Question

Identify from following cell reactions that is spontaneous under standard state of conditions.

• A. \(\text{Ca(s)}+\text{Cd}^{2+}\text{(aq)}\rightarrow \text{Ca}^{2+}\text{(aq)}+\text{Cd(s)}\), \([E_{\text{Ca}}^0 = -2.866\) V & \(E_{\text{Cd}}^0 = -0.403\) V\(]\)
• B. \(2\text{Br}^-\text{(s)}+\text{Sn}^{2+}\text{(aq)}\rightarrow \text{Br}_2\text{(l)}+\text{Sn(s)}\), \([E_{\text{Br}}^0 = 1.08\) V & \(E_{\text{Sn}}^0 = -0.136\) V\(]\)
• C. \(2\text{Ag(s)}+\text{Ni}^{2+}\text{(aq)}\rightarrow 2\text{Ag}^+\text{(aq)}+\text{Ni(s)}\), \([E_{\text{Ag}}^0 = 0.799\) V & \(E_{\text{Ni}}^0 = -0.257\) V\(]\)
• D. \(2\text{Au(s)}+\text{Zn}^{2+}\text{(aq)}\rightarrow 2\text{Au}^+\text{(aq)}+\text{Zn(s)}\), \([E_{\text{Au}}^0 = 1.68\) V & \(E_{\text{Zn}}^0 = -0.763\) V\(]\)

Hint:

A cell reaction is spontaneous when its standard cell EMF is positive.

Answer 1

The Correct Option is A

Step 1: Rule of thumb.
A metal with a lower (more negative) reduction potential displaces ions of a metal with a higher reduction potential.

Step 2: Apply to each option.
(A) Ca ($-2.866$ V) displaces $\text{Cd}^{2+}$ ($-0.403$ V): allowed. (C) Ag ($+0.799$ V) cannot displace $\text{Ni}^{2+}$ ($-0.257$ V). (D) Au ($+1.68$ V) cannot displace $\text{Zn}^{2+}$ ($-0.763$ V). (B) $\text{Br}^-$ would need $\text{Sn}^{2+}$ to oxidise it, but $E^0$ of Sn is far below that of bromine.

Step 3: Confirm with numbers.
For (A), $E^0_{cell} = -0.403 + 2.866 = 2.463$ V, positive. The others come out negative.

Final Answer:
Option (A) is spontaneous. \[ \boxed{E^0_{cell} = +2.463\text{ V}} \]