Question

The emf values of three galvanic cells I, II and III are \(E_1\), \(E_2\) and \(E_3\) respectively. Determine the correct order among them. \[ \text{(I)}\quad Zn|Zn^{2+}(1M)||Cu^{2+}(0.1M)|Cu \] \[ \text{(II)}\quad Zn|Zn^{2+}(1M)||Cu^{2+}(1M)|Cu \] \[ \text{(III)}\quad Zn|Zn^{2+}(0.1M)||Cu^{2+}(1M)|Cu \]

• A. \(E_3 > E_2 > E_1\)
• B. \(E_1 > E_2 > E_3\)
• C. \(E_2 > E_3 > E_1\)
• D. \(E_1 > E_3 > E_2\)

Hint:

For the Daniell cell, \[ Zn + Cu^{2+} \rightarrow Zn^{2+}+Cu \] emf increases when:

• \(Cu^{2+}\) concentration increases.

• \(Zn^{2+}\) concentration decreases.
A quick way is to compare the ratio \[ \frac{[Zn^{2+}]}{[Cu^{2+}]} \] Smaller ratio means larger emf.

Answer 1

The Correct Option is A

Concept: The emf of a galvanic cell under non-standard conditions is calculated using the Nernst equation. For the cell \[ Zn + Cu^{2+} \rightarrow Zn^{2+}+Cu \] the reaction quotient is \[ Q=\frac{[Zn^{2+}]}{[Cu^{2+}]} \] The Nernst equation is \[ E=E^\circ-\frac{0.0591}{2}\log Q \] Therefore, \[ E=E^\circ-\frac{0.0591}{2} \log \left( \frac{[Zn^{2+}]} {[Cu^{2+}]} \right) \] From this expression we conclude:

• Larger \(Cu^{2+}\) concentration increases emf.

• Larger \(Zn^{2+}\) concentration decreases emf.

Step 1: Calculating emf relation for Cell I For Cell I: \[ [Zn^{2+}]=1M \] \[ [Cu^{2+}]=0.1M \] Therefore, \[ Q=\frac{1}{0.1}=10 \] Since \(Q>1\), \[ \log Q >0 \] Hence \[ E_1<E^\circ \] Thus emf decreases below standard emf.

Step 2: Calculating emf relation for Cell II For Cell II: \[ [Zn^{2+}] = [Cu^{2+}] = 1M \] Hence \[ Q=1 \] and \[ \log 1=0 \] Therefore \[ E_2=E^\circ \] Cell II has standard emf.

Step 3: Calculating emf relation for Cell III For Cell III: \[ [Zn^{2+}] = 0.1M \] \[ [Cu^{2+}] = 1M \] Therefore \[ Q=\frac{0.1}{1} = 0.1 \] Since \[ \log(0.1)=-1 \] the Nernst correction becomes positive. Thus \[ E_3>E^\circ \] Therefore Cell III has emf greater than standard emf.

Step 4: Comparing all three emf values We obtained: \[ E_1<E^\circ \] \[ E_2=E^\circ \] \[ E_3>E^\circ \] Hence \[ \boxed{ E_3>E_2>E_1 } \] which corresponds to \[ \boxed{\text{Option (A)}} \]