ_{\text{cell}}$	Voltage when all species are at 1 M (standard state)
$-\frac{RT}{nF} \ln Q$	Correction factor — adjusts voltage for real concentrations
$Q$	Tells you how far the reaction is from equilibrium

Q.Write Nernst's equation for the following cell and find out the emf (electro motive force) of the cell at $298\,{}^\circ K$ . ( $E^0_{cell} = 2.71\,V$ ) $Mg(s)\,|\,Mg^{+2}(0.001M)\,||\,Cu^{+2}(0.0001M)\,|\,Cu(s)$

Concept understanding — Cell Representation Nernst Equation

Cell Representation and the Nernst Equation: From Intuition to Precision

The Intuition First

The Precise Statement

Cell Representation: How We Write It

Applying the Nernst Equation to a Cell Representation

A Worked Example

Why this formula?

Cell Representation & the Nernst Equation: Why It Works

The Core Question

1. The Fundamental Link: Gibbs Free Energy & Cell Potential

2. The Chemical Side: $\Delta G$ Depends on Concentration

3. Combining Both Sides: The Derivation

4. The "Why" in Plain Terms

5. The Common Form (log base 10)

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